{"id":1105,"date":"2023-07-26T12:13:38","date_gmt":"2023-07-26T12:13:38","guid":{"rendered":"https:\/\/website.prod.unilu.spikeseed.cloud\/fstm-en\/study-programs\/bachelor-in-mathematics\/programme\/"},"modified":"2025-06-12T11:29:09","modified_gmt":"2025-06-12T09:29:09","slug":"programme","status":"publish","type":"study-programs","link":"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/programme\/","title":{"rendered":"Programme"},"content":{"rendered":"<div class=\"section py-0 static\">\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><!-- SecondaryNavigationMirror --><div class=\"js-secondary-nav--sticky wp-block-unilux-blocks-secondary-navigation\" id=\"8db8eef9-152f-4377-9618-6ca3536d9c82\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Overview\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Overview<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Overview<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/programme\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link isactived\" aria-current=\"page\">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Programme<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/mobility\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Mobility <\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/career\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Career<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/testimonials\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Testimonials<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/teaching-staff\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Teaching staff<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/admissions\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Admissions<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n<section class=\"section section wp-block-unilux-blocks-headline-text-and-image \">\n    \n<div class=\"wp-block-unilux-blocks-wrapper container xl:max-w-screen-xl\">\n<h2 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"programme\"\n    >\nProgramme<\/h2>\n\n\n\n<div class=\"wp-block-unilux-blocks-wrapper flex flex-wrap lg:-mx-32\">\n<div class=\"wp-block-unilux-blocks-wrapper w-full lg:w-7\/12 lg:order-2 lg:px-32\">\n<div class=\"wp-block-unilux-blocks-image-video-wrapper\">\n    <figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--cover\">\n    \n<img decoding=\"async\" class=\"wp-block-image unilux-custom-image-block\"\n                alt=\"\"\n            src=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-scaled.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-300x225.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-1024x768.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-768x576.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-1536x1152.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/UNI-1005-57-2048x1536.jpg 2048w\"\n                style=\"object-position: 33.00% 32.00%; font-family: &quot;object-fit: cover; object-position: 33.00% 32.00%;&quot;; aspect-ratio: 3\/2; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div><\/div>\n\n\n\n<div class=\"wp-block-unilux-blocks-wrapper w-full lg:w-5\/12 lg:order-1 lg:px-32\">\n<p>The Bachelor in Mathematics at the 8xav福利导航 of Luxembourg offers the following programme:<br><br>Year 1 introduces analysis, algebra and geometry, alongside optional courses: didactics, computer science or physics.<br><br>Year 2 adds probability &amp; statistics to further analysis and algebra. Optional courses help with professional orientation.<br><br>Year 3 combines a mobility semester, optional courses (number theory, numerical analysis, Markov chains, etc.) and a supervised report on a specific subject.<\/p>\n\n\n\n<ul class=\"wp-block-unilux-blocks-custom-buttons btn-list\"><li class=\"wp-block-unilux-blocks-custom-button\"    aria-disabled=\"false\"\n    >\n    <a\n        role=\"link\"\n        aria-disabled=\"false\"\n                    href=\"https:\/\/www.uni.lu\/fstm-en\/study-programs\/bachelor-in-mathematics\/admissions\/\"\n                target=\"_self\"\n        class=\"btn btn--primary\"\n            >Admissions<\/a>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h2 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"academic-contents\"\n    >\nAcademic Contents<\/h2>\n\n\n\n<div id=\"tab-nav\" class=\"tab-nav\">\n    <button\n        type=\"button\"\n        class=\"button-toggle btn btn--white w-full\"\n        aria-expanded=\"false\"\n        aria-controls=\"tab-nav__listing\"\n        title=\"The selected tab is CONTENT OF THE CURRENT LABEL\"\n    >\n        <span class=\"btn__name mr-auto\">Semester 1<\/span>\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n        <\/svg>\n    <\/button>\n    <ul\n        id=\"tab-nav__listing\"\n        class=\"tab-nav__listing nav manual\"\n        role=\"tablist\"\n        aria-label=\"About me\"\n    >\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-7c8438f8-c26c-4c9f-9f51-35362ffcda7b\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-7c8438f8-c26c-4c9f-9f51-35362ffcda7b\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-7c8438f8-c26c-4c9f-9f51-35362ffcda7b\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 1<\/span>\n            <\/button>\n        <\/li>\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-b412a128-5f24-4db3-912a-3ae44f6ef234\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-b412a128-5f24-4db3-912a-3ae44f6ef234\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-b412a128-5f24-4db3-912a-3ae44f6ef234\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 2<\/span>\n            <\/button>\n        <\/li>\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-f60582d4-38bb-4eb6-8c0a-e57d6999eb40\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-f60582d4-38bb-4eb6-8c0a-e57d6999eb40\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-f60582d4-38bb-4eb6-8c0a-e57d6999eb40\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 3<\/span>\n            <\/button>\n        <\/li>\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-e6a81c39-8505-43ae-9b09-af8aeac54ae0\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-e6a81c39-8505-43ae-9b09-af8aeac54ae0\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-e6a81c39-8505-43ae-9b09-af8aeac54ae0\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 4<\/span>\n            <\/button>\n        <\/li>\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-55dd3e7c-2cc9-495a-a4a8-98be25c7b179\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-55dd3e7c-2cc9-495a-a4a8-98be25c7b179\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-55dd3e7c-2cc9-495a-a4a8-98be25c7b179\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 5<\/span>\n            <\/button>\n        <\/li>\n                <li role=\"presentation\" class=\"tab-nav__item\" key={button.id}>\n            <button\n                type=\"button\"\n                id=\"tab-eb4d8f34-3d30-4e55-ad17-9ec7191d588d\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-eb4d8f34-3d30-4e55-ad17-9ec7191d588d\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-eb4d8f34-3d30-4e55-ad17-9ec7191d588d\"\n                aria-selected=\"false\"\n                aria-current=\"false\"\n                class=\"tab-nav__button\"\n                tabIndex=\"-1\"\n            >\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                    <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n                <\/svg>\n                <span class=\"tab-nav__name\">Semester 6<\/span>\n            <\/button>\n        <\/li>\n            <\/ul>\n<\/div>\n<div class=\"tab-content\">\n    <section\n    id=\"tabpanel-7c8438f8-c26c-4c9f-9f51-35362ffcda7b\"\n    aria-labelledby=\"tab-7c8438f8-c26c-4c9f-9f51-35362ffcda7b\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 1 (2025-2026 Winter)<\/h3>\n    \n<div id=\"accordion-module-6a13f62385d34\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385d63\"\n        >\n            <span class=\"accordion__title\">\n                Analyse 1                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            10                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-1                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385d63\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse 1 <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 10<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 1.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Ma\u00eetriser les bases de l&#8217;analyse math\u00e9matiques et du raisonnement math\u00e9matique.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Les \u00e9tudiants apprendront \u00e0 conna\u00eetre et \u00e0 utiliser les bases de l&#8217;analyse : suites, fonctions r\u00e9elles \u00e0 une variable, d\u00e9veloppements de Taylor, et quelques bases sur des espaces m\u00e9triques. <br>Par ailleurs le cours et les exercices les aideront \u00e0 acqu\u00e9rir les bases du raisonnement math\u00e9matique.<br><\/p><ul><li>entiers, rationnels, nombres r\u00e9els<\/li><li>suites de nombres r\u00e9els<\/li><li>fonctions, limites de fonctions<\/li><li>continuit\u00e9 et d\u00e9riv\u00e9es<\/li><li>d\u00e9veloppements de Taylor<\/li><li>espaces m\u00e9triques, notions de topologie dans les espaces m\u00e9triques<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>First session<br>End of course assessment + Continuous assessment<\/p><br><p><br>Retake exam<br>End of course assessment\u00a0<\/p><br><p><br>Absence plan<br>In case an exam in the continuous assessment plan cannot be taken (for a valid reason) the corresponding grade will not be taken into account in the final grade of the course.<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature\u00a0<br><\/p><br><ul><br><li><br>\u00ab Principles of Mathematical Analysis \u00bb, Walter Rudin, MacGrawHill Ed. (traduction fran\u00e7aise: \u00ab Principes d&#8217;analyse math\u00e9matique \u00bb, Ed. Dunod, traduction allemande \u00ab Analysis \u00bb, Oldenbourg Verlag)<\/li><br><li>\u00ab Math\u00e9matiques L1 \u00bb J-P. Marco L. Lazzarini, Ed. Pearson<\/li><br><li>\u00ab Elementary Analysis (The Theory of Calculus) \u00bb, Kenneth A. Ross, Springer Ed.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385d80\"\n        >\n            <span class=\"accordion__title\">\n                Structures math\u00e9matiques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-2                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385d80\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Structures math\u00e9matiques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 1.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Apprendre des fondements du langage math\u00e9matique et des techniques et structures de base.<br>L\u2019\u00e9tudiant(e) ayant valid\u00e9 l\u2019unit\u00e9 d\u2019enseignement est capable de :<\/p><br><ul><br><li>se servir du langage math\u00e9matique, <\/li><br><li>ma\u00eetriser les d\u00e9finitions et les propri\u00e9t\u00e9s fondamentales des groupes, anneaux et corps, <\/li><br><li>les illustrer par des exemples, <\/li><br><li>trouver et \u00e9crire des d\u00e9monstrations math\u00e9matiques simples. <br><\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programme<br><\/p><ul><li>logique, ensembles, applications<\/li><li>d\u00e9monstrations (types et pratique)<\/li><li>nombres naturels, entiers et rationnels<\/li><li>groupes : d\u00e9finition, exemples, groupe sym\u00e9trique, morphismes, sous-groupes, (sous-groupes distingu\u00e9s), (quotients)<\/li><li>anneaux : d\u00e9finition, exemples, corps, morphismes, (sous-anneaux), (id\u00e9aux), (quotients), congruences, algorithme d&#8217;Euclide, Z\/nZ<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Examen final et partiel (facultatif).                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature\u00a0<br><\/p><br><p>Hermann Schichl, Roland Steinbauer: Einf\u00fchrung in das mathematische Arbeiten, Springer-Verlag Berlin Heidelberg, 978-3-642-28645-2<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385d8e\"\n        >\n            <span class=\"accordion__title\">\n                Alg\u00e8bre lin\u00e9aire 1                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            9                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-3                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385d8e\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Alg\u00e8bre lin\u00e9aire 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 1.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>A l&#8217;issue du cours, l&#8217;\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de :<\/p><br><ul><br><li>ma\u00eetriser les notions et les algorithmes fondamentaux de l&#8217;alg\u00e8bre lin\u00e9aire ainsi que les principaux outils d\u00e9velopp\u00e9s pour l&#8217;\u00e9tude g\u00e9n\u00e9rale des espaces vectoriels<\/li><br><li>acqu\u00e9rir un raisonnement rigoureux et syst\u00e9matique, indispensable \u00e0 l&#8217;analyse et \u00e0 l&#8217;interpr\u00e9tation des objets de l&#8217;alg\u00e8bre lin\u00e9aire<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Au terme du cours, l\u2019\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de : <\/p><br><ul><br><li>comprendre le r\u00f4le central de l\u2019alg\u00e8bre lin\u00e9aire dans les sciences math\u00e9matiques <\/li><br><li>ma\u00eetriser les notions et les algorithmes fondamentaux de l\u2019alg\u00e8bre lin\u00e9aire ainsi que les principaux outils d\u00e9velopp\u00e9s pour l\u2019\u00e9tude g\u00e9n\u00e9rale des espaces vectoriels <\/li><br><li>acqu\u00e9rir un raisonnement rigoureux et syst\u00e9matique, indispensable \u00e0 l\u2019analyse et \u00e0 l\u2019interpr\u00e9tation des objets de l\u2019alg\u00e8bre lin\u00e9aire <\/li><br><li>formuler et r\u00e9soudre math\u00e9matiquement certains probl\u00e8mes concrets mod\u00e9lisables au moyen de l\u2019alg\u00e8bre lin\u00e9aire. <br><\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00a0<p>Programme<br><\/p><ul><li>Matrices : d\u00e9finitions et op\u00e9rations de base, matrices particuli\u00e8res, transpos\u00e9e, inverse, lien avec les syst\u00e8mes lin\u00e9aires et m\u00e9thode du pivot<\/li><li>Espaces vectoriels : d\u00e9finitions, premi\u00e8res propri\u00e9t\u00e9s, exemples, sous-espace vectoriel, bases, dimension, suppl\u00e9mentaire, <\/li><li>Applications lin\u00e9aires : d\u00e9finition, noyau, image, th\u00e9or\u00e8me du rang, matrice d&#8217;une application lin\u00e9aire, changement de bases<\/li><li>D\u00e9terminant : rappels sur le groupe sym\u00e9trique, formes n-lin\u00e9aires altern\u00e9es, d\u00e9finition du d\u00e9terminant, propri\u00e9t\u00e9s, applications, calculs, comatrice<\/li><li>G\u00e9om\u00e9trie dans le plan et l&#8217;espace : produit scalaire, bases orthonorm\u00e9es, proc\u00e9d\u00e9 de Gram-Schmidt, orthogonal, isom\u00e9trie et classification<\/li><\/ul>\u00a0                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Exam modalities for the first session<br>un examen partiel (\u00e9crit) sera organis\u00e9 pendant le semestre et un examen final (\u00e9crit) sera organis\u00e9 pendant la p\u00e9riode des examens de janvier. La note finale sera calcul\u00e9e comme suit: max(final,0,4*partiel+0,6*final).<\/p><br><p><br>Exam modalities for the retake exam<br>un examen de rattrapage \u00e9crit sera organis\u00e9 pendant la p\u00e9riode des examens de juillet. La note finale sera la note obtenue \u00e0 cet examen de rattrapage.<\/p><br>Absence plan<br>en cas d&#8217;absence \u00e0 l&#8217;examen partiel \u00e9crit de la 1\u00e8re session, la note finale de la premi\u00e8re session est \u00e9gale \u00e0 la note de l&#8217;examen final.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature<br><\/p><br><ul><br><li>Les notes de cours (sous forme de transparents) sont disponibles sur Moodle, ainsi que les feuilles d\u2019exercices.<\/li><br><li>Le cours ne suit pas de livre particulier. Le contenu est toutefois classique, et n\u2019importe quel ouvrage d\u2019alg\u00e8bre lin\u00e9aire pour les \u00e9tudiants de 1\u00e8re ann\u00e9e de bachelor ou de licence de math\u00e9matiques peut \u00eatre utilis\u00e9 par l\u2019\u00e9tudiant qui souhaite aller plus loin et\/ou avoir plus d\u2019exercices.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385d9b\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch allgemein A1.1 (Belval)                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-255                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385d9b\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch allgemein A1.1 (Belval) <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-255<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            This course aims to develop basic language skills with the objective of enabling complete beginners to reach A1 level (A1.1 in the winter term and A1.2 in the summer term).<br>Communication skills: Students will learn to understand simple written texts and engage in oral communication on topics such as family, food and shopping, appointments, hobbies and leisure activities, furniture and living arrangements, tourist attractions, and urban living.<br>Grammar: The students will learn regular and irregular verbs in the present and perfect tenses, articles and nouns with gender and cases, modal verbs, interrogative and imperative forms, sentence structure, pronouns, prepositions, connectors, participles, and other basic grammatical structures.<br>Course design: This is a blended learning course in which students develop their language skills both in class and on an e-learning platform (Moodle).<br>The objective of the classroom work is the continued acquisition of basic oral and written skills through communicative activities in speaking, listening, writing, and reading\u2013individually, in pairs, and in groups.<br>The objective of the Moodle activities is to consolidate and deepen what has been learned in class. Additionally, in A1.2, students will create a writing portfolio with two short texts as part of these activities. They will also give a hort in-class presentation on an everyday topic during the semester. The course concludes with a test covering the communicative activities listening, reading, and writing as well as grammar.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        By the end of this course, students should be able to:<br><br><ul><br><li>Understand and provide information about themselves and general personal matters<\/li><br><li>Understand and give information about their leisure activities and making appointments<\/li><br><li>Understand and provide information about rooms, apartments, and furniture<\/li><br><li>Understand and provide information about clothes, fashion, and shopping<\/li><br><li>Understand and give information about attractions and towns in the German-speaking countries<\/li><br><li>Perform everyday linguistic actions<\/li><br><li>Understand and write simple texts like emails or SMS messages.<\/li><br><\/ul><br><br><br><br><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The objective is the continued acquisition of basic oral and written skills. Students will engage in speaking, listening, writing, and reading communicative activities through individual, pair, and group work. Additionally, students will be provided with links to interactive exercises, quizzes, and games as well as to tutorials and other informative tools. The course concludes with a language examination covering all four communicative activities.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><br><li><br>Speaking skills will be evaluated through an oral presentation.<\/li><br><li>Listening, writing, and reading skills will be evaluated through a handwritten exam.<\/li><br><\/ul><br><p>Listening: Key information from listening texts (radio, TV, etc.) must be understood.<br>Reading: Key information must be found in short reading texts or derived by answering related questions.<br>Writing: Basic text production is required.<br>Notes on the use of AI<br>The unauthorized or inappropriate use of AI, as well as the copying of work created by others and presenting it as one&#8217;s own in the preparation of oral or written texts, may result in the initiation of disciplinary proceedings by the 8xav福利导航. See: https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/9\/2025\/03\/VRA_Disciplinary-procedure-fraud-plagiarism_directive_v4_EN.pdf<\/p>\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Bibliography<br>Birgit Braun et. al.: DaF kompakt ne uA1(Deutsch als Fremdsprache) Kurs- und \u00dcbungsbuch +2 Audio CDs. Klett. Stuttgart 2017<\/p><br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385da8\"\n        >\n            <span class=\"accordion__title\">\n                Didactique des math\u00e9matiques 1                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-4                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385da8\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Didactique des math\u00e9matiques 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Faire \u00e9merger ses repr\u00e9sentations sur<br><ul><br><li>\u00ab c\u2019est quoi les maths ?\u00bb, <\/li><br><li>\u00ab pourquoi les maths \u00e0 l\u2019\u00e9cole ?\u00bb, <\/li><br><li>\u00ab qu\u2019est-ce que faire des maths \u00e0 l\u2019\u00e9cole ?\u00bb <\/li><br><li>\u00ab aimer ou d\u00e9tester les maths : pourquoi ?\u00bb <\/li><br><\/ul><br>\u00a0                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Cours visant une interaction \u00e9troite entre observation, analyse et th\u00e9orisation de pratiques de classe (math\u00e9matique, historique, didactique et \u00e9pist\u00e9mologique)<br>Comprendre les fondements du programme de math\u00e9matiques au secondaire                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programme<br><\/p><ul><li>Comment donner go\u00fbt aux math\u00e9matiques \u00e0 l&#8217;aide de jeux math\u00e9matiques ? <\/li><li>Comment combler des lacunes ou am\u00e9liorer sa rapidit\u00e9 en calcul \u00e0 l&#8217;aide de jeux math\u00e9matiques ? <\/li><li>D\u00e9couverte de divers jeux. Recherche des points forts et faibles de ces jeux <\/li><li>Premier contact en classe pour v\u00e9rifier aupr\u00e8s des \u00e9l\u00e8ves ces points forts et faibles et confrontation <\/li><li>Situations-probl\u00e8mes, probl\u00e8mes d\u2019application, probl\u00e8mes ouverts <\/li><li>Histoire, symboles, \u00e9tymologie<\/li><li>Capacit\u00e9, comp\u00e9tence, connaissance et savoir math\u00e9matiques\u00a0 \u00a0<\/li><li>Recourir \u00e0 des logiciels de calcul formel et de g\u00e9om\u00e9trie dynamique<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><br><li>Engagement r\u00e9gulier,<\/li><br><li>Elaboration d\u2019un portfolio personnel (pi\u00e8ces cr\u00e9\u00e9es \u00e0 partir des \u00e9l\u00e9ments trait\u00e9s en cours),<\/li><br><li>Pr\u00e9sentation du portfolio.<\/li><br><\/ul><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385db4\"\n        >\n            <span class=\"accordion__title\">\n                Experimental Physics 1a and 1b: Mechanics, Oscillations and Waves (CM, 1a) and TD(1b)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_PHYS_GEN-28                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385db4\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Experimental Physics 1a and 1b: Mechanics, Oscillations and Waves (CM, 1a) and TD(1b)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_PHYS_GEN-28<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p><br>Physique exp\u00e9rimentale 1a: M\u00e9canique newtonienne, oscillations et ondes:<\/p><br><p>Le cours vise<br>&#8211; \u00e0 familiariser l\u2019\u00e9tudiant avec les principes et lois de la m\u00e9canique newtonienne<br>&#8211; \u00e0 l\u2019apprendre \u00e0 appliquer ces principes et lois \u00e0 des ph\u00e9nom\u00e8nes oscillatoires et ondulatoires<br>&#8211; et \u00e0 fournir \u00e0 l\u2019\u00e9tudiant de mani\u00e8re cibl\u00e9e des outils math\u00e9matiques indispensables en physique.<\/p><br><p><br>Physique Exp\u00e9rimentale 1b: TD (Travaux Dirig\u00e9s)<br>:<br><br>L\u2019\u00e9tudiant est amen\u00e9 \u00e0<br>&#8211; r\u00e9soudre d\u2019une mani\u00e8re autonome des probl\u00e8mes en physique<br>&#8211; appliquer les lois physiques<br>&#8211; manipuler correctement les outils math\u00e9matiques indispensables en physique<br><\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Physique exp\u00e9rimentale 1a: M\u00e9canique newtonienne, oscillations et ondes:<br><br>L\u2019\u00e9tudiant(e) ayant valid\u00e9 l\u2019uni<br>t\u00e9 d\u2019enseignement<br>&#8211; ma\u00eetrise les principes et lois de la m\u00e9canique newtonienne<br>&#8211; sait appliquer les lois de la m\u00e9canique newtonienne \u00e0 des ph\u00e9nom\u00e8nes oscillatoires et ondulatoires<br>&#8211; arrive \u00e0 r\u00e9soudre des probl\u00e8mes inconnus en relation avec la m\u00e9canique newtonienne et les ph\u00e9nom\u00e8nes oscillatoires ou ondulatoires<br>&#8211; r\u00e9ussit \u00e0 manipuler les outils math\u00e9matiques indispensables en m\u00e9canique.<br>Physique Exp\u00e9rimentale 1b : TD (Travaux Dirig\u00e9s):<br>L\u2019\u00e9tudiant(e) ayant valid\u00e9 l\u2019unit\u00e9 d\u2019enseignement<br>&#8211; arrive \u00e0 r\u00e9soudre des probl\u00e8mes inconnus en relation avec la m\u00e9canique newtonienne et les ph\u00e9nom\u00e8nes oscillatoires ou ondulatoires<br>&#8211; r\u00e9ussit \u00e0 manipuler les outils math\u00e9matiques indispensables en m\u00e9canique newtonienne<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Motion of point masses\/kinematics<br>Forces and Newton&#8217;s laws of mechanics<br>Work and (potential and kinetic) energy<br>Relative motion (Galilei transformation, inertial system, Centrifugal and Coriolis forces)<br>Conservation principles (momentum, angular momentum, energy)<br>Dynamic properties of rigid bodies (center of mass, moment of inertia, Euler equations)<br>Oscillations and resonance (harmonic oscillator)<br>Wave equation and propagation of waves<br>Principle of Huygens<br>Interference phenomena<br>Diffraction of waves<br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br><p><br>Experimental Physics 1a<br><\/p><br><p><br>Written exam during the exam session.<br>The student has to answer comprehension questions and solve problems comparable to those treated in the exercise class.<br>During the exam he\/she can use a pocket calculator and any mathematical tool.<br>Duration of the exam: 120 min<br>The exam is graded out of 20\u00a0<br>A student is only allowed to take the written exam if he got a grade for\u00a0<br>Experimental Physics 1b at the end of the exercise class.<br><br>Experimental Physics 1b<br>The participation in the exercise class is mandatory.<br>Continuous assessment (12-13 assignments) and midterm test.<br>The midterm test counts for 50% of the final grade for the exercise class.<br>The exercise class is graded out of 20.<br>Students who do not regularly participate in the TD\u00a0 are excluded from the exercise class (after two absences without a valid excuse or three absences with a valid excuse) = valid excuse : deregistration from the course by the study programme administrator \/ without valid excuse: ABSNJ (unjustified absence) &#8211; 1 attempt out of 2.<\/p><br><p>\u00a0<\/p><br><p>To be admitted to the final exam in Experimental Physics 1a the student must have completed the exercise class (Experimental Physics 1b) with a fin al grade.<br><br>Calculation of the final grade for Experimental Physics 1a and 1b:<br>Mark = (4xgradeexam+gradeTD)\/5<br><br><br>Retake exam offered<br>Written exam<br>Mark = (4xgradeexam+gradeTD)\/5<br>GradeTD = grade obtained at the end of the exercise class previously followed\u00a0 by the student\u00a0<br><br><\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        P. A. Tipler, G. Mosca: Physics for Scientists and Engineers, vol 1, Worth Publishers.<br>D. Halliday, R. Resnick, J. Walker: Physik, Wiley-VCH.<br>H. Benson: Physique 1: M\u00e9canique, De Boeck Universit\u00e9.<br>R. P. Feynman, R. B. Leighton, M. Sands: The Feynman Lectures on Physics, vol 1 and 2, Addison-Wesley (recommended for physicists).<br>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385dc1\"\n        >\n            <span class=\"accordion__title\">\n                Programming Fundamentals 1                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            F1_BAINFOR-9                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385dc1\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Programming Fundamentals 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_BAINFOR-9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            This course introduces the fundamentals of programming using the Python programming language. This is not primarily a Python programming course but rather a discussion of the fundamental concepts underlying computation using Python code examples as illustration. At the same time enough of the Python language is covered for the students to be able to tackle non-trivial problems (e.g., in the context of projects). This introductory course forms the basis for more advanced courses on algorithms and object-oriented programming.<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Upon completion of this course the student should be able to:<br>move from a problem description to a Python program by successively reducing the level of abstraction with the help of pseudo-code.<br>document the implementation choices.\u00a0<br>make use of available data types and program libraries.<br>extend and adapt code written by other programmers.<br>test and debug computer programs.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        1. Introduction to computational problem solving and the Python programming language.<br>2. Basic syntax and semantics of Python.<br>3. Functions and modules.<br>4. Problem solving and recursion.<br>5. Structured types and function objects.<br>6. Files and exceptions.<br>7. Testing.<br>8. Debugging.<br>9. Iterators and generators.<br>10. Floating-point numbers.<br>11. Introduction to object-oriented programming in Python.<br>12. Introduction to popular libraries: mathplotlib, NumPy and Pandas.<br>13. Introduction to software engineering.<br><br><br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Assessment modality: Combined assessment<br>Assessment tasks<\/p><br>Task 1:<br>Written exam (50%)<br><br>Grading scheme: 20 points (0-20)<br>Objectives: The objective of this final exam is to test the student\u2019s understanding of the course material.<br>Assessment rules: The student has to answer questions with pencil and paper. This is a closed-book exam. No cheat sheet allowed.<br>Assessment criteria: The student must answer the stipulated questions in a way that clearly demonstrates understanding of underlying concepts.<br>Task 2:Written exam (50%)<br>Grading scheme: 20 points (0-20)<br>Objectives: To test the student\u2019s ability to implement Python programs for concrete problems.<br>Assessment rules: The student has to solve programming tasks with pencil and paper. This is a closed-book exam. No cheat sheet allowed.<br>Assessment criteria: The exam consists of two parts: mid-term evaluation and final evaluation, each of which counts 25%.<br>Task 3:Written exam &#8211; RETAKE (100%)<br>Grading scheme: 20 points (0-20)<br>Objectives: The objective of this final exam is to test the student\u2019s understanding of the course material.<br>Assessment rules: The student has to answer questions with pencil and paper. This is a closed-book exam. No cheat sheet allowed.<br>Assessment criteria: The student must answer the stipulated questions in a way that clearly demonstrates understanding of underlying concepts.<br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Course materials<br><\/p><br><p>Syllabus\u2610Yes\u2612No<br>Remarks:<br>Literature list\u2610Yes\u2612No<br>Remarks:<br>Moodle page\u2612Yes\u2610No<br>Remarks:https:\/\/moodle.uni.lu\/course\/view.php?id=321<br>Other, please specify:<br><\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385dce\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch allgemein A1.1 (Kirchberg)                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-93                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385dce\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch allgemein A1.1 (Kirchberg) <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-93<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        In this course (30h) you will learn to understand basic German sentences, to express easy statements, present yourself and others and to write some simple sentences and expressions. You will read very simple textes and understand the main information and important words. You will be able to ask basic questions and to interact in a very short dialogue.<br>In diesem Kurs (30 Stunden total) lernen totale Anf\u00e4nger Deutsch zu verstehen, sehr einfache S\u00e4tze zu schreiben, leichte Texte zu lesen, wichtige Informationen zu verstehen, Aufgaben dazu zu bearbeiten und sich m\u00fcndlich vorzustellen sowie \u00fcber Alltagsthemen kurz zu sprechen. Die Teilnehmer lernen auch Fragen zu stellen und k\u00f6nnen somit an einem kurzen Dialog teilnehmen.<br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Evaluation and attendance requirements:<br>Two small written exams and one oral test during the classes. Each counts 10% and the end test 70%.\u00a0<br>The participation during the classes counts also. Usine AI programs during exams is not allowed!<br>Using AI during the classes is only allowed if anounced by the professor.\u00a0<br>In order to get your ECTS you also need to be present in the classes (a maximum of 2 absences is authorized)<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Required Textbook<br>Hermann Funk et.al: Das Leben A1 (Deutsch als Fremdsprache) Kurs- und \u00dcbungsbuch. Cornelsen. Berlin 2020; E-book and PagePlayer-App are included in the book.<br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385ddb\"\n        >\n            <span class=\"accordion__title\">\n                Entrepreneurship                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            F1_MA_HPC_1-10                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385ddb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Entrepreneurship<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_HPC_1-10<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Many of students will make a switch to the modern labour market at some point in their career. Knowledge of business aspects such as innovation, marketing, leadership, team building, intellectual property rights, finance and business models is essential to succeed. However, in the academic arena in which students learn their core educational skills, these subjects may not be often elaborated upon. The course offers immersive and interactive workshops and activities, designed to test participants\u2019 entrepreneurial appetite and jumpstart their entrepreneurial adventure. Whether students want to ignite theirs entrepreneurial spirit or get just enough flavour of entrepreneurship to flourish as entrepreneurs within any organization, they will learn the basic building blocks to excel. Looking at the world with an opportunity-oriented mindset, we put them in the entrepreneurial roles to work on their chosen ideas and concepts. Students will gain experience in following an inter-disciplinary approach as well as the capability to brainstorm, think outside the box, and to generate ideas with the aim to improve their entrepreneurial skillset including: communication, teamwork, networking, decision-making, complex problem-solving, critical thinking, creativity, time management, marketing skills, leadership among others.<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        With a wide breadth of knowledge of entrepreneurship, creativity, innovation and business essentials, the skills learned are vital for the success of any business, in new ventures as well as in established companies. The goal of this course is to provide students guidance with an overarching framework: # To be aware of entrepreneurship opportunities # Debunk the top myths of entrepreneurship #To be able to professionalize their startup or research projects # To be aware of how to develop an entrepreneurial project: Identify an opportunity or a problem worth solving; Evaluate an idea; Perform market research and choose the target audience; Brainstorm and design a creative innovative solution; Test the solution with potential customers; Strategize the venture growth development ; Pinpoint and manage the critical risks ; Build a financial model and discover the key financial information; Learn to pitch effectively # Interact effectively with students\u2019 peers with diverse skills and experience # Network with relevant stakeholders in the entrepreneurial, startup and business ecosystems in Luxembourg                    <\/div>\n                <\/li>\n                \n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>The final grade is composed by:<br><\/p><br><p><br>1.\u00a0<br>Fundamentals of Entrepreneurship :\u00a0<br>20%\u00a0<br>\u00a0\u00a0<br>Take-home assignment\u00a0<br><\/p><br><p>We aim to provide a structured framework for the self-paced workshops, focusing on equipping participants with the knowledge, skills, and mindset required to succeed in innovation, entrepreneurship, and intrapreneurship. Four objectives: (1) Develop Understanding of Innovation and Creativity (2) Establish a Strong Foundation for a New Business Venture (3) Cultivate Intrapreneurial and Entrepreneurial Mindsets (4) Active Engagement and Completion of Workshops. <\/p><br><p><br>2. Co-Founders Nights :\u00a0<br>15%\u00a0<br>\u00a0Active participation\u00a0<br><\/p><br><p>We aim to create a dynamic and supportive environment for participants to learn from experienced entrepreneurs, network, and potentially find co-founders for their entrepreneurial ventures, ultimately empowering them to take meaningful steps towards realizing their entrepreneurial aspirations. Objectives are (1) Gain Insights into Entrepreneurship (2) Find Potential Co-Founders for your idea or join a team (3) learn how to network <\/p><br><p><br>3. My Big Idea :<br>\u00a015 %\u00a0<br>\u00a0Take-home assignment<br><\/p><br><p>We aim to provide participants with a clear understanding of developing a simple but effective executive summary. Objectives are: (1) Develop Entrepreneurial Skills (2) Foster Collaboration and Teamwork (3) Idea Development and Refinement <\/p><br><p><br>4. Inception Sprint Day:\u00a0<br>30%\u00a0<br>Active participation\u00a0<br><\/p><br><p>We aim to provide participants with a structured framework for learning and skill development during the Inception Sprint Day, focusing on collaboration, problem-solving, leadership, startup dynamics, multidisciplinary teamwork, pitching, and communication. Objectives are (1) Develop Cross-Disciplinary Collaboration Skills (2) Enhance Problem-Solving Abilities (3) Gain Insight into Ventures Dynamics (4) Practice Pitching and Communication Skills (5) Gain Real-World Experience <\/p><br><p><br>5.<br>Self-reflection \/ learning diary :\u00a0<br>10%\u00a0<br>Take-home assignment\u00a0<br><\/p><br><p>By engaging in individual reflection, participants can gain valuable insights into their own learning experiences, personal growth, and professional development. The reflection process serves as a tool for self-discovery, critical thinking, and ongoing improvement, enhancing the overall learning journey for each participant. <\/p><br><p><br>6.<br>Final debriefing session :\u00a0<br>10%\u00a0<br>Active participation\u00a0<br><\/p><br><p>The debriefing session serves as a valuable opportunity for reflection, feedback, and collaboration, benefiting both participants and organizers. <\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Please check the Moodle page to know where the sessions are taking place                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385de7\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch allgemein A2.1 (online)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-280                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385de7\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch allgemein A2.1 (online)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-280<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            \u00a0<br><p>The objective of the online-classroom work is the continued acquisition of basic oral and written skills through communicative activities in speaking, listening, writing, and reading\u2013individually, in pairs, and in groups.<br>The objective of the Moodle activities is to consolidate and deepen what has been learned in class. A reading project tailored to the students\u2019 proficiency level will be integrated into these activities. Additionally, students will develop a writing portfolio with two short texts and give a short in-class presentation on a university-related topic during the semester. The course concludes with a test covering the communicative activities listening, reading and writing as well as grammar.<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Learning outcomes<br>By the end of this course, students should be able to:<br><ul><li>Understand\u00a0 \u00a0 and\u00a0 \u00a0 provide\u00a0 \u00a0 information\u00a0 \u00a0 about\u00a0 \u00a0 university life, family, profession, tourism and culture, sports and food, learning experiences, media and communication, travel and climate, as well as mobility and professional life.<\/li><li>Understand and provide information about past activities.<\/li><li>Ask for help, make recommendations and suggestions, and convey hope and surprise. Students will also be able to discuss learning experiences and habits, express happiness, enthusiasm, and disappointment, as well as satisfaction and dissatisfaction, and show interest and disinterest. Additionally, students will be able to book rooms, give directions, talk about the weather, and explain things.<\/li><li>Give a short presentation on a university-related topic.<\/li><li>Compose basic texts and revise them with the support of the teacher.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        This online-course aims to develop language skills to achieve levelA2inGerman(A2.1 in the winter term and A2.2 in the summer term).<br>Communication skills: Students will learn to understand written and oral texts about everyday life and, to some extent, university life. They will be able to speak about a variety of everyday topics and handle different everyday situations linguistically. Additionally, they will write typical short texts used in daily communication.<br>Grammar: The course covers the perfect tense (regular and irregular verbs), possessive pronouns, prepositions, adjective declension, common conjunctions, reflexive verbs, temporal conjunctions, local prepositions, the passive voice, phrase construction, dative and accusative objects, verbs with prepositions, the past tense, demonstrative pronouns, relative clauses, and relative pronouns.<br>Course design: This is a blended learning course in which students develop their language skills both in presence online and on an e-learning platform (Moodle).                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Evaluation<br><p>Speaking skills will be evaluated through an oral presentation online.<br>Listening, writing and reading skills will be evaluated through a handwritten exam. Attention: This exam will be organized on-site in the last week of the seminar.<\/p><br><p>Listening: Key information from listening texts(radio, TV, etc.) must be understood.<br>Reading: Key information must be found in short reading texts, or questions about these texts must be answered.<br>Writing: Basic text production is required.<\/p><br><p><br>Notes on the use of AI<br>The unauthorized or inappropriate use of AI, as well as the copying of work created by others and presenting it as one&#8217;s own in the preparation of oral or written texts, may result in the initiation of disciplinary proceedings by the 8xav福利导航. See: https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/9\/2025\/03\/VRA_Disciplinary-procedure-fraud-plagiarism_directive_v4_EN.pdf\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00a0<br><p><br>Bibliography<br><\/p><br><p>Habersack, Charlotte(2020): Menschen A2. Deutsch als Fremdsprache. Kursbuch. Ismaning: Hueber.<br>Breitsameter, Anna(2023): Menschen A2. Deutsch als Fremdsprache. Arbeitsbuch. Ismaning: Hueber.<br>Luger, Urs: Schiller, Schiller. Hueber-Verlag (will be made available online as a PDF and as an audio file)<\/p><br>\u00a0<br>\u00a0<br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385df4\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch B1  wissenschaftlich (Belval)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-125                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385df4\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch B1  wissenschaftlich (Belval)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-125<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Im Kurs werden unterschiedliche Themen aus den Bereichen Alltag, Studium und Beruf behandelt und Hilfsmittel gegeben, um sich in diversen Situationen m\u00fcndlich und schriftlich ad\u00e4quater auszudr\u00fccken. Die Teilnehmer werden in Einzel-, Paar- und Gruppenarbeiten alle vier Fertigkeiten (H\u00f6ren, Sprechen, Lesen, Schreiben) trainieren und grammatikalische Strukturen erlernen, die auf diesem Niveau h\u00e4ufig Schwierigkeiten bereiten.<br><p>\u00a0<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Am Ende des Kurses sollen die Teilnehmer in der Lage sein,<br><ul><br><li><br>die Hauptinformationen eines geschriebenen oder gesprochenen Textes zu verstehen, wenn klare Standardsprache verwendet wird und es um vertraute Dinge aus Alltag und Beruf geht.<br><\/li><br><li><br>die meisten Situationen, denen man im Alltag im deutschsprachigen Raum begegnet, bew\u00e4ltigen zu k\u00f6nnen.<br><\/li><br><li><br>sich zusammenh\u00e4ngend \u00fcber vertraute Themen und pers\u00f6nliche Interessengebiete \u00e4u\u00dfern zu k\u00f6nnen.<br><\/li><br><li><br>\u00fcber Erfahrungen und Ereignisse zu berichten und Tr\u00e4ume, Hoffnungen und Ziele zu beschreiben sowie kurze Begr\u00fcndungen oder Erkl\u00e4rungen zu geben<br><\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Der Kurs richtet sich an Studierende mit dem Niveau B1, die ihren m\u00fcndlichen und schriftlichen Ausdruck verbessern und ihre Grammatikkenntnisse vertiefen m\u00f6chten.\u00a0<br>Im Kurs werden unterschiedliche Themen aus den Bereichen Alltag, Studium und Beruf behandelt und Hilfsmittel gegeben, um sich in diversen Situationen m\u00fcndlich und schriftlich ad\u00e4quater auszudr\u00fccken. Die Teilnehmer werden in Einzel-, Paar- und Gruppenarbeiten alle vier Fertigkeiten (H\u00f6ren, Sprechen, Lesen, Schreiben) trainieren und grammatikalische Strukturen erlernen, die auf diesem Niveau h\u00e4ufig Schwierigkeiten bereiten.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        F\u00fcr einen erfolgreichen Abschluss des Kurses sind eine kontinuierliche und aktive Teilnahme am Unterricht erforderlich und maximal drei Fehltage zul\u00e4ssig. Die KursteilnehmerInnen bekommen regelm\u00e4\u00dfig Haus\u00fcbungen, die korrigiert und mit Feedback versehen, aber nicht benotet werden.<br>Die Gesamtnote des Kurses setzt sich zu 50% aus drei Minitests (Hausarbeiten oder kurze Tests im Unterricht) sowie zu 50% aus einem schriftlichen Abschlusstest in der letzten Kurswoche zusammen.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Bibliografie<br><br>Braun-Podeschwa, J., Habersack, C., Pude, A. (2015). Menschen. Deutsch als Fremdsprache B1. M\u00fcnchen: Hueber-Verlag.<br>Buscha, A., Szita, S. (2013). Begegnungen. Deutsch als Fremdsprache. Sprachniveau B1+.\u00a0 \u00a0Leipzig: Schubert-Verlag.<br>Koithan, U., Schmitz, H., Sieber, S., Sonntag, B. (2014). Aspekte neu B1 plus: Mittelstufe Deutsch. Lehr- und Arbeitsbuch.\u00a0 \u00a0M\u00fcnchen: Klett.\u00a0\u00a0\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385e01\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch B2 wissenschaftlich (Belval)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-222                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385e01\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch B2 wissenschaftlich (Belval)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-222<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Im Kurs trainieren Sie den Umgang mit wissenschaftlichen Texten und Vortr\u00e4gen, die Sie m\u00fcndlich (in Form einer Pr\u00e4sentation) oder schriftlich zusammenfassen. Sie analysieren Textzusammenh\u00e4nge und wiederholen die grammatischen Strukturen und den Wortschatz, die f\u00fcr die Wissenschaftssprache typisch sind. Dar\u00fcber hinaus erarbeiten Sie Techniken, mit denen Sie Ihren Wortschatz erweitern k\u00f6nnen.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Am Ende des Kurses sollen die Teilnehmer in der Lage sein,<\/p><br><ul><br><li>die Hauptinhalte komplexer Texte zu konkreten und abstrakten Themen zu verstehen.<\/li><br><li>Fachdiskussionen im eigenen Spezialgebiet\u00a0 zu verstehen.<\/li><br><li>sich zu einem breiten wissenschaftsbezogenenen Themenspektrum klar und detailliert auszudr\u00fccken, einen Standpunkt zu einer aktuellen Frage zu erl\u00e4utern und Vor- und Nachteile anzugeben.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Der Kurs richtet sich an Studierende, die bereits Vorkenntnisse in Deutsch besitzen (Niveau B1) und die ihren schriftlichen und m\u00fcndlichen Ausdruck auf Niveau B2 verbessern und ihre Grammatikkenntnisse vertiefen m\u00f6chten.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        In diesem Kurs k\u00f6nnen 3 ECTS-Punkte erworben werden. Voraussetzungen f\u00fcr einen erfolgreichen Abschluss sind die regelm\u00e4\u00dfige Teilnahme am Unterricht (maximal 3 Abwesenheiten), die Bearbeitung von mindestens 80% der Online-\u00dcbungen, eine m\u00fcndliche Pr\u00e4sentation und die erfolgreiche Teilnahme (mindestens 60%) an einem Abschlusstest.<br>\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Bibliographie<br><\/p><br><ul><br><li>Bayerlein, Oliver (Hrsg.): Campus Deutsch. M\u00fcnchen: Hueber 2015<\/li><br><li>Esselborn-Krumbiegel, Helga: Richtig wissenschaftlich schreiben (5. Auflage). utb 2017<\/li><br><li>Gruber, Helmut, Huemer, Birgit, Rheindorf, Markus: Wissenschaftliches Schreiben: Ein Praxisbuch f\u00fcr Studierende der Geistes- und Sozialwissenschaften. Wien: B\u00f6hlau 2009<\/li><br><\/ul><br><p>\u00a0<\/p><br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385e0d\"\n        >\n            <span class=\"accordion__title\">\n                Deutsch C1 wissenschaftlich (Belval)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-217                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385e0d\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Deutsch C1 wissenschaftlich (Belval)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-217<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Im Mittelpunkt des Kurses stehen das Lesen und Verfassen wissenschaftlicher Texte sowie das \u00dcben von Pr\u00e4sentation und Diskussion im wissenschaftlichen Bereich. Ein besonderes Augenmerk liegt auf dem Umgang mit Deutsch als Wissenschaftssprache, u. a. Struktur und Aufbau wissenschaftlicher Texte, Schwierigkeiten mit wissenschaftlicher Lexik und Syntax, andere studienrelevante Problembereiche der deutschen Grammatik etc.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Ziel des Kurses ist es, einen sicheren Umgang mit den Merkmalen, Strukturen und Ausdrucksformen wissenschaftlicher Texte zu erlangen \u2013 sowohl im Hinblick auf das Textverst\u00e4ndnis als auch auf die eigenst\u00e4ndige Erstellung wissenschaftlicher Arbeiten.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Beschreibung<br>Der Kurs richtet sich an Studierende aller Fachrichtungen mit dem Sprachniveau C1, die ihre m\u00fcndlichen und schriftlichen Ausdrucksf\u00e4higkeiten im wissenschaftlichen Kontext vertiefen m\u00f6chten.<br>Inhalte<br>Im Mittelpunkt des Kurses stehen das Lesen, \u00dcberarbeiten und Verfassen wissenschaftlicher Texte sowie das \u00dcben von Pr\u00e4sentationen und Diskussionen im akademischen Kontext. Ein besonderer Schwerpunkt liegt dabei auf dem Gebrauch des Deutschen als Wissenschaftssprache \u2013 insbesondere in Bezug auf den Aufbau und die Struktur wissenschaftlicher Texte, den gezielten Einsatz fachsprachlicher Lexik und komplexer Satzstrukturen sowie grammatikalische Herausforderungen, die im Studium von zentraler Bedeutung sind.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00a0<br>F\u00fcr einen erfolgreichen Abschluss des Kurses sind eine kontinuierliche und aktive Teilnahme am Unterricht erforderlich und maximal drei Fehltage zul\u00e4ssig. Die Gesamtnote setzt sich zu gleichen Teilen aus vier unterschiedlichen Aufgaben zusammen \u2013 dazu z\u00e4hlen unter anderem das Verfassen und \u00dcberarbeiten von Texten, m\u00fcndliche Pr\u00e4sentationen sowie gezielte Wortschatzarbeit.<br>\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00a0<br>Bibliographie<br>Bayerlein, Oliver (2013): Campus Deutsch \u2013 Lesen. M\u00fcnchen: Hueber Verlag<br>Bayerlein, Oliver (2014): Campus Deutsch \u2013 Pr\u00e4sentieren und Diskutieren. M\u00fcnchen: Hueber Verlag<br>Bayerlein, Oliver (2015): Campus Deutsch \u2013 H\u00f6ren und Mitschreiben. M\u00fcnchen: Hueber Verlag<br>Bayerlein, Oliver (2015): Campus Deutsch \u2013 Schreiben. M\u00fcnchen: Hueber Verlag<br>Esselborn-Krumbiegel, Helga (2010): Richtig wissenschaftlich schreiben. Paderborn: Verlag Ferdinand Sch\u00f6ningh<br>Gruber, Helmut, Huemer Brigit Rheindorf, Markus (2009): Wissenschaftliches Schreiben: Ein Praxisbuch f\u00fcr Studierende der Geistes- und Sozialwissenschaften. Wien: B\u00f6hlau<br>Lange, Ulrike (2013): Fachtexte lesen \u2013 verstehen \u2013 wiedergeben. Paderborn: Verlag Ferdinand Sch\u00f6ningh<br>\u00a0<br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385e1a\"\n        >\n            <span class=\"accordion__title\">\n                English B2.1 academic (Thursdays) &#8211; online course                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-241                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385e1a\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> English B2.1 academic (Thursdays) &#8211; online course<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-241<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            This\u00a0course\u00a0aims\u00a0to\u00a0develop\u00a0your\u00a0academic\u00a0writing,\u00a0speaking,\u00a0reading,\u00a0and\u00a0listening\u00a0skills\u00a0to\u00a0a\u00a0B2 CEFR (Common European Framework) level (upper intermediate).                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <br>By the end of the 20-week course, you should be able to do the following at B2 level:<br>Write well-structured, coherent and cohesive texts;<br>Speak to present your opinions in well-structured oral presentations, and participate in academic discussions and debates;<br>Understand and critically evaluate academic texts and sources;<br>Understand lectures, presentations and academic discussions;<br>Use a wide range of academic vocabulary, grammatical structures and anappropriate academic register.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        You will develop your academic vocabulary and grammar while improving your reading, writing, listening, and speaking skills within academic contexts.<br>This course is designed to reach the target level in 20 sessions spread over two semesters. You can take one semester only and get ECTS for that semester, but you will not have reached a B2 level.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Note that you must attend at least 8 out of 10 sessions per semester and pass the course to be awarded credits.<br>Per semester, your grade is composed of the following:<br><ul><li>Written and oral assignments (40%).<\/li><li>Final test (60%)that will cover reading, writing, listening, grammar and vocabulary. This test will take place in person, without the use of aids.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Required Textbook<br><\/p>Hewings, M. (2012). Cambridge Academic English, an integrated skills course for EAP. Upper Intermediate Student\u2019s Book + audio CD and DVD. Cambridge 8xav福利导航 Press. ISBN 978-0521165204<br>Note: Do not buy the textbook immediately!                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62385e27\"\n        >\n            <span class=\"accordion__title\">\n                Fran\u00e7ais acad\u00e9mique C1  (Belval)                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            LC_CAT-171                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62385e27\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62385d34\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Fran\u00e7ais acad\u00e9mique C1  (Belval)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> LC_CAT-171<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 1.3 (choisir 5 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Cours en pr\u00e9sentiel &#8211; Belval<\/p><br><p>\u00a0<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br>Objectifs et r\u00e9sultats d\u2019apprentissage ( learning outcomes) :<br>L\u2019objectif de ce cours est d\u2019acqu\u00e9rir les connaissances suffisantes en fran\u00e7ais pour r\u00e9diger\u00a0 diff\u00e9rents \u00e9crits longs et complexes afin d\u2019acc\u00e9der aux niveaux C1 et C2 du CECRL. Cette mise \u00e0 niveau s\u2019organise par le biais de travaux de groupes et par une approche ludique et concr\u00e8te. Le contenu sera adapt\u00e9 en fonction des besoins du groupe.<br>A l\u2019issue de ce cours, vous serez capable de :<br><ul><li>lire des articles complexes sur n\u2019importe quel sujet<\/li><li>\u00e9crire des textes clairs et d\u00e9taill\u00e9s<\/li><li>r\u00e9diger un r\u00e9sum\u00e9 fid\u00e8le<\/li><li>exposer votre argumentation<\/li><li>r\u00e9diger un devoir de synth\u00e8se<\/li><\/ul><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Ce cours a pour but de renforcer vos connaissances et vos pratiques en langue fran\u00e7aise \u00e9crite\u00a0 afin de produire des textes \u00e9labor\u00e9s, limpides et fluides dans un style appropri\u00e9 et efficace, de votre domaine ou non, avec une structure logique qui aide le destinataire \u00e0 remarquer les points importants\u00a0 (comp\u00e9tences sp\u00e9cifiques du CECRL de niveau C1 ).<br>Apr\u00e8s avoir analys\u00e9 les diff\u00e9rents registres de langue du Fran\u00e7ais, nous nous attacherons \u00e0 l\u2019\u00e9tude de l\u2019organisation des \u00e9crits acad\u00e9miques pour\u00a0 exposer, r\u00e9sumer, argumenter et synth\u00e9tiser.<br>L\u2019\u00e9tude se fera sur base d\u2019\u00e9tude de textes choisis pr\u00e9texte \u00e0 la r\u00e9vision de points d\u00e9licats de grammaire, de syntaxe et de vocabulaire.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        L\u2019\u00e9valuation sera constitu\u00e9e :<br>-pour 40% d\u2019un devoir de r\u00e9sum\u00e9 en classe\u00a0<br>-pour 60 % d\u2019un devoir de synth\u00e8se ( \u00e0 r\u00e9aliser en bin\u00f4me en classe) ;\u00a0<br>Des points bonus seront attribu\u00e9s pour la r\u00e9alisation des devoirs maison .\u00a0<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Bibliographie<br>Communiquer \u00e0 l\u2019\u00e9crit, Guy Capelle, Cle international\u00a0<br>Production \u00e9crite Niveaux C1, C2 Edition Didier<br>Documents DALF C1, C2<br>Grammaire progressive du Fran\u00e7ais, niveau perfectionnement B2-C2\u00a0\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-b412a128-5f24-4db3-912a-3ae44f6ef234\"\n    aria-labelledby=\"tab-b412a128-5f24-4db3-912a-3ae44f6ef234\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 2 (2025-2026 Summer)<\/h3>\n    \n<div id=\"accordion-module-6a13f62390533\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62390568\"\n        >\n            <span class=\"accordion__title\">\n                Analyse 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            7                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-6                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62390568\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 2.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ol><br><li>Understanding the fundamental results of differential and integral calculus for real-valued functions of one or several real variables.<\/li><br><li>Developing proficiency in key mathematical tools used in physics and engineering. Gaining both an intuitive understanding and a rigorous grasp of core concepts in analysis.<\/li><br><li>Building a strong foundation in mathematical reasoning and proof techniques, while learning to approach analysis with precision and rigor.<\/li><br><\/ol>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Students who successfully complete the Analysis 2a and 2b courses will be able to:<\/p><br><ul><br><li>Master the fundamentals of differential and integral calculus for functions of one or several real variables<\/li><br><li>Solve both applied and basic theoretical exercises<\/li><br><li>Understand, explain, and apply various proof techniques<\/li><br><li>Correctly use fundamental tools of analysis<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><li>Chapter 1. Several variable differential calculus<\/li><li>Chapter 2. Integration in several variables<\/li><li>Chapter 3. Series<\/li><li>Chapter 4 The Lebesgue integral<\/li><li>Chapter 5. Metric spaces<\/li><li>Chapter 6. Uniform convergence<\/li><li>Chapter 7. Power series<\/li><li>Chapter 8. Ordinary differential equations<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>First Take:<br><\/p><br><p>Continuous assessments :\u00a010% Quizz<\/p><br><p>Final written exam: 90%<\/p><br><p><br>Retake:<br><\/p><br><p>Written exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Note \/ Literature \/ Bibliography\u00a0<br><br>We strongly recommend studying the course notes available at https:\/\/gruetznotes.xyz. For additional references or further reading, students can contact the instructors directly.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62390585\"\n        >\n            <span class=\"accordion__title\">\n                G\u00e9om\u00e9trie  euclidienne et non euclidienne                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-7                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62390585\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> G\u00e9om\u00e9trie  euclidienne et non euclidienne<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 2.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Understanding of the basic properties of four fundamental geometric structures:<br>the Euclidean geometry, the hyperbolic geometry, the elliptic geometry and the projective geometry.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>Euclid\u2019s axioms and the parallel postulate; <\/li><li>Euclidean geometry (complements of analytic Euclidean geometry); <\/li><li>Elliptic geometry (analytic approach)<\/li><li>Hyperbolic geometry (analytic approach)<\/li><li>Basics of the projective geometry: projective spaces, projective transformations, homogeneous coordinates, conics<\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Written examination                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note\/Book<br><br>Supplemental material will be provided<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f62390592\"\n        >\n            <span class=\"accordion__title\">\n                Alg\u00e8bre lin\u00e9aire 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            7                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-8                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f62390592\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Alg\u00e8bre lin\u00e9aire 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 2.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Apprendre et ma\u00eetriser les th\u00e9or\u00e8mes fondamentaux d&#8217;alg\u00e8bre lin\u00e9aire abstraite. <\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Les \u00e9tudiant(e)s ayant suivi avec succ\u00e8s le cours d&#8217;alg\u00e8bre lin\u00e9aire seront capables :\u00a0<br><\/p><br><ul><br><li>de ma\u00eetriser les th\u00e9or\u00e8mes principaux de l&#8217;alg\u00e8bre lin\u00e9aire abstraite,\u00a0<\/li><br><li>d&#8217;appliquer leurs connaissances pour r\u00e9soudre des exercices et de probl\u00e8mes d&#8217;application.\u00a0<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Contenu\u00a0<br>Polyn\u00f4me caract\u00e9ristique et minimal, th\u00e9or\u00e8me de Cayley-Hamilton, diagonalisation, d\u00e9composition spectrale, r\u00e9duction de Jordan, endomorphismes auto-adjoints et normaux, quadriques, dualit\u00e9.<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Examen \u00e9crit et contr\u00f4le continu<\/p><br><p>Retake: Examen \u00e9crit comptant 100% de la note<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Notes &#8211; Lit\u00e9rature<br><\/p>Notes du cours disponibles sur Moodle.<br>Il est conseill\u00e9 aux \u00e9tudiants de consulter des livres pour approfondir leurs connaissances.<br>Une liste de r\u00e9f\u00e9rences sera mise \u00e0 la disposition des \u00e9tudiants au d\u00e9but du cours.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239059f\"\n        >\n            <span class=\"accordion__title\">\n                Introduction to Geophysics: Learning to think like a scientist                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            2                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_PHYS_GEN-42                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239059f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Introduction to Geophysics: Learning to think like a scientist<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_PHYS_GEN-42<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The module will develop your understanding of Earth. We will use MATLAB to explore the different types of geophysical data to understand the physical properties of the Earth. Students will learn how<br>Search the Web for different types of geophysical data<br>Use MATLAB for data analysis<br>Create 2D plots of time series data<br>Understand the mean, scatter, and trend of geophysical time series<br>Fit seasonal signals and calculate residuals<br>Use geophysical data to measure plate tectonic velocities and estimate natural hazards<br>Plot and interpret the pattern of seismicity globally in terms of plate tectonics<br>Determine their location on Earth using GNSS<br>Understand mass changes on Earth from satellite gravity observations.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students that successfully complete this course will be able:<br>To understand why the Earth looks like it does<br>To understand why earthquakes and volcanoes occur where they do<br>To understand how to use GNSS to measure plate velocities<br>To understand how GNSS and satellite gravity can tell us about Earth                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Class Outline: Questions to Explore<br> How do geophysicists approach problem-solving and analysis?<br> What is the step-by-step process of the scientific method in geophysics?<br> What roles and tasks are undertaken by geophysicists in their field?<br> In what ways can MATLAB be effectively used to enhance our understanding of Earth&#8217;s dynamics?<br> What fundamental principles define plate tectonics and its role in shaping the Earth&#8217;s surface?<br> Why do seismic activities like earthquakes and volcanic eruptions occur in specific geographical locations?<br> What is the significance of satellite geodesy in geophysical research, and how does it contribute to our understanding of Earth?<br> How does GNSS play a key role in investigating seismic hazards, and what insights can be gained from such studies?<br> Distinguish between absolute gravity and relative gravity, and understand their respective applications in geophysics.<br> Explore the methodologies involved in measuring mass changes from space and the reasons behind these measurements.<br> What is optical imaging, and how does it serve as a tool for comprehending Earth&#8217;s processes and features?<br> What key components constitute the water cycle, and how does it influence various Earth processes and ecosystems?                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Task 1: Written exam during exam session (45%)<br>Task 2: Home-Assignment and Project (45%)<br>Assessment Rules: Submission of reports via Moodle within the stipulated timeframe.<br>Assessment Criteria: Graded out of 20 for each exercise, assessing depth of understanding, application of concepts, and overall quality of work.<br>Task3: Participation (10%)<br>Assessment Rules: Active and constructive engagement in class activities, discussions, and collaborative projects.<br>Assessment Criteria: Evaluation based on the frequency and quality of contributions, demonstrating a commitment to the learning process.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        To be defined in the lecture as required.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905ac\"\n        >\n            <span class=\"accordion__title\">\n                Didactique des math\u00e9matiques 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-10                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905ac\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Didactique des math\u00e9matiques 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-10<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ul><br><li>Pratiquer la construction des comp\u00e9tences math\u00e9matiques<\/li><br><li>Planifier et pr\u00e9senter des projets didactiques int\u00e9grant les notions d\u00e9velopp\u00e9es et favorisant un apprentissage efficient<\/li><br><li>Construire des activit\u00e9s interactives et collaboratives en ligne<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Conception, r\u00e9alisation et \u00e9valuation de diverses activit\u00e9s math\u00e9matiques en classe, respectivement d\u2019activit\u00e9s d\u2019apprentissage en ligne (tests formatifs autocorrig\u00e9s et activit\u00e9s \u00ab peer to peer \u00bb<br><\/p><ul><li>Le concept d\u2019autonomie<\/li><li>D\u00e9veloppement de th\u00e8mes pluridisciplinaires<\/li><li>Regards sur l\u2019histoire des d\u00e9finitions et concepts<\/li><li>Correction de devoirs au cycle inf\u00e9rieur<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Engagement r\u00e9gulier et \u00e9laboration d\u2019un portfolio personnel, pr\u00e9sentation du portfolio.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Literature<\/p><br><ul><br><li>Portfolio personnel<\/li><br><li>Bibliographie compl\u00e9t\u00e9e progressivement et recherche personnelle Lecture conseill\u00e9e : \u00ab Lettre \u00e0 un jeune professeur \u00bb, Philippe Meirieu, Co-Edition ESF-France Inter ISBN 2-7101-1740-1 (22 ao\u00fbt 2005)<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905b8\"\n        >\n            <span class=\"accordion__title\">\n                Logiciels math\u00e9matiques                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-13                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905b8\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Logiciels math\u00e9matiques <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-13<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The first part of the course will cover the basics of the LaTeX markup language.<br>We will see how to use it to write a mathematical text, such as lecture notes or a Thesis, and to prepare slides for a presentation.<br>In the second part we will focus on SageMath and other mathematical software to carry out computations. We will also briefly talk about computational complexity and how to write more efficient code.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student who completes the course will be able to use the LaTeX markup language to write documents and prepare slide-based presentations and to use SageMath and other mathematical software to carry out computations.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>LaTeX [1] is a markup language to write and format documents of any type. It is particularly well-suited for scientific documents, but it can be used for any type of document, including books, CVs and even presentation slides.<br>It can be used together with a graphical front-end (such as TexMaker, TexStudio, Overleaf&#8230;) to immediately see the pdf output. The main advantage over a more classical word processor such as Microsoft Word, besides a much better support for writing mathematical formulas and theorems, is that in LaTeX &#8220;What you see is what you mean&#8221; [2]: by typing commands instead of visually changing the appearence of the text, the &#8220;compiler&#8221; will always try to produce an output that is faithful to what the user indicated, so the user does not have to manually adjust the result after every major modification.<br>SageMath [3] is a free and open-source Mathematical software system which builds on top of many existing: NumPy, SciPy, matplotlib, Sympy, Pari\/GP, GAP, R and many more. Thanks to it, all the features all these languages can be accessed from a common python-based interface.<br>In practice, the SageMath &#8220;language&#8221; is almost identical to python, but it provides a complete set of libraries to deal with many mathematical objects and computations.<\/p><ol><li>https:\/\/en.wikipedia.org\/wiki\/LaTeX<\/li><li>https:\/\/en.wikipedia.org\/wiki\/WYSIWYM<\/li><li>https:\/\/www.sagemath.org\/<\/li><\/ol><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The evaluation of the course will be based Quiz and Final project.\u00a0<br><\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><\/p><br><p><br>https:\/\/doc.sagemath.org\/html\/en\/tutorial\/index.html<br><\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905c5\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matique Physique                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-9                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905c5\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matique Physique<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Le cours vise \u00e0<br><\/p><br><ul><br><li>illustrer sur l\u2019exemple de la m\u00e9canique que la physique th\u00e9orique d\u00e9crit les lois et les principes de la physique en se basant sur des mod\u00e8les math\u00e9matiques et r\u00e9ussit \u00e0 faire des pr\u00e9dictions sur des syst\u00e8mes complexes ;<\/li><br><li>initier l\u2019\u00e9tudiant(e) \u00e0 r\u00e9soudre des probl\u00e8mes en m\u00e9canique en se basant sur le formalisme de la physique th\u00e9orique.<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        L\u2019\u00e9tudiant(e) ayant valid\u00e9 l\u2019unit\u00e9 d\u2019enseignement est capable de comprendre la m\u00e9canique newtonienne appliqu\u00e9e \u00e0 la masse ponctuelle et au syst\u00e8me de points.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Partie 1 : Introduction math\u00e9matique \u00e0 la m\u00e9canique.<br>Partie 2 : \u00c9l\u00e9ments de cin\u00e9matique et de statique.<br>Partie 3 : Dynamique du point (r\u00e9f\u00e9rentiels inertiaux et non-inertiaux). Int\u00e9grales premi\u00e8res. Diagramme du potentiel. R\u00e9f\u00e9rentiel g\u00e9ocentrique, r\u00e9f\u00e9rentiel terrestre.<br>Partie 4 : Dynamique des syst\u00e8mes de points.<br>Partie 5 : Probl\u00e8mes classiques tels que particules charg\u00e9es dans un champ \u00e9lectromagn\u00e9tique, mouvements plan\u00e9taires, mar\u00e9es, satellites, pendule de Foucault, \u2026.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Examen \u00e9crit et contr\u00f4le continu                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Lit\u00e9rature<br><\/p><br><ul><br><li>F. Viot, M\u00e9canique du point. Dunod, 2005.<\/li><br><li>W. Nolting, Grundkurs Theoretische Physik 1 : Klassische Mechanik. Springer, 2006.<\/li><br><li>T.W.B. Kibble F.H. Berkshire, Classical Mechanics. Imperial College Press, 2009.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905d2\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matiques exp\u00e9rimentales 1                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-14                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905d2\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matiques exp\u00e9rimentales 1 <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-14<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Learn and use in a practical context mathematical notions beyond the content of other courses. Develop programming skills. Discover a research-oriented aspect of mathematics and participate in research projects.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students who have successfully followed this unit will have learned and been able to use in a practical context mathematical notions beyond the content of other courses. They will have developed their programming skills, and discovered a research-oriented aspect of mathematics and, in some cases, participated in research projects.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Les \u00e9tudiants suivant ce module prendront part, en groupes de 2 ou 3 ou exceptionnellement seul, \u00e0 un projet de math\u00e9matiques exp\u00e9rimentales qui comportera une partie importante de programmation, exp\u00e9rimentation ou visualisation sur ordinateur et qui fera appel \u00e0 des notions math\u00e9matiques enseign\u00e9es jusqu&#8217;au semestre 2. L&#8217;encadrement est assur\u00e9 par un enseignant du D\u00e9partement de Math\u00e9matiques. Il n&#8217;y aura pas de contrainte horaire particuli\u00e8re pour participer \u00e0 ce module : un calendrier de suivi sera \u00e9tabli en d\u00e9but de semestre entre l&#8217;enseignant et le (les) \u00e9tudiant(s) concern\u00e9s.<br>La liste des projets disponibles peut \u00eatre consult\u00e9e sur https:\/\/math.uni.lu\/eml. <br>Le nombre de places pour participer \u00e0 ce module \u00e9tant limit\u00e9, les \u00e9tudiants int\u00e9ress\u00e9s sont pri\u00e9s de participer \u00e0 la r\u00e9union de pr\u00e9sentation qui leur sera propos\u00e9e et de suivre la proc\u00e9dure de choix de projets expliqu\u00e9e dans la r\u00e9union. <\/p><p>S&#8217;il y a plus de personnes int\u00e9ress\u00e9es que de places disponibles, le seul crit\u00e8re retenu sera l&#8217;excellence du dossier.<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>L&#8217;\u00e9valuation consistera en la r\u00e9daction d&#8217;un m\u00e9moire de projet (contenant entre autres le code et son explication, un r\u00e9sum\u00e9 des math\u00e9matiques utilis\u00e9es, une discussion des r\u00e9sultats exp\u00e9rimentaux obtenus quand c&#8217;est le cas, &#8230;) et sa d\u00e9fense pendant une soutenance orale.<\/p><br><p>Retake: un nouveau projet doit etre fait<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Literature \/ Notes<br><\/p><br><p>sera mis \u00e0 disposition au d\u00e9but du projet<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905de\"\n        >\n            <span class=\"accordion__title\">\n                Programming Fundamentals 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            F1_BAINFOR-15                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905de\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Programming Fundamentals 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_BAINFOR-15<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            This course is about object-oriented programming, a paradigm that enables programmers to deal with program complexity by decomposing programs into small, self-contained units that can easily be reused and adapted across projects. The course will have a practical flavour, with demonstrations, examples, and assignments.<br>\u00a0<br>We will rely on the Java programming language to concretize object-oriented concepts through the development of programs.\u00a0 Java is among the five most popular and most demanded programming languages on the job market; it is used in Web-based, Android, and embedded systems. Java is popular because it is easy to learn, has a rich set of programming APIs, and is supported by many development tools.<br>\u00a0<br>In this course, through Java, the students will learn to develop software applications of medium complexity relying on class inheritance and decomposition, known Java data structures, exception handling, file processing, GUIs, and concurrency support.<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The course will lead to the following learning outcomes:<br><ul><li>Design, code, test, and debug Java programs that follow an object-oriented design and uses each of the following fundamental programming constructs: classes, assignment and expressions, console I\/O, conditional and iterative structures, functions with parameter passing, structured data types provided with the language, use file I\/O to provide persistence across multiple executions, rely on exception-handling mechanism.<\/li><li>Write programs of medium complexity that use Java GUI APIs and rely on concurrency mechanisms.<\/li><li>Develop tests for program modules and apply a variety of strategies to design test cases.<\/li><li>Build, execute and debug programs using a modern IDE and associated tools such as visual debuggers.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The course has the following lesson topics:<br>1. Development environments: shell, editor, java compiler vs runtime, source code control, build automation tools, IDEs,<br>2. Java Basics: Types, Control Flow, and I\/O operations,<br>3. Inheritance and Polymorphism in Java,<br>4. Implementing data structures in Java,<br>5. Java collections,<br>6. Parametric polymorphism and generics,<br>7. Exception handling in Java,<br>8. File processing,<br>9. Concurrency in Java,<br>10. Java GUIs,\u00a0<br>11. Event-driven programming in Java,<br>12. Static methods, Nested classes, Networking,<br>13. Persistence,<br>14. Lambda and Streams.<br>They cover for the following teaching objectives:<br>A) Principles of object-oriented programming and design<br>A.1) Decomposition into objects carrying state and having behaviour through the definition of classes (fields, methods, and constructors), subclasses, inheritance, and method overriding.<br>A.2) Idioms for encapsulation (visibility, interfaces, and abstract classes).<br>A.3) Dynamic dispatching of method calls definition of method-call.<br>B) The Java language as an example of object-oriented language<br>B.1) Basic concepts such as variables, primitive data types, expression evaluation, assignment.\u00a0<br>B.2) Basic constructs such as conditional and iterative structures and flow of control.\u00a0<br>B.3) Key modularity constructs such as methods and classes, and related concepts like parameter passing, scope, abstraction, data encapsulation.<br>B.4) Input and output using files, console, and APIs\u00a0<br>B.5) Structured data types available in the Java APIs (e.g., the collection framework)\u00a0<br>B.6) GUI Libraries\u00a0<br>B.7) Recursion<br>B.8) Dealing with runtime errors in programs (exception handling)\u00a0<br>B.9) Strings and string processing<br>C) Data structures in Java<br>C.1) Implementing standard abstract data types such as lists and trees in Java<br>C.2) The Java Collections package for lists, trees, stacks, queues, sets, and maps<br>C.3) Performance implications of choice of data structure(s)<br>D) Principles of reactive programming<br>D.1) Components of reactive programming: event-source, event signals,\u00a0<br>listeners and dispatchers, event objects, adapters, event-handlers.<br>D.2) Use of reactive programming in Java, with a GUI case study: Defining event handlers\/listeners, Parameterization of event senders and event arguments, externally generated events, and program-generated events\u00a0<br>D.3) Conceptual separation between Model, View, and Controller.<br>E) Parallelism and concurrency in Java<br>E.1) Basic constructs and the concurrent Package.<br>F) Basic software testing principles<br>F.1) Deriving test cases from functional specifications and implementation<br>F.2) The Junit framework<br>F.3) Code coverage<br>G) Development environments<br>G.1) Shells, editors, java compiler vs runtime.<br>G.2) Source code control, build automation tools, IDEs.<br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Task 1: Written exam (30%)<br><br><br>Mid-term, First-time students<br><br>Grading scheme: 20 points (0-20)<br>Objectives: Written exam to assess students\u2019 knowledge of the basics of Java and OO programming. Consists of short programming exercises, open questions, and quizzes.<br>Assessment rules: All enrolled students. Laptop, smartphones, cheat sheets, and books are not allowed.<br>Assessment criteria: Correctness of answers, program design, functioning, and code style.<br>Task 2: Written exam (70%)<br>Final exam, First-time students<br>Grading scheme: 20 points (0-20)<br>Objectives: Programming exercises to assess that students have reached the objectives of the course.\u00a0<br>Assessment rules: All enrolled students. Laptop, smartphones, cheat sheets, and books are not allowed.<br>Assessment criteria: Correctness of program design, functioning, and code style.<br>Task 3: Written exam 100% or 70% + 30% (Task 1)<br>Repeat students<br>Grading scheme: 20 points (0-20)<br>Objectives: Programming exercises to assess that students have reached the objectives of the course. If the student participated to the previous mid-term exam, the highest grade between `100% Task 3\u2019 and `70%(Task 3)+30%(Task 1)\u2019 will be considered.\u00a0 Otherwise, only the grade for Task 3 will be considered.<br>Assessment rules: All enrolled students. Laptop, smartphones, cheat sheets, and books are not allowed.<br>Assessment criteria: Correctness of program design, functioning, and code style.\u00a0<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Course materials<br>Syllabus\u00a0<br>\u200b\u200b\u2612\u200bYes\u200b\u2610\u200bNo\u00a0<br>Remarks:\u00a0<br>Available on Moodle.\u00a0<br>Literature list\u00a0<br>\u200b\u200b\u2612\u200bYes\u200b\u2610\u200bNo\u00a0<br>Remarks:\u00a0<br>1) Building Java Programs, 4th Edition. Stuart Reges, Marty Stepp. Pearson.\u00a0<br>2) Learning Java. Marc Loy, Patrick Niemeyer, Daniel Leuck. 6th Edition. O\u2019Reilly Media.\u00a0<br>Moodle page\u00a0<br>\u200b\u200b\u2612\u200bYes\u200b\u2610\u200bNo\u00a0<br>Remarks:\u00a0<br>https:\/\/moodle.uni.lu\/course\/view.php?id=2452\u00a0<br>Other, please specify:\u00a0<br>\u00a0<br>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623905eb\"\n        >\n            <span class=\"accordion__title\">\n                Experimental Physics 2a and 2b: Electromagnetism (2a, CM) and TD (2b)                   <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_PHYS_GEN-27                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623905eb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f62390533\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Experimental Physics 2a and 2b: Electromagnetism (2a, CM) and TD (2b)   <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_PHYS_GEN-27<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module options 2.3 (choisir 10 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ul><br><li>Familiarizing the student with the principles and laws of electromagnetism<\/li><br><li>Sensitizing the student to the certainty that Maxwell\u2019s theory of electromagnetism results from nature observation and is based on reproducible experimental facts<\/li><br><li>Guiding the student to apply the principles and laws of electromagnetism to solve problems<\/li><br><\/ul><br>\u00a0                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        After completion of the course, the student is expected<br>&#8211; to set up Maxwell\u2019s equations using experimental laws deduced from nature observation;<br>&#8211; to exploit Maxwell\u2019s equations to prove that light propagates in form of electromagnetic waves;<br>&#8211; to understand and apply the laws of electromagnetism.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Loi de Coulomb, Champ et potentiel \u00e9lectriques, Loi de Gauss et applications, Condensateur, Energie du champ \u00e9lectrique, Di\u00e9lectriques dans le champ \u00e9lectrique, Polarisation di\u00e9lectrique, Champ de d\u00e9placement<br>Courant \u00e9lectrique:<br>Intensit\u00e9 du courant \u00e9lectrique, Densit\u00e9 de courant, Conductivit\u00e9 et r\u00e9sistivit\u00e9, Loi d&#8217;Ohm, R\u00e9sistance \u00e9lectrique, puissance \u00e9lectrique, Effet Joule, Equation de continuit\u00e9, Courant de polarisation dans un di\u00e9lectrique, Circuits \u00e9lectriques, Lois de Kirchhoff<br>Champ d&#8217;induction magn\u00e9tique:<br>Force de Lorentz et champ d&#8217;induction magn\u00e9tique, Force de Laplace, Effet Hall, Sources du champ d&#8217;induction magn\u00e9tique : lois d&#8217;Amp\u00e8re et de Biot-Savart, Propri\u00e9t\u00e9s magn\u00e9tiques de la mati\u00e8re, Magn\u00e9tisation, Champ magn\u00e9tique, Paramagn\u00e9tisme et diamagn\u00e9tisme, Ferro\u00e9lectricit\u00e9<br>Induction \u00e9lectromagn\u00e9tique:<br>Lois de Faraday et Lenz, Courants de Foucault, Induction mutuelle et auto-induction, Energie du champ d&#8217;induction magn\u00e9tique, Courant de d\u00e9placement, Equations de Maxwell<br>Courant alternatif:<br>Tension et intensit\u00e9 efficaces, Dip\u00f4les passifs, Puissance du courant alternatif, R\u00e9sonance et anti-r\u00e9sonance \u00e9lectriques, Oscillations \u00e9lectriques amorties, Transformateur<br>Ondes \u00e9lectromagn\u00e9tiques:<br>Equations t\u00e9l\u00e9graphiques, Ondes \u00e9lectromagn\u00e9tiques, Propagation de l&#8217;\u00e9nergie \u00e9lectromagn\u00e9tique et vecteur de Poynting, Dip\u00f4le de Hertz, Dip\u00f4les secondaires et diffusion, Dispersion et absorption                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Experimental Physics 1b: TD (exercise class)<br><br>Homework: assignments on a weekly basis<br>Midterm test\u00a0<br>The regular participation in the exercise class is mandatory: students with more than two unexcused absences are excluded from the exercise class.<br>Experimental Physics 1a: CM (lecture)<br>Written exam<br>To be admitted to the written exam, the student needs a grade in Experimental Physics 1b.<br>Final grade:<br>Written exam counts for 80%<br>Take-home assignments and midterm test count for 10% respectively.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Syllabus                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-f60582d4-38bb-4eb6-8c0a-e57d6999eb40\"\n    aria-labelledby=\"tab-f60582d4-38bb-4eb6-8c0a-e57d6999eb40\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 3 (2025-2026 Winter)<\/h3>\n    \n<div id=\"accordion-module-6a13f6239a8f2\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a930\"\n        >\n            <span class=\"accordion__title\">\n                Analyse 3                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            7                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-17                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a930\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-17<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Les \u00e9tudiants ayant suivi avec succ\u00e8s le cours d&#8217;analyse 3 seront capables de : <ul><li>Manipuler correctement les s\u00e9ries de fonctions et s\u00e9ries enti\u00e8res en particulier<\/li><li>Appliquer les r\u00e9sultats classiques de la th\u00e9orie des fonctions de plusieurs variables r\u00e9elles<\/li><li>R\u00e9soudre des probl\u00e8mes d&#8217;application simples <\/li><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Dans ce cours, on diversifie et approfondit diverses connaissances et techniques de l\u2019analyse math\u00e9matique. On s\u2019int\u00e9resse \u00e0 d\u00e9montrer plusieurs th\u00e9or\u00e8mes fondamentaux dans l\u2019\u00e9tude des fonctions de plusieurs variables, des \u00e9quations diff\u00e9rentielles et des suites de fonctions.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programme<br><\/p><ul><li>Fonctions implicites et applications<\/li><li>Th\u00e9orie locale des \u00e9quations diff\u00e9rentielles ordinaires<\/li><li>Convergence de suites de fonctions<\/li><li>S\u00e9rie de puissances<\/li><li>L\u2019exponentielle matricielle<\/li><li>Th\u00e9or\u00e8me d\u2019approximation de Stone-Weierstrass<br><\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Contr\u00f4le continu et examen \u00e9crit<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature\u00a0<\/p><br><ul><br><li>W. Rudin: Principes d&#8217;analyse math\u00e9matique.<\/li><br><li>Des notes de cours sont mises \u00e0 disposition des \u00e9tudiants.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a95b\"\n        >\n            <span class=\"accordion__title\">\n                Probabilit\u00e9s                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-18                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a95b\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Probabilit\u00e9s <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-18<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Le but de ce cours est de faire acqu\u00e9rir \u00e0 l&#8217;\u00e9tudiant une connaissance de base des principaux concepts en probabilit\u00e9 et statistique.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programme<br><\/p><p>1. Espace de probabilit\u00e9 et variable al\u00e9atoire<\/p><ul><li>Univers<\/li><li>Tribu et variable al\u00e9atoire<\/li><li>Probabilit\u00e9<\/li><li>Cas o\u00f9 l&#8217;univers est fini ou d\u00e9nombrable<\/li><li>Ind\u00e9pendance d&#8217;\u00e9v\u00e9nements<\/li><li>Loi d&#8217;une variable al\u00e9atoire<\/li><li>Fonction de r\u00e9partition<\/li><li>Lois discr\u00e8tes vs continues<\/li><li>Variables al\u00e9atoires ind\u00e9pendantes<\/li><\/ul><p>2. Lois classiques<\/p><ul><li>Loi uniforme discr\u00e8te<\/li><li>Loi de Bernoulli<\/li><li>Loi binomiale<\/li><li>Loi hyperg\u00e9om\u00e9trique<\/li><li>Loi g\u00e9om\u00e9trique<\/li><li>Loi de Poisson<\/li><li>Loi uniforme continue<\/li><li>Loi gaussienne<\/li><li>Loi exponentielle<\/li><li>Loi de Cauchy<\/li><\/ul><p>3. Esp\u00e9rance<\/p><ul><li>Introduction<\/li><li>Esp\u00e9rance d&#8217;une variable positive<\/li><li>Moments, variance, \u00e9cart-type<\/li><li>Esp\u00e9rance et variance des lois classique<\/li><li>In\u00e9galit\u00e9 de Markov, Bienaym\u00e9-Tchebicheff et Jensen<\/li><li>Fonction g\u00e9n\u00e9ratrice<\/li><li>Fonction caract\u00e9ristique<\/li><li>Covariance et coefficient de corr\u00e9lation lin\u00e9aire<br><\/li><\/ul><p>4. Th\u00e9or\u00e8me limite<\/p><ul><li>Loi faible des grands nombres<\/li><li>Th\u00e9or\u00e8me central limite<\/li><\/ul><p>5. Estimation de param\u00e8tres (si le temps le permet)<br><\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Exam modalities for the first session<br><br>un examen partiel (\u00e9crit) sera organis\u00e9 pendant le semestre et un examen final (\u00e9crit) sera organis\u00e9 pendant la p\u00e9riode des examens de janvier. La note finale sera calcul\u00e9e comme suit: max(final,0,4*partiel+0,6*final).<\/p><br><p><br>Exam modalities for the retake exam<br><br>un examen de rattrapage \u00e9crit sera organis\u00e9 pendant la p\u00e9riode des examens de juillet. La note finale sera la note obtenue \u00e0 cet examen de rattrapage.<\/p><br>Absence plan<br><br>en cas d&#8217;absence \u00e0 l&#8217;examen partiel \u00e9crit de la 1\u00e8re session, la note finale de la premi\u00e8re session est \u00e9gale \u00e0 la note de l&#8217;examen final.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature<br><\/p><br><p>N&#8217;importe quel ouvrage d&#8217;introduction \u00e0 la th\u00e9orie de probabilit\u00e9s et de la statistique.<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a976\"\n        >\n            <span class=\"accordion__title\">\n                Alg\u00e8bre                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            7                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-19                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a976\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Alg\u00e8bre<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-19<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Dans l&#8217;histoire on comprend par l&#8217;alg\u00e8bre l&#8217;\u00e9tude des \u00e9quations. Au cours des 2000 ans de cette \u00e9tude, les gens se sont aper\u00e7us que certaines structures revenaient tr\u00e8s souvent, et en plus dans des contextes tout \u00e0 fait diff\u00e9rents ! Depuis, les alg\u00e9bristes s&#8217;occupent aussi de l&#8217;\u00e9tude et du d\u00e9veloppement de ces structures, ainsi que, \u00e9videmment, de leurs applications dans d&#8217;autres domaines en sciences, ing\u00e9nierie et math\u00e9matiques.<br>L&#8217;objet principal du cours sera l&#8217;\u00e9tude des anneaux et des extensions alg\u00e9briques des corps commutatifs. En particulier, la th\u00e9orie de Galois sera d\u00e9velopp\u00e9e et appliqu\u00e9e. Elle permet entre autres de d\u00e9montrer que l&#8217;\u00e9quation g\u00e9n\u00e9rale de degr\u00e9 au moins 5 ne peut pas \u00eatre r\u00e9solue en radicaux et de r\u00e9soudre (parfois de mani\u00e8re n\u00e9gative) plusieurs probl\u00e8mes classiques (provenant des anciens Grecs) de construction \u00e0 la r\u00e8gle et au compas comme la trisection d&#8217;un angle et la quadrature du cercle.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Le cours couvrira les sujets suivants :<\/p><ul><li>th\u00e9or\u00e8mes d&#8217;isomorphismes pour groupes et anneaux (sous-groupes distingu\u00e9s, id\u00e9aux, quotients)<\/li><li>anneaux g\u00e9n\u00e9raux: id\u00e9aux premiers et maximaux, quotients, corps des fractions d&#8217;un anneau int\u00e8gre<\/li><li>anneaux euclidiens et anneaux factoriels<\/li><li>crit\u00e8res d&#8217;irr\u00e9ductibilit\u00e9 pour polyn\u00f4mes<\/li><li>extensions alg\u00e9briques de corps<\/li><li>corps : caract\u00e9ristique, cl\u00f4ture alg\u00e9brique, corps de rupture, corps de d\u00e9composition, corps finis<\/li><li>quelques constructions \u00e0 la r\u00e8gle et au compas<\/li><li>extensions de corps: normales, s\u00e9parables, galoisiennes<\/li><li>correspondance de Galois<\/li><li>groupes solubles, (non-)solubilit\u00e9 d&#8217;\u00e9quations polynomiales par radicaux, groupes de Galois de polyn\u00f4mes<\/li><li>constructions \u00e0 la r\u00e8gle et au compas<\/li><li>(Hilbert 90 et Th\u00e9orie de Kummer : caract\u00e9risation des extensions solubles)<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Examen \u00e9crit et contr\u00f4le continu                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a991\"\n        >\n            <span class=\"accordion__title\">\n                Topologie g\u00e9n\u00e9rale                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-20                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a991\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Topologie g\u00e9n\u00e9rale<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-20<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Au terme du cours l&#8217;\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de<br><\/p><br><ul><br><li>ma\u00eetriser les concepts de base de la topologie g\u00e9n\u00e9rale ainsi que les outils pour l&#8217;\u00e9tude, la description et la construction des espaces topologiques et des applications continues ;<\/li><br><li>appliquer les outils de la topologie g\u00e9n\u00e9rale pour r\u00e9soudre des probl\u00e8mes pos\u00e9s sur des espaces topologiques<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Apprendre les fondements de la topologie g\u00e9n\u00e9rale au travers des propri\u00e9t\u00e9s de base des espaces topologiques et des fonctions continues.<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programm<\/p>\tEspaces topologiques;<br>\u00a0 \u00a0 \u2002\u2002-\u00a0 Int\u00e9rieur, adh\u00e9rence, bord;<br>\tContinuit\u00e9, compacit\u00e9, connexit\u00e9;<br>\tEspaces m\u00e9triques, compl\u00e9tude;<br>\u00a0 \u00a0 \u2002\u2002-\u00a0 Applications \u00e0 l&#8217;analyse.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        La note finale sera la plus grande des deux notes suivantes :<br>\u00a0 \u00a0 &#8211; la note \u00e0 l&#8217;examen final;<br>\u00a0 \u00a0 &#8211; la moyenne pond\u00e9r\u00e9e entre : la note \u00e0 l&#8217;examen final (qui compte pour 50%), la note \u00e0 l&#8217;examen partiel (qui compte pour 40%) et la moyenne des 3 quiz (qui compte pour 10%).<br>                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a9ac\"\n        >\n            <span class=\"accordion__title\">\n                Didactique des math\u00e9matiques 3                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-21                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a9ac\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Didactique des math\u00e9matiques 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-21<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.3. (choisir au moins 6 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Cours visant une interaction \u00e9troite entre observation, analyse et th\u00e9orisation de pratiques de classe (math\u00e9matique, historique, didactique et \u00e9pist\u00e9mologique).<\/p><br><ul><br><li>Pratiquer l&#8217;\u00e9valuation des comp\u00e9tences math\u00e9matiques<\/li><br><li>S\u00e9lectionner des outils didactiques susceptibles d&#8217;aider l&#8217;enseignant dans sa pratique<\/li><br><\/ul><br><p>\u00a0<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Programme <br><\/p><ul><li>Conception et r\u00e9alisation de s\u00e9quences d\u2019enseignement en classe <\/li><li>Analyse critique de l&#8217;activit\u00e9 apr\u00e8s le passage en classe <\/li><li>Utilisation d\u2019une calculatrice graphique (TI-V200) et d\u2019un logiciel de g\u00e9om\u00e9trie (Cabri G\u00e9om\u00e8tre ; Geogebra) en classe <\/li><li>Correction d\u2019un devoir en classe et \u00e9laboration d\u2019un corrig\u00e9 mod\u00e8le<\/li><li>Analyse d\u2019erreurs d\u2019\u00e9l\u00e8ves <\/li><li>Examen critique de manuels <\/li><li>Examen critique de pratiques courantes <\/li><li>Obstacles et facilitateurs de la transposition didactique <\/li><li>R\u00e9daction d\u2019un devoir en classe \u00e0 l\u2019aide du traitement de texte Word <\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><br><li>Engagement r\u00e9gulier<\/li><br><li>Elaboration d\u2019un portfolio<\/li><br><li>Pr\u00e9sentation du portfolio <\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature\u00a0<br><\/p><br><ul><br><li>Portfolio personnel\u00a0<\/li><br><li>Bibliographie compl\u00e9t\u00e9e progressivement et recherche personnelle\u00a0<\/li><br><li>Lectures conseill\u00e9es : \u00ab Maths \u00bb, (2004) Andr\u00e9 Deledicq, La petite encyclop\u00e9die coll\u00e8ge et lyc\u00e9e, Editions de la Cit\u00e9\/SEJER\u00a0<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a9c6\"\n        >\n            <span class=\"accordion__title\">\n                Experimental Physics 3 : Modern physics                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_PHYS_GEN-12                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a9c6\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Experimental Physics 3 : Modern physics<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_PHYS_GEN-12<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.3. (choisir au moins 6 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The course on modern physics describes the new physics, that was developed in the first half of the 20th century. As an experimental course, we will emphasise the experimental evidence that triggered the development of modern physics. The course lays the foundations for the rigorous treatment of quantum mechanics in the 4th semester.<br>The course aims to clarify the fact, that physics is a science in evolution, where new observations may lead to completely new theories.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students will\u00a0<br>-understand the challenges for classical physics and how they led to the development of the theory of special relativity and of quantum mechanics<br>-understand the basic laws and principles of special relativity and of quantum mechanics, in particular, where they are counter-intuitive with respect to everyday experience<br>-deal confidently with the laws and principles of basic atomic physics<br>-can apply these laws to unknown problems                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        1. Einstein\u2019s trains and elevators \u2013 relativity\u00a0<br>2. Particles and waves \u2013 quantisation and uncertainty<br>3. An introduction to quantum mechanics \u2013 Schr\u00f6dinger\u2019s equation<br>4. Atomic physics \u2013 the periodic system of elements<br>5. A short introduction to molecular physics                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br>Task 1: written midterm exam<br>\u00a0<br>Task 2: oral final exam<br>\u00a0<br>Assessment rules:<br>task 1:\u00a0 first part: no resources, second part: any paper resource allowed, no devices that can connect to the internet<br>At least 6\/20 points from task1 are necessary to participate in task 2<br>task 2: QA, no detailed calculations or derivations<br>\u00a0<br>Assessment criteria:<br>task 1: 6\/20 points is prerequisite for final exam<br>weight for final grade: 1\/3<br>task 2: weight for final grade: 2\/3<br>\u00a0<br>Retake exam \u2013 rules:<br>new oral exam.<br>final grade: 1\/3 midterm of previous semester + 2\/3 new oral exam<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Copies of the slides available on Moodle.<\/p><br><p>Books:<br>Paul Tipler, Ralph Llewellyn \u201cModern Physics\u201d (in English and German)<br>Randy Harris \u201cModern Physics\u201d<br>Stephen Thornton, Andrew Rex &#8220;Modern Physics for Scientists and Engineers&#8221;<br>\u201cThe Feynman lectures on physics\u201d (in English, French and German)\u00a0<br>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 https:\/\/feynmanlectures.caltech.edu\u00a0<br>Harris Benson \u201cPhysique\u201d 3 (in English and French)<br>Wolfgang Demtr\u00f6der &#8220;Experimentalphysik&#8221; (in German)<br><\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a9e0\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matiques exp\u00e9rimentales 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-33                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a9e0\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matiques exp\u00e9rimentales 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-33<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.3. (choisir au moins 6 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN, DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Learn and use in a practical context mathematical notions beyond the content of other courses. Develop programming skills. Discover a research-oriented aspect of mathematics and participate in research projects. They will have developed their programming skills, and discovered a research-oriented aspect of mathematics and, in some cases, participated in research projects.<br>\u00a0                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students who have successfully followed this course will have learned and been able to use in a practical context mathematical notions beyond the content of other courses.\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        We are all accustomed to the idea of experiments in physics, chemistry or biology. But mathematics can be done at an equally experimental level, often using computational methods. This applies to statistics, algebra, analysis, geometry, and other flavours of mathematics, and includes\u00a0<br> visualising complex mathematical objects,<br> using computers to work with examples that go beyond what is possible using pen and paper,<br> finding patterns in complicated data.<br>Even in highly abstract areas of mathematics the value of experimentation has increased dramatically in recent years, with computers, programming languages and computer algebra systems getting stronger and easier to use.\u00a0<br>This course allows students to participate in a research like project in an area of experimental mathematics. The students work in small groups under the guidance of a researcher of the Department of Mathematics. They produce a project report (a pdf document) and other material (such as images, videos, code, data), depending on the project. Finally, they also present their work in a small presentation during the exam period.<br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The students are evaluated on the project report and the additional material they produced, on a midterm report, their performance during the semester, and the final presentation.<br>In justified cases, it is possible to propose different marks for different students working in the same group.<br>Retake exam\u00a0<br>If a project is failed, a new project should be done in the next or a later semester. The project group, the topic and the supervisor(s) can change.<br>Absence plan\u00a0<br>In the case of a justified absence from the final project presentation, a separate presentation will be proposed as close to the originally planned date as possible.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The literature will be provided by the supervisor for each group.<br>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f6239a9fb\"\n        >\n            <span class=\"accordion__title\">\n                Algorithms and Complexity                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            F1_BAINFOR-21                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f6239a9fb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f6239a8f2\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Algorithms and Complexity<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_BAINFOR-21<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 3.3. (choisir au moins 6 ECTS)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            This course presents the following topics:<br>a) basic concepts from theory of algorithms, algorithms design strategies, and computational models where to reason about correctness and complexity.<br>b) fundamental algorithms and data structures (e.g., lists, trees, and graphs) required to solve classical problems, such as searching and sorting.<br>c) introduction to computational complexity of algorithms, and to the technique of analysis of complexity of the algorithms (e.g., recurrence equations)<br>b) introduction to theory of problem complexity.<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Upon completion of this course the student should be able to:<br>&#8211; design and analyse an algorithm for a given problem<br>&#8211; evaluate the computational complexity of an algorithm<br>&#8211; reason about the correctness of an algorithm<br>&#8211; classify an algorithm according to the basic approach it uses<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        &#8211; Algorithms, and complexity, upper and lower bounds<br>&#8211; Elementary data structures:\u00a0 lists, stacks, queue, sets<br>&#8211; Advanced data structures: trees and graphs<br>&#8211; Basic Algorithms<br> Sorting<br> Searching<br> Hashing\u00a0<br> Problems and algorithms on trees<br> Problems and algorithms on graphs\u00a0<br>&#8211; Complexity theory: P, NP, NP completeness<br>&#8211; Algorithm on secondary memory<br>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Assessment modality:\u00a0 \u00a0Combined assessment<br>Assessment tasks<br>Task 1: Written final exam (70%)<br>Grading scheme: 20 points (0-20)<br>Objectives: Test the student\u2019s understanding of the course material.<br>Assessment rules: The student has to answer questions with pencil and paper. This is a closed-book exam. No cheat sheet allowed.<br>Assessment criteria: The student must answer the stipulated questions in a way that clearly demonstrates understanding of underlying concepts.<br>Task 2: Active participation &#8211; 6 Quizzes in Class (20%)<br>Grading scheme: 20 points (0-20)<br>Objectives: To track and test the student\u2019s understanding for each topic.<br>Assessment rules: The student must answer questions with pen\/pencil. Each quiz will be 10 minutes. No cheat sheet allowed.<br>Assessment criteria: The student must answer the stipulated questions in a way that clearly demonstrates understanding of underlying concepts.<br>Task 3: Take-home assignment &#8211; 2 Assignments (10%)<br>Grading scheme: 20 points (0-20)<br>Objectives: Check the abilities of the students in analytic thinking and in group collaboration<br>Assessment rules: The assignments are group based. For each assignment there will be a weekly track where each member must write his\/her related task in this worksheet.\u00a0<br>Assessment criteria: Students must be separated into several groups. Evaluation will be individual.<br>Task 4: Written exam &#8211; RETAKE (100%)<br>Grading scheme: 20 points (0-20)<br>Objectives: Test the student\u2019s understanding of the course material<br>Assessment rules: The student has to answer questions with pencil and paper. This is a closed-book exam. No cheat sheet allowed.<br>Assessment criteria: The student must answer the stipulated questions in a way that clearly demonstrates understanding of underlying concepts.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Course materials<br><\/p><br><p>Syllabus\u2612Yes\u2610No<br>Remarks:Available on Moodle.<br>Literature list\u2610Yes\u2612No<br>Remarks:<br>Moodle page\u2612Yes\u2610No<br>Remarks:https:\/\/moodle.uni.lu\/course\/view.php?id=3331\u00a0<br><\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-e6a81c39-8505-43ae-9b09-af8aeac54ae0\"\n    aria-labelledby=\"tab-e6a81c39-8505-43ae-9b09-af8aeac54ae0\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 4 (2025-2026 Summer)<\/h3>\n    \n<div id=\"accordion-module-6a13f623a3d93\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3dcd\"\n        >\n            <span class=\"accordion__title\">\n                Introduction \u00e0 la th\u00e9orie des graphes                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-40                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3dcd\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Introduction \u00e0 la th\u00e9orie des graphes<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-40<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Au travers de la pr\u00e9sentation de diff\u00e9rents sujets, le cours est une introduction autonome \u00e0 la th\u00e9orie des graphes et \u00e0 ses applications.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Les \u00e9tudiant\u00b7e\u00b7s qui r\u00e9ussissent l&#8217;\u00e9valuation seront capables de\u00a0<\/p><br><ul><br><li>Expliquer les probl\u00e8mes de base de la th\u00e9orie des graphes et les diff\u00e9rentes approches pour les r\u00e9soudre,<\/li><br><li>Prouver des r\u00e9sultats classiques en th\u00e9orie des graphes (par exemple, la caract\u00e9risation des graphes eul\u00e9riens, la formule d&#8217;Euleur pour les graphes planaires, le th\u00e9or\u00e8me de Chvatal pour les graphes Hamiltonien, le th\u00e9or\u00e8me des cinq couleurs&#8230;)\u00a0<\/li><br><li>Appliquer des outils classiques de la th\u00e9orie des graphes pour r\u00e9soudre certains probl\u00e8mes : construire des sous-graphes couvrant de poids minimum, rechercher des chemins les plus courts (probl\u00e8me du GPS)&#8230;\u00a0<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><li>Graphes, graphes dirig\u00e9s, multi-graphes, repr\u00e9sentations matricielles et applications<\/li><li>Connectivit\u00e9, recherche de plus courts chemins, coupes, graphes hamiltioniens<\/li><li>Arbres, sous-arbres couvrants, nombre de sous-arbres couvrants<\/li><li>Graphes planaires, formule d&#8217;Euler<\/li><li>Probl\u00e8mes de coloriage de graphes.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Examen de fin de semestre \u00e9crit et\/ou oral.\u00a0                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3df8\"\n        >\n            <span class=\"accordion__title\">\n                Analyse fonctionnelle                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-35                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3df8\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse fonctionnelle<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-35<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ol><br><li>Become familiar with the basic results in functional analysis\u00a0<\/li><br><li>Learn how to use the main abstract tricks and strategies in order to prove such statements\u00a0<\/li><br><li>Appreciate the power of abstraction in pure and applied mathematics\u00a0<\/li><br><li>Understand the connection between seemingly unrelated mathematical disciplines\u00a0<\/li><br><\/ol><br><br>\u00a0<br><p>\u00a0<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Etre capable d&#8217;utiliser les espaces de fonctions pour r\u00e9soudre des probl\u00e8mes d&#8217;analyse                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The course will cover the following topics:<\/p><ol><li>Banach spaces and bounded linear functionals.<\/li><li>Hanh-Banach theorem and Baire Category theorem.<\/li><li>Uniform boundedness principle. Open mapping theorem. Closed graph theorem.<\/li><li>Unbounded linear operators.<\/li><li>Issues of classical compactness. Weak topology. Weak* topology.<\/li><li>Reflexive and separable spaces.<\/li><li>Lp spaces (reflexivity, separability, duality, strong compactness).<\/li><li>Hilbert spaces and their duals. Theorems of Stampacchia and Lax-Milgram. Hilbert sums. Orthonormal bases.<\/li><li>Compact operators. Riesz-Fredholm theory. Spectrum.<br><\/li><\/ol><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Final exam with written and oral components<br><\/p>Retake:<br>the retake is a written exam (2 hours).                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br><p><br>Notes &#8211; Literatur<br><\/p><br><p>\u00a0<\/p><br><p>Exercises and examples will be uploaded on Moodle.<br><\/p><br><ul><br><li>Main: Functional analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis.<\/li><br><li>Supplementary: Elementary functional analysis, B. MacCluer.<br><\/li><br><\/ul><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e11\"\n        >\n            <span class=\"accordion__title\">\n                Analyse num\u00e9rique                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-38                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e11\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse num\u00e9rique<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-38<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Au terme du cours, l\u2019\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de :<\/p><br><ul><br><li>comprendre le r\u00f4le central de l\u2019analyse num\u00e9rique dans les sciences math\u00e9matiques pures et appliqu\u00e9es<\/li><br><li>ma\u00eetriser les notions et les algorithmes fondamentaux de l\u2019analyse num\u00e9rique (approximation de fonctions, r\u00e9solution d\u2019\u00e9quations, calcul approch\u00e9s d\u2019int\u00e9grales\u2026)<\/li><br><li>acqu\u00e9rir un raisonnement rigoureux et syst\u00e9matique, indispensable \u00e0 l\u2019analyse et \u00e0 l\u2019interpr\u00e9tation des objets \u00e9tudi\u00e9s en analyse num\u00e9rique<\/li><br><li>formuler et r\u00e9soudre math\u00e9matiquement certains probl\u00e8mes num\u00e9riques mod\u00e9lisables au moyen de l\u2019analyse math\u00e9matique et de l\u2019alg\u00e8bre lin\u00e9aire.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Normes d\u2019op\u00e9rateursApproximation polynomialeR\u00e9solution d\u2019\u00e9quations non lin\u00e9airesR\u00e9solution num\u00e9rique de syst\u00e8mes lin\u00e9airesInt\u00e9gration num\u00e9rique\u00a0                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>examen \u00e9crit en fin de semestre<\/p><br><p>Retake: Examen \u00e9crit<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Support \/ Arbeitsunterlagen \/ Support\u00a0:<br><p>Notes de cours et slides (disponibles sur Moodle)<\/p><br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e28\"\n        >\n            <span class=\"accordion__title\">\n                Compl\u00e9ments de probabilit\u00e9s et statistiques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-26                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e28\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Compl\u00e9ments de probabilit\u00e9s et statistiques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-26<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Preparation for advanced courses in probability and statistics.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Compare different notions of convergence (convergence in distribution, almost sure convergence, etc.)<br>Translate different notions of convergence into each other and use their stability under continuous function application<br>Use the interplay of these convergence concepts to prove the strong law of large numbers<br>Use Moment Generating functions to proof the Central Limit Theorem<br>Get introduced to Large Deviation Theory (Cramer\u2019s theorem)<br>Use concentration inequalities (Hoeffding\u2019s inequality)<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Probabilistic convergence concepts and their relation, Borel Cantelli, Strong Law of Large Numbers, Moment generating functions, Central Limit Theorem, Cr\u00e1mer\u2019s theorem and Hoeffding\u2019s inequality.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>To be announced depending on the size of the course<br><\/p><br><p><br>Retake: oral exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Literature<br><br>Anton Thalmaier (2021). Compl\u00e9ments de probabilit\u00e9s et statistique (Lecture notes).<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e41\"\n        >\n            <span class=\"accordion__title\">\n                Courbes alg\u00e9briques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-36                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e41\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Courbes alg\u00e9briques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-36<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Introduction to the theory of algebraic curves over arbitrary fields, in particular also over finite fields. Of particular interest will be the theory of elliptic curves due to its relations to cryptography.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>On successful completion of this course the student should be able to :<br><\/p><br><ul><br><li>demonstrate the knowledge of the notion of an algebraic curve<\/li><br><li>demonstrate the special properties for curves over finite fields<\/li><br><li>master the basic technique of the theory<\/li><br><li>identify the most important examples<\/li><br><li>independently apply the required techniques to explicitly given situations. <\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>Introduction<\/li><li>Affine varieties and curves<\/li><li>projective curves<\/li><li>quadrics<\/li><li>Elliptic Curves<\/li><li>Complex tori and elliptic curves<\/li><li>The group law on elliptic curves<\/li><li>Affine coordinate ring<\/li><li>Projective coordinate ring<\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Written examination.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Lecture notes for the course, tutorial questions and solutions are all available to the students via the moodle. <\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e5b\"\n        >\n            <span class=\"accordion__title\">\n                G\u00e9om\u00e9trie des courbes et des surfaces                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-25                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e5b\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> G\u00e9om\u00e9trie des courbes et des surfaces <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-25<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Ce cours a pour but d\u2019\u00e9tudier les courbes (dans le plan et dans l\u2019espace) et les surfaces plong\u00e9es dans l\u2019espace euclidien.\u00a0                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>G\u00e9n\u00e9ralit\u00e9s sur les courbes param\u00e9tr\u00e9es : longueurs, angles, courbes r\u00e9guli\u00e8res, champs de vecteurs\u00a0<\/li><li>Courbes en dimension 3 : rep\u00e8re de Frenet, courbure, torsion\u00a0<\/li><li>Courbes en dimension 2, courbure orient\u00e9e, courbes de B\u00e9zier, in\u00e9galit\u00e9 isop\u00e9rim\u00e9trique\u00a0<\/li><li>Surfaces : espace tangent, premi\u00e8re forme fondamentale, longueurs de courbes, deuxi\u00e8me forme fondamentale et notions de courbures<\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>1st take:<\/p><br><p>The grade is calculated from 6-7 quizzes throughout the semester, together with a midterm and a final exam.\u00a0<\/p><br><p>Retake:<\/p><br><p>Oral exam to replace the quizzes + midterm and then a written exam to replace the final exam.<br><\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature \/ Literatur \/ Literature\u00a0<br><\/p><br><p>Reprise dans le syllabus \u2013 quatre titres<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e74\"\n        >\n            <span class=\"accordion__title\">\n                Number theory and cryptography                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-34                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e74\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Number theory and cryptography<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-34<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-a (choisir au moins 13 ECTS dans le 4.2, dont au moins 8 dans le 4.2-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Recently (and not so recently) number theory has found unexpected applications in cryptography, and nowadays everyone uses it on a daily basis (without realising it) when paying electronically or using the internet.<br>The course will introduce the students to some basic aspects of number theory, most importantly the theory of elliptic curves over finite fields. We will use the group law for elliptic curves (and other number-theoretic methods) to discuss modern ciphers, such as RSA, Diffie-Hellman, El Gamal, &#8230;<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student will<br>understand basic number-theoretic objects<br>be able to illustrate their properties with examples<br>understand the group law on an elliptic curve<br>be able to apply the different ciphers discussed in the course in simplified settings                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>The course will cover the following subjects<br> elementary aspects of number theory<br> finite fields<br> elliptic curves over finite fields<br> RSA encryption<br> El Gamal<br> Diffie&#8211;Hellman                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Written final exam. Weekly exercises will also be evaluated.<\/p><br><p>Retake: Written exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Course notes and exercise sheets on Moodle.<\/p>* Neal Koblitz, A Course in Number Theory and Cryptography, Springer.<br>* S.C. Coutinho, The Mathematics of Ciphers: Number Theory and RSA Cryptography, A. K. Peters.<br>* Douglas R. Stinson, Cryptography: theory and practice, Chapman and Hall.<br>* Paul Garrett, Making, Breaking Codes: Introduction to Cryptology.<br>* Michael Rosing, Implementing elliptic curve cryptography, Greenwich: Manning.<br>* A. J. Menezes, Elliptic curve public key cryptosystems, Boston: Kluwer Academic Publishers\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3e8d\"\n        >\n            <span class=\"accordion__title\">\n                Analyse complexe                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-23                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3e8d\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse complexe <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-23<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Knowledge of basic notions and techniques in complex analysis<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Au terme du cours, l\u2019\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de :<br><\/p><br><ul><br><li>comprendre le r\u00f4le central de l\u2019analyse complexe dans les sciences math\u00e9matiques pures et appliqu\u00e9es<\/li><br><li>ma\u00eetriser les notions fondamentales de l\u2019analyse complexes (derivation et integration, calcul des r\u00e9sidus\u2026)<\/li><br><li>acqu\u00e9rir un raisonnement rigoureux et syst\u00e9matique, indispensable \u00e0 l\u2019analyse et \u00e0 l\u2019interpr\u00e9tation des objets \u00e9tudi\u00e9s en analyse complexe.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>Nombres complexes et fonctions complexes<\/li><li>D\u00e9rivation et integration des fonctions complexes<\/li><li>S\u00e9ries de Taylor et s\u00e9ries de Laurent<\/li><li>Calcul des r\u00e9sidus et applications<\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>examen \u00e9crit en fin de semestre<\/p><br><p>Retake: Examen \u00e9crit<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Notes<br><\/p><br><p>Notes de cours et\/ou slides (disponibles sur Moodle)<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3eb1\"\n        >\n            <span class=\"accordion__title\">\n                Statistiques                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-24                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3eb1\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Statistiques <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-24<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ol><br><li>Variables al\u00e9atoires continues <br>Calcul de densit\u00e9s, loi uniforme, loi normale, loi exponentielle, applications.<\/li><br><li>Loi des grands nombres, loi du tout ou rien, lemme de Borel-Cantelli, loi forte des grands nombres, th\u00e9or\u00e8me de la limite centrale.<\/li><br><li>Introduction \u00e0 la statistique <br>Echantillonnage, intervalles de confiance, estimation de param\u00e8tres, intervalles de confiance, tests d&#8217;hypoth\u00e8ses.<br><\/li><br><\/ol>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><br><li>Understand and apply standard limit theorems.<\/li><br><li>Use basic tools of statistics: Estimation of parameters and testing of hypotheses.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Initiation au calcul des probabilit\u00e9s et \u00e0 la statistique.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>First session<br>Written exam.<\/p><br><p><br>Retake session<br>Written exam on both theory and exercises. The student can choose whether they wish to keep their midterm exam mark or not.<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note \/ Literatur<br><br><\/p><br><p>K.L. Chung: A course in probability theory. Harcourt, Brace World, Inc., 1968. <br>D. Foata et A. Fuchs: Calculs des probabilit\u00e9s. Cours, exercices et probl\u00e8mes corrig\u00e9s, Dunod, 1998. <br>C.M. Grinstead and J.L. Snell: Introduction to probability. American Mathematical Society, 1997. <br>U. Krengel: Einf\u00fchrung in die Wahrscheinlichkeitstheorie und Statistik. Vieweg, 1988. <br>J.Y. Ouvrard : Probabilit\u00e9s 1, Cassini, 1999.<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3eca\"\n        >\n            <span class=\"accordion__title\">\n                Alg\u00e8bre 2                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-53                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3eca\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Alg\u00e8bre 2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-53<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Acquire a solid background in commutative algebra and representation theory.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student can take further algebraic and geometric courses, which build on the material of this course.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>We will develop some aspects commutative algebra and representation theory. This will include<\/p><ul><li>A further development of rings and ideals<\/li><li>Modules over rings<\/li><li>Localization<\/li><li>Properties of important classes of rings, such as discrete valuation rings and Dedekind domains in commutative algebra, and<\/li><li>Quivers and their representations<\/li><li>Representations of groups in representation theory.<br><\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>1st take: Written final exam<\/p><br><p>Retake: Written exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Literature<br><br><br><\/p><br><ul><br><li>Atiyah\u2014Macdonald, Introduction to commutative algebra<\/li><br><li>Burrow, Representation theory of finite groups<\/li><br><li>Schiffler, Quiver representations<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3ee2\"\n        >\n            <span class=\"accordion__title\">\n                Didactique des math\u00e9matiques 4                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-44                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3ee2\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Didactique des math\u00e9matiques 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-44<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ul><br><li>S\u00e9lectionner des outils didactiques susceptibles d&#8217;aider l&#8217;enseignant dans sa pratique<\/li><br><li>S\u2019initier \u00e0 la pratique en milieu r\u00e9el<\/li><br><li>Planifier et pr\u00e9senter un projet didactique favorisant un apprentissage efficient<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><li>Conception, r\u00e9alisation et analyse critique d&#8217;une le\u00e7on compl\u00e8te, puis \u00e9laboration d&#8217;un devoir en rapport avec la le\u00e7on et corrig\u00e9 de ce devoir<\/li><li>Analyse du fonctionnement des \u00e9l\u00e8ves<\/li><li>Contenus issus de la recherche actuelle en didactique des math\u00e9matiques et mise en \u0153uvre pratique: diff\u00e9renciation, \u00ab blended learning \u00bb,\u2026<\/li><li>Approfondissement de th\u00e8mes pluridisciplinaires<\/li><li>D\u00e9veloppement d\u2019une activit\u00e9 de recherche<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Engagement r\u00e9gulier et \u00e9laboration d\u2019un portfolio, pr\u00e9sentation du portfolio<\/p><br><br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Bibliographie compl\u00e9t\u00e9e progressivement et recherche personnelle                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3efc\"\n        >\n            <span class=\"accordion__title\">\n                Histoire des sciences math\u00e9matiques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-39                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3efc\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Histoire des sciences math\u00e9matiques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-39<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Nous allons \u00e9tudier quelques \u00e9tapes dans l\u2019histoire des math\u00e9matiques. Le prochain cours sera consacr\u00e9 \u00e0 l\u2019\u00e9tude de la g\u00e9om\u00e9trie dans l\u2019espace. Un \u00e9vennement d\u00e9cisif en \u00e9tait la d\u00e9couverte de la perspective pendant le 15e si\u00e8cle. Nous consid\u00e9rons aussi les \u00ab El\u00e9ments d\u2019Euclide \u00bb y compris les constructions \u00e0 la r\u00e8gle et au compas, la st\u00e9reom\u00e9trie et les corps r\u00e9guliers (platoniciens). Ainsi nous arriverons \u00e0 l\u2019histoire de la g\u00e9om\u00e9trie moderne en particulier \u00e0 la fameuse formule d\u2019Euler. On va\u00a0 \u00e9tudier aussi le lien entre la d\u00e9couverte de la perspective et la g\u00e9om\u00e9trie projective. Pour terminer on va jeter un coup d\u2019\u0153il \u00e0 la quatri\u00e8me dimension.<br>Wir beginnen mit der Entdeckung der Perspektive im 15. Jh. Dann wenden wir uns den \u201eElementen\u201c des Euklid zu. Hier betrachten wir die Konstruktionen mit Zirkel und Lineal, die Stereometrie und die regul\u00e4ren (Platonischen) K\u00f6rper. Anschlie\u00dfend kommen wir zur modernen Raumgeometrie, insbesondere zur Formel von Euler. Schlie\u00dflich m\u00f6chte ich auf die Zusammenh\u00e4nge zwischen der Perspektive und der projektiven Geometrie eingehen. Wir warden auch einen Blick in die vierte Dimension werfen.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        L\u2019\u00e9tudiant(e) devra \u00eatre capable de lire un texte math\u00e9matique ancien, d\u2019en d\u00e9chiffrer les notations et de comprendre la construction de l\u2019objet math\u00e9matique dans un contexte tr\u00e8s diff\u00e9rent de celui qui est le sien aujourd\u2019hui. A travers la confrontation avec des textes originaux, l\u2019\u00e9tudiant sera sensibilis\u00e9 \u00e0 l\u2019historicit\u00e9 des math\u00e9matiques et d\u00e9veloppera une r\u00e9flexivit\u00e9 sur sa propre discipline. De plus on fait l\u2019exp\u00e9rience que des exemples pris des math\u00e9matiques anciennes sont utiles m\u00eame aujourd\u2019hui par exemple dans l\u2019enseignement.\u00a0<br>Die TeilnehmerInnen k\u00f6nnen \u00e4ltere mathematische Texte verstehen und deren Notationen entschl\u00fcsseln. Sie gewinnen Zugang zum mathematischen Wissen fr\u00fcherer Zeiten und k\u00f6nnen dieses mit dem heutigen verbinden. Die Studierenden entwickeln ein Bewusstsein f\u00fcr die historische Bedingtheit der Mathematik und k\u00f6nnen diese kritisch reflektieren. Zudem erweisen sich Beispiele aus fr\u00fcheren Zeiten auch heute noch als n\u00fctzlich, z. B. f\u00fcr Unterrichtszwecke.\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00c9tudier les divers acteurs et leur production math\u00e9matique de diverses \u00e9poques. L\u2019\u00e9tude des textes originaux permettra de saisir comment se construisent les objets math\u00e9matiques. On comprend que les math\u00e9matiques modernes sont encore influenc\u00e9es par des mod\u00e8les anciens \u2013 des paradigmes en sont la m\u00e9thode dite axiomatique-d\u00e9ductive et les constrcutions \u00e0 la r\u00e8gle et au compas.\u00a0\u00a0<br>Wir werden verschiedenen Mathematiker aus unterschiedlichen Epochen und ihre mathematische Werke kennenlernen. Das Studium von Originaltexten hilft zu verstehen, wie mathematische Erkenntnisse zustande kommen. Dabei werden wir sehen, wie die moderne Mathematik immer noch stark von alten Vorbildern beeinflusst wird. Paradigmatische Beispiele hierf\u00fcr liefern die axiomatisch-deduktive Methode und die Konstruktionen mit Zirkel und Lineal.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Assidu\u00eft\u00e9 en particulier travail sur les probl\u00e8mes pos\u00e9s et r\u00e9daction d\u2019un m\u00e9moire personnel ; <br>aktive Teilnahme insbesondere Bearbeitung von \u00dcbungsaufgaben und schriftliche Ausarbeitung.\u00a0<\/p><br><p>Themen f\u00fcr BA-Thesen werden im zentralen Themenpool bekannt gegeben.\/<br>Des sujets pour des th\u00e8ses de BA sont propos\u00e9s cf. le pool central des th\u00e8mes.<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><\/p><br><p>Textes et probl\u00e8mes \u00e0 travailler d\u00e9pos\u00e9s sur Moodle\u00a0<br>Die zu bearbeitenden Texte und Aufgaben sind in Moodle zug\u00e4nglich.\u00a0<\/p><br><p><br>Literature<br><\/p><br><p>Une bibliographie sera d\u00e9pos\u00e9e sur Moodle .<\/p>Voici \u00e0 titre indicatif quelques titres : Amy Dahan Jeanne Peiffer, Une histoire des math\u00e9matiques. Routes et d\u00e9dales, Points Seuil, Paris, 1986<ul><li>Amy Dahan\/Jeanne Peiffer, Wege und Irrwege. Eine Geschichte der Mathematik, Birkh\u00e4user, Basel, 1994.\u00a0<\/li><li>Euclide, Les \u00e9l\u00e9ments (beaucoup d\u2019\u00e9ditions num\u00e9ris\u00e9es sont disponibles en ligne) &#8211; Euklid, Die Elemente (verschiedene Ausgaben sind im Internet zug\u00e4nglich).<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3f15\"\n        >\n            <span class=\"accordion__title\">\n                Logiciels math\u00e9matiques                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-13                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3f15\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Logiciels math\u00e9matiques <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-13<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The first part of the course will cover the basics of the LaTeX markup language.<br>We will see how to use it to write a mathematical text, such as lecture notes or a Thesis, and to prepare slides for a presentation.<br>In the second part we will focus on SageMath and other mathematical software to carry out computations. We will also briefly talk about computational complexity and how to write more efficient code.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student who completes the course will be able to use the LaTeX markup language to write documents and prepare slide-based presentations and to use SageMath and other mathematical software to carry out computations.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>LaTeX [1] is a markup language to write and format documents of any type. It is particularly well-suited for scientific documents, but it can be used for any type of document, including books, CVs and even presentation slides.<br>It can be used together with a graphical front-end (such as TexMaker, TexStudio, Overleaf&#8230;) to immediately see the pdf output. The main advantage over a more classical word processor such as Microsoft Word, besides a much better support for writing mathematical formulas and theorems, is that in LaTeX &#8220;What you see is what you mean&#8221; [2]: by typing commands instead of visually changing the appearence of the text, the &#8220;compiler&#8221; will always try to produce an output that is faithful to what the user indicated, so the user does not have to manually adjust the result after every major modification.<br>SageMath [3] is a free and open-source Mathematical software system which builds on top of many existing: NumPy, SciPy, matplotlib, Sympy, Pari\/GP, GAP, R and many more. Thanks to it, all the features all these languages can be accessed from a common python-based interface.<br>In practice, the SageMath &#8220;language&#8221; is almost identical to python, but it provides a complete set of libraries to deal with many mathematical objects and computations.<\/p><ol><li>https:\/\/en.wikipedia.org\/wiki\/LaTeX<\/li><li>https:\/\/en.wikipedia.org\/wiki\/WYSIWYM<\/li><li>https:\/\/www.sagemath.org\/<\/li><\/ol><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The evaluation of the course will be based Quiz and Final project.\u00a0<br><\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><\/p><br><p><br>https:\/\/doc.sagemath.org\/html\/en\/tutorial\/index.html<br><\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623a3f2f\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matiques exp\u00e9rimentales 3                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-46                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623a3f2f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623a3d93\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matiques exp\u00e9rimentales 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-46<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.2-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Learn and use in a practical context mathematical notions beyond the content of other courses. Develop programing skills. Discover a research-oriented aspect of mathematics and participate in research projects.<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students who have successfully followed this unit will have learned and been able to use in a practical context mathematical notions beyond the content of other courses. They will have developed their programing skills, and discovered a research-oriented aspect of mathematics and, in some cases, participated in research projects.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Les \u00e9tudiants suivant ce module prendront part, seuls ou en groupes de 2 ou 3, \u00e0 un projet de math\u00e9matiques exp\u00e9rimentales qui comportera une partie importante de programmation sur ordinateur et qui fera appel aux notions math\u00e9matiques enseign\u00e9es jusqu&#8217;au semestre 2. L&#8217;encadrement est assur\u00e9 par un enseignant de l&#8217;Unit\u00e9 de Math\u00e9matiques. Il n&#8217;y aura pas de contrainte horaire particuli\u00e8re pour participer \u00e0 ce module: un calendrier de suivi sera \u00e9tabli en d\u00e9but de semestre entre l&#8217;enseignant et le (les) \u00e9tudiant(s) concern\u00e9s.<br>La liste des projets disponibles peut \u00eatre consult\u00e9e sur http:\/\/math.uni.lu\/eml. Le nombre de places pour participer \u00e0 ce module \u00e9tant limit\u00e9, les \u00e9tudiants int\u00e9ress\u00e9s sont pri\u00e9s de participer \u00e0 la r\u00e9union de pr\u00e9sentation qui leur sera propos\u00e9e, puis de se faire connaitre dans les deux jours qui suivent. S&#8217;il y a plus de personnes int\u00e9ress\u00e9es que de places disponibles, le seul crit\u00e8re retenu sera l&#8217;excellence du dossier. <p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>L&#8217;\u00e9valuation consistera en la r\u00e9daction d&#8217;un m\u00e9moire de projet (contenant entre autre le code et son explication, un r\u00e9sum\u00e9 des math\u00e9matiques utilis\u00e9es, une discussion des r\u00e9sultats exp\u00e9rimentaux obtenus quand c&#8217;est le cas, &#8230;) et sa d\u00e9fense pendant une soutenance orale.<br><\/p><br><p>Retake: un nouveau projet doit etre fait<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Support \/ Arbeitsunterlagen \/ Support\u00a0:<br>sera mis \u00e0 disposition au d\u00e9but du projet<br>Litt\u00e9rature \/ Literatur \/ Literature\u00a0:<br>sera communiqu\u00e9e au d\u00e9but du projet <p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-55dd3e7c-2cc9-495a-a4a8-98be25c7b179\"\n    aria-labelledby=\"tab-55dd3e7c-2cc9-495a-a4a8-98be25c7b179\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 5 (2025-2026 Winter)<\/h3>\n    \n<div id=\"accordion-module-6a13f623ad17f\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623ad1c3\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matiques exp\u00e9rimentales 4                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-28                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623ad1c3\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623ad17f\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matiques exp\u00e9rimentales 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-28<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 5.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN, DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Learn and use in a practical context mathematical notions beyond the content of other courses. Develop programming skills. Discover a research-oriented aspect of mathematics and participate in research projects.<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students who have successfully followed this course will have learned and been able to use in a practical context mathematical notions beyond the content of other courses. They will have developed their programming skills, and discovered a research-oriented aspect of mathematics and, in some cases, participated in research projects.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>We are all accustomed to the idea of experiments in physics, chemistry or biology. But mathematics can be done at an equally experimental level, often using computational methods. This applies to statistics, algebra, analysis, geometry, and other flavours of mathematics, and includes\u00a0<br> visualising complex mathematical objects,<br> using computers to work with examples that go beyond what is possible using pen and paper,<br> finding patterns in complicated data.<br>Even in highly abstract areas of mathematics the value of experimentation has increased dramatically in recent years, with computers, programming languages and computer algebra systems getting stronger and easier to use.\u00a0<br>This course allows students to participate in a research like project in an area of experimental mathematics. The students work in small groups under the guidance of a researcher of the Department of Mathematics. They produce a project report (a pdf document) and other material (such as images, videos, code, data), depending on the project. Finally, they also present their work in a small presentation during the exam period.<br>\u00a0<p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>The students are evaluated on the project report and the additional material they produced, on a midterm report, their performance during the semester, and the final presentation.<br>In justified cases, it is possible to propose different marks for different students working in the same group.<br>Retake exam\u00a0<br>If a project is failed, a new project should be done in the next or a later semester. The project group, the topic and the supervisor(s) can change.<br>Absence plan\u00a0<br>In the case of a justified absence from the final project presentation, a separate presentation will be proposed as close to the originally planned date as possible.<br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The literature will be provided by the supervisor for each group.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623ad1df\"\n        >\n            <span class=\"accordion__title\">\n                Reading Course 1 &#8211; Information theory\/entropy                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            9                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-29                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623ad1df\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623ad17f\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Reading Course 1 &#8211; Information theory\/entropy<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-29<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 5.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The reading course is about information theory\/entropy and uses the book &#8220;Elements of information theory&#8221; by Joy A. Thomas and Thomas M. Cover<\/p>We cover chapters 2-5 and 11.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Assessment will be based primarily on a short presentation, including answers to questions, at the end of the semester.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623ad1ed\"\n        >\n            <span class=\"accordion__title\">\n                Reading Course 2 &#8211; Mod\u00e8les probabilistes et temps d&#039;arr\u00eats                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            9                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-30                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623ad1ed\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623ad17f\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Reading Course 2 &#8211; Mod\u00e8les probabilistes et temps d&#039;arr\u00eats<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-30<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 5.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                \n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        First session<br>Continuous assessment<br>                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623ad1fa\"\n        >\n            <span class=\"accordion__title\">\n                Reading Course 3 &#8211; Statistical Inference                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            9                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-31                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623ad1fa\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623ad17f\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Reading Course 3 &#8211; Statistical Inference <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-31<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 5.1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><br><li>Students will understand the foundational principles of statistical learning, including the shift from classical to computer age statistical methods.<\/li><br><li>Students will learn key algorithms for data analysis and statistical inference in modern data science.<\/li><br><li>Students will explore real-world applications and the importance of empirical evidence in the development of statistical methods.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>There will be two groups, one focused on the algorithms and statistical inference methodologies, and the other on the applications and evidence-based data science approaches. Students are required to present the material they read during the group meetings, which will take place every week or every two weeks.<\/p><p>Comments<\/p><ul><li>The study group will be highly interactive, with students encouraged to discuss their interpretations and insights from the readings.<\/li><li>Students should collaborate on problem sets and projects to solidify their understanding.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        No written exam. Evaluation will be based on participation in group meetings and a final presentation.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note \/ Literature \/ Bibliography<br><br><\/p><br><ul><br><li>Primary Textbook: &#8220;Computer Age Statistical Inference: Algorithms, Evidence, and Data Science&#8221; by Trevor Hastie and Bradley Efron.<\/li><br><li>Additional Resources: Supplementary research papers and online resources will be provided to deepen understanding of specific topics.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-eb4d8f34-3d30-4e55-ad17-9ec7191d588d\"\n    aria-labelledby=\"tab-eb4d8f34-3d30-4e55-ad17-9ec7191d588d\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Bachelor in Mathematics, Semestre 6 (2025-2026 Summer)<\/h3>\n    \n<div id=\"accordion-module-6a13f623b625e\" class=\"accordion accordion--theme\">\n            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6290\"\n        >\n            <span class=\"accordion__title\">\n                Introduction \u00e0 la th\u00e9orie des graphes                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-40                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6290\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Introduction \u00e0 la th\u00e9orie des graphes<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-40<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Au travers de la pr\u00e9sentation de diff\u00e9rents sujets, le cours est une introduction autonome \u00e0 la th\u00e9orie des graphes et \u00e0 ses applications.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Les \u00e9tudiant\u00b7e\u00b7s qui r\u00e9ussissent l&#8217;\u00e9valuation seront capables de\u00a0<\/p><br><ul><br><li>Expliquer les probl\u00e8mes de base de la th\u00e9orie des graphes et les diff\u00e9rentes approches pour les r\u00e9soudre,<\/li><br><li>Prouver des r\u00e9sultats classiques en th\u00e9orie des graphes (par exemple, la caract\u00e9risation des graphes eul\u00e9riens, la formule d&#8217;Euleur pour les graphes planaires, le th\u00e9or\u00e8me de Chvatal pour les graphes Hamiltonien, le th\u00e9or\u00e8me des cinq couleurs&#8230;)\u00a0<\/li><br><li>Appliquer des outils classiques de la th\u00e9orie des graphes pour r\u00e9soudre certains probl\u00e8mes : construire des sous-graphes couvrant de poids minimum, rechercher des chemins les plus courts (probl\u00e8me du GPS)&#8230;\u00a0<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><li>Graphes, graphes dirig\u00e9s, multi-graphes, repr\u00e9sentations matricielles et applications<\/li><li>Connectivit\u00e9, recherche de plus courts chemins, coupes, graphes hamiltioniens<\/li><li>Arbres, sous-arbres couvrants, nombre de sous-arbres couvrants<\/li><li>Graphes planaires, formule d&#8217;Euler<\/li><li>Probl\u00e8mes de coloriage de graphes.<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Examen de fin de semestre \u00e9crit et\/ou oral.\u00a0                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b62ba\"\n        >\n            <span class=\"accordion__title\">\n                Analyse fonctionnelle                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-35                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b62ba\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse fonctionnelle<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-35<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ol><br><li>Become familiar with the basic results in functional analysis\u00a0<\/li><br><li>Learn how to use the main abstract tricks and strategies in order to prove such statements\u00a0<\/li><br><li>Appreciate the power of abstraction in pure and applied mathematics\u00a0<\/li><br><li>Understand the connection between seemingly unrelated mathematical disciplines\u00a0<\/li><br><\/ol><br><br><br>\u00a0<br><p>\u00a0<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Etre capable d&#8217;utiliser les espaces de fonctions pour r\u00e9soudre des probl\u00e8mes d&#8217;analyse                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The course will cover the following topics:<\/p><ol><li>Banach spaces and bounded linear functionals.<\/li><li>Hanh-Banach theorem and Baire Category theorem.<\/li><li>Uniform boundedness principle. Open mapping theorem. Closed graph theorem.<\/li><li>Unbounded linear operators.<\/li><li>Issues of classical compactness. Weak topology. Weak* topology.<\/li><li>Reflexive and separable spaces.<\/li><li>Lp spaces (reflexivity, separability, duality, strong compactness).<\/li><li>Hilbert spaces and their duals. Theorems of Stampacchia and Lax-Milgram. Hilbert sums. Orthonormal bases.<\/li><li>Compact operators. Riesz-Fredholm theory. Spectrum.<br><\/li><\/ol><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Final exam with written and oral components<br><\/p>Retake:<br>the retake is a written exam (2 hours).                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p><br><p><br>Notes &#8211; Literatur<br><\/p><br><p>\u00a0<\/p><br><p>Exercises and examples will be uploaded on Moodle.<br><\/p><br><ul><br><li>Main: Functional analysis, Sobolev Spaces and Partial Differential Equations, H. Brezis.<\/li><br><li>Supplementary: Elementary functional analysis, B. MacCluer.<br><\/li><br><\/ul><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b62d4\"\n        >\n            <span class=\"accordion__title\">\n                Analyse num\u00e9rique                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-38                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b62d4\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Analyse num\u00e9rique<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-38<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Au terme du cours, l\u2019\u00e9tudiant doit \u00eatre \u00e0 m\u00eame de :<\/p><br><ul><br><li>comprendre le r\u00f4le central de l\u2019analyse num\u00e9rique dans les sciences math\u00e9matiques pures et appliqu\u00e9es<\/li><br><li>ma\u00eetriser les notions et les algorithmes fondamentaux de l\u2019analyse num\u00e9rique (approximation de fonctions, r\u00e9solution d\u2019\u00e9quations, calcul approch\u00e9s d\u2019int\u00e9grales\u2026)<\/li><br><li>acqu\u00e9rir un raisonnement rigoureux et syst\u00e9matique, indispensable \u00e0 l\u2019analyse et \u00e0 l\u2019interpr\u00e9tation des objets \u00e9tudi\u00e9s en analyse num\u00e9rique<\/li><br><li>formuler et r\u00e9soudre math\u00e9matiquement certains probl\u00e8mes num\u00e9riques mod\u00e9lisables au moyen de l\u2019analyse math\u00e9matique et de l\u2019alg\u00e8bre lin\u00e9aire.<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Normes d\u2019op\u00e9rateursApproximation polynomialeR\u00e9solution d\u2019\u00e9quations non lin\u00e9airesR\u00e9solution num\u00e9rique de syst\u00e8mes lin\u00e9airesInt\u00e9gration num\u00e9rique\u00a0                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>examen \u00e9crit en fin de semestre<\/p><br><p>Retake: Examen \u00e9crit<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Support \/ Arbeitsunterlagen \/ Support\u00a0:<br><br><p>Notes de cours et slides (disponibles sur Moodle)<\/p><br>\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b62ee\"\n        >\n            <span class=\"accordion__title\">\n                Cha\u00eenes de Markov                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-49                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b62ee\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Cha\u00eenes de Markov <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-49<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        By the end of the course, students will have become familiarized with the basic theory of discrete-time Markov chains on countable state spaces, together with an awareness of applications. Students will understand the elementary definitions and theorems about Markov chains, and how these lead to structural properties, stability concepts, stationary distributions and convergence theorems.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Probability spaces, elementary Markov property, transition matrices, initial distributions, Chapman-Kolmogorov equations, hitting times, communication and periodicity, strong Markov property, recurrence and transience, random walks, invariant distributions, convergence to equilibrium, ergodicity.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>First take: Oral exam<\/p><br><p>Retake: Oral exam\u00a0\u00a0(Approx. 20min)<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Litt\u00e9rature \/ Literature\u00a0<br><\/p><br><p>Pierre Br\u00e9maud. Markov chains: Gibbs fields, Monte Carlo simulation, and queues, volume 31 of Texts in Applied Mathematics. Springer-Verlag, New York, 1999.<\/p><br><ul><br><li>David A. Levin and Yuval Peres. Markov chains and mixing times. American Mathematical Society, Providence, RI, 2017<\/li><br><li>J. R. Norris. Markov chains, volume 2 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge 8xav福利导航 Press, Cambridge, 1998. Reprint of 1997 original.<\/li><br><li>Richard Serfozo . Basics of applied stochastic processes. Probability and its Applications (New York). Springer-Verlag, Berlin, 2009.<\/li><br><\/ul><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6307\"\n        >\n            <span class=\"accordion__title\">\n                Courbes alg\u00e9briques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-36                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6307\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Courbes alg\u00e9briques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-36<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Introduction to the theory of algebraic curves over arbitrary fields, in particular also over finite fields. Of particular interest will be the theory of elliptic curves due to its relations to cryptography.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>On successful completion of this course the student should be able to :<br><\/p><br><ul><br><li>demonstrate the knowledge of the notion of an algebraic curve<\/li><br><li>demonstrate the special properties for curves over finite fields<\/li><br><li>master the basic technique of the theory<\/li><br><li>identify the most important examples<\/li><br><li>independently apply the required techniques to explicitly given situations. <\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>Introduction<\/li><li>Affine varieties and curves<\/li><li>projective curves<\/li><li>quadrics<\/li><li>Elliptic Curves<\/li><li>Complex tori and elliptic curves<\/li><li>The group law on elliptic curves<\/li><li>Affine coordinate ring<\/li><li>Projective coordinate ring<\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Written examination.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Lecture notes for the course, tutorial questions and solutions are all available to the students via the moodle. <\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b631f\"\n        >\n            <span class=\"accordion__title\">\n                Differential geometry                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-48                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b631f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Differential geometry<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-48<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The objective is to allow the student to familiarize her\/himself with a very active field of mathematics, with broad applications throughout science. A special attention will be put on providing an intuitive understanding of the very concrete ideas that are behind the abstract notions of this subject.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>On successful completion of the course, the student should be able to:<\/p><br><p>\u00a0<\/p><br><ul><br><li>Explain the main definitions and results of Differential Geometry<\/li><br><li>Comment on new concepts <\/li><br><li>Apply the new techniques and solve related problems<\/li><br><li>Structure the acquired abilities and summarize essential aspects adopting a higher standpoint<\/li><br><li>Give a talk for peers or students on a related topic and write scientific texts or lecture notes, observing modern standards in scientific writing, in Didactics and in Pedagogy<\/li><br><li>Being ready for more advanced courses (e.g., Riemannian geometry)<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ol><li>Nonlinear analysis: immersions, submersions, embeddings, submanifolds in R^n, implicit and inverse function theorems, constant rank theorem, link with classical mechanics.<\/li><li>Smooth manifolds: definition, examples, topology.<\/li><li>Tangent maps (differential) of smooth maps: smooth maps, tangent and cotangent spaces, tangent map, vector fields.<\/li><li>Embedded submanifolds: definition, cartesian and parametric equations, embedded submanifolds versus abstract manifolds, the Whitney embedding theorem, tubular neighborhoods.<\/li><li>(Possible additional topics) Transversality, Sard\u2019s theorem and applications. Approximation of continuous functions. Orientability, differential forms and integration. Frobenius theorem\u2026. <\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>First take and retake:\u00a0<\/p><br><p>a written part (2hours) and an oral exam (max 45 minutes)<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><br>The lecture notes will be uploaded to Moodle<\/p><br><p><br>Literature<br><br><br>Main reference<br><\/p><br><ul><br><li><br>John M. Lee \u2013 Introduction to Smooth manifolds<\/li><br><\/ul><br><p><br>Other standard references<br><\/p><br><ul><br><li><br>Frank W. Warner \u2013 Foundations of Differentiable Manifolds and Lie Groups<\/li><br><li>Michael Spivak \u2013 A Comprehensive Introduction to Differential Geometry Vol. 1<\/li><br><li>Morris Hirsch \u2013 Differential Topology<\/li><br><li>Shoshichi Kobayashi Katsumi Nomizu \u2013 Foundations of Differential Geometry<\/li><br><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6335\"\n        >\n            <span class=\"accordion__title\">\n                Measure theory and integration                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            6                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-47                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6335\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Measure theory and integration<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 6<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-47<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            L&#8217;objectif de ce cours est de fournir les fondements math\u00e9matiques sur lesquels se base l&#8217;int\u00e9gration moderne. Cela inclut l&#8217;int\u00e9grale par rapport \u00e0 la mesure de Lebesgue, que l&#8217;on utilise en analyse, et l&#8217;int\u00e9grale par rapport \u00e0 une mesure abstraite finie qui constitue la base de la th\u00e9orie moderne des probabilit\u00e9s. Le cours montrera comme cette nouvelle th\u00e9orie de l&#8217;int\u00e9gration permet de d\u00e9finir une int\u00e9grale non seulement plus g\u00e9n\u00e9rale mais aussi plus simple \u00e0 utiliser. En particulier, nous verrons les grands th\u00e9or\u00e8mes permettant d\u2019intervertir une limite et une int\u00e9grale ou d&#8217;intervertir deux int\u00e9grales.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00c0 l&#8217;issue de ce cours, un ou une \u00e9tudiant(e) devra connaitre les notions de mesure, de tribu, et d&#8217;int\u00e9grale par rapport \u00e0 une mesure. Il ou elle devra maitriser l&#8217;utilisation des th\u00e9or\u00e8mes fondamentaux comme les th\u00e9or\u00e8mes de convergence monotone, domin\u00e9e, ainsi que les th\u00e9or\u00e8mes de Fubini-Tonelli et Fubini-Lebesgue. Les \u00e9tudiants et \u00e9tudiantes devront \u00eatre en mesure d\u2019\u00e9tudier la continuit\u00e9 et la d\u00e9rivabilit\u00e9 d\u2019une int\u00e9grale d\u00e9pendant d\u2019un param\u00e8tre et de comprendre les liens qui unissent la th\u00e9orie de l&#8217;int\u00e9gration abstraite et celle des probabilit\u00e9s modernes.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Le programme du cours est le suivant :<\/p><ol><li>Espace mesur\u00e9<\/li><li>Fonctions mesurables <\/li><li>Int\u00e9gration par rapport \u00e0 une mesure <\/li><li>Int\u00e9grale d\u00e9pendant d&#8217;un param\u00e8tre <\/li><li>Mesure produit <\/li><li>Fondement de la th\u00e9orie des probabilit\u00e9s. <\/li><\/ol>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>First session<br><\/p><br><p>There will be two exams for this class: a partial exam and a final exam. Both of them will last two hours. Zero document is allowed for these two exams.\u00a0<br>The final mark will be given by the following formula:\u00a0<br>max{final exam,60%*final exam +40%*partial exam}<\/p><br><p><br>Retake session<br><\/p><br><p>2 hours written exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Note \/ Literature \/ Bibliography<br><br>P. Cannarsa and T. D&#8217;Aprile. Introduction to measure theory and functional analysis. Vol. 89. Springer, 2015.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6344\"\n        >\n            <span class=\"accordion__title\">\n                Number theory and cryptography                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-34                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6344\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Number theory and cryptography<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-34<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-a (choisir au moins 13 ECTS dans le 6.1-a)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN, FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Recently (and not so recently) number theory has found unexpected applications in cryptography, and nowadays everyone uses it on a daily basis (without realising it) when paying electronically or using the internet.<br>The course will introduce the students to some basic aspects of number theory, most importantly the theory of elliptic curves over finite fields. We will use the group law for elliptic curves (and other number-theoretic methods) to discuss modern ciphers, such as RSA, Diffie-Hellman, El Gamal, &#8230;<br>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student will<br>understand basic number-theoretic objects<br>be able to illustrate their properties with examples<br>understand the group law on an elliptic curve<br>be able to apply the different ciphers discussed in the course in simplified settings                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>The course will cover the following subjects<br> elementary aspects of number theory<br> finite fields<br> elliptic curves over finite fields<br> RSA encryption<br> El Gamal<br> Diffie&#8211;Hellman                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Written final exam. Weekly exercises will also be evaluated.<\/p><br><p>Retake: Written exam<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Course notes and exercise sheets on Moodle.<\/p>* Neal Koblitz, A Course in Number Theory and Cryptography, Springer.<br>* S.C. Coutinho, The Mathematics of Ciphers: Number Theory and RSA Cryptography, A. K. Peters.<br>* Douglas R. Stinson, Cryptography: theory and practice, Chapman and Hall.<br>* Paul Garrett, Making, Breaking Codes: Introduction to Cryptology.<br>* Michael Rosing, Implementing elliptic curve cryptography, Greenwich: Manning.<br>* A. J. Menezes, Elliptic curve public key cryptosystems, Boston: Kluwer Academic Publishers\u00a0                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6350\"\n        >\n            <span class=\"accordion__title\">\n                Didactique des math\u00e9matiques 4                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            5                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-44                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6350\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Didactique des math\u00e9matiques 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 5<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-44<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <ul><br><li>S\u00e9lectionner des outils didactiques susceptibles d&#8217;aider l&#8217;enseignant dans sa pratique<\/li><br><li>S\u2019initier \u00e0 la pratique en milieu r\u00e9el<\/li><br><li>Planifier et pr\u00e9senter un projet didactique favorisant un apprentissage efficient<\/li><br><\/ul>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul><li>Conception, r\u00e9alisation et analyse critique d&#8217;une le\u00e7on compl\u00e8te, puis \u00e9laboration d&#8217;un devoir en rapport avec la le\u00e7on et corrig\u00e9 de ce devoir<\/li><li>Analyse du fonctionnement des \u00e9l\u00e8ves<\/li><li>Contenus issus de la recherche actuelle en didactique des math\u00e9matiques et mise en \u0153uvre pratique: diff\u00e9renciation, \u00ab blended learning \u00bb,\u2026<\/li><li>Approfondissement de th\u00e8mes pluridisciplinaires<\/li><li>D\u00e9veloppement d\u2019une activit\u00e9 de recherche<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Engagement r\u00e9gulier et \u00e9laboration d\u2019un portfolio, pr\u00e9sentation du portfolio<\/p><br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Bibliographie compl\u00e9t\u00e9e progressivement et recherche personnelle                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b635d\"\n        >\n            <span class=\"accordion__title\">\n                Histoire des sciences math\u00e9matiques                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-39                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b635d\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Histoire des sciences math\u00e9matiques<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-39<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, DE<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Nous allons \u00e9tudier quelques \u00e9tapes dans l\u2019histoire des math\u00e9matiques. Le prochain cours sera consacr\u00e9 \u00e0 l\u2019\u00e9tude de la g\u00e9om\u00e9trie dans l\u2019espace. Un \u00e9vennement d\u00e9cisif en \u00e9tait la d\u00e9couverte de la perspective pendant le 15e si\u00e8cle. Nous consid\u00e9rons aussi les \u00ab El\u00e9ments d\u2019Euclide \u00bb y compris les constructions \u00e0 la r\u00e8gle et au compas, la st\u00e9reom\u00e9trie et les corps r\u00e9guliers (platoniciens). Ainsi nous arriverons \u00e0 l\u2019histoire de la g\u00e9om\u00e9trie moderne en particulier \u00e0 la fameuse formule d\u2019Euler. On va\u00a0 \u00e9tudier aussi le lien entre la d\u00e9couverte de la perspective et la g\u00e9om\u00e9trie projective. Pour terminer on va jeter un coup d\u2019\u0153il \u00e0 la quatri\u00e8me dimension.<br>Wir beginnen mit der Entdeckung der Perspektive im 15. Jh. Dann wenden wir uns den \u201eElementen\u201c des Euklid zu. Hier betrachten wir die Konstruktionen mit Zirkel und Lineal, die Stereometrie und die regul\u00e4ren (Platonischen) K\u00f6rper. Anschlie\u00dfend kommen wir zur modernen Raumgeometrie, insbesondere zur Formel von Euler. Schlie\u00dflich m\u00f6chte ich auf die Zusammenh\u00e4nge zwischen der Perspektive und der projektiven Geometrie eingehen. Wir warden auch einen Blick in die vierte Dimension werfen.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        L\u2019\u00e9tudiant(e) devra \u00eatre capable de lire un texte math\u00e9matique ancien, d\u2019en d\u00e9chiffrer les notations et de comprendre la construction de l\u2019objet math\u00e9matique dans un contexte tr\u00e8s diff\u00e9rent de celui qui est le sien aujourd\u2019hui. A travers la confrontation avec des textes originaux, l\u2019\u00e9tudiant sera sensibilis\u00e9 \u00e0 l\u2019historicit\u00e9 des math\u00e9matiques et d\u00e9veloppera une r\u00e9flexivit\u00e9 sur sa propre discipline. De plus on fait l\u2019exp\u00e9rience que des exemples pris des math\u00e9matiques anciennes sont utiles m\u00eame aujourd\u2019hui par exemple dans l\u2019enseignement.\u00a0<br>Die TeilnehmerInnen k\u00f6nnen \u00e4ltere mathematische Texte verstehen und deren Notationen entschl\u00fcsseln. Sie gewinnen Zugang zum mathematischen Wissen fr\u00fcherer Zeiten und k\u00f6nnen dieses mit dem heutigen verbinden. Die Studierenden entwickeln ein Bewusstsein f\u00fcr die historische Bedingtheit der Mathematik und k\u00f6nnen diese kritisch reflektieren. Zudem erweisen sich Beispiele aus fr\u00fcheren Zeiten auch heute noch als n\u00fctzlich, z. B. f\u00fcr Unterrichtszwecke.\u00a0                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        \u00c9tudier les divers acteurs et leur production math\u00e9matique de diverses \u00e9poques. L\u2019\u00e9tude des textes originaux permettra de saisir comment se construisent les objets math\u00e9matiques. On comprend que les math\u00e9matiques modernes sont encore influenc\u00e9es par des mod\u00e8les anciens \u2013 des paradigmes en sont la m\u00e9thode dite axiomatique-d\u00e9ductive et les constrcutions \u00e0 la r\u00e8gle et au compas.\u00a0\u00a0<br>Wir werden verschiedenen Mathematiker aus unterschiedlichen Epochen und ihre mathematische Werke kennenlernen. Das Studium von Originaltexten hilft zu verstehen, wie mathematische Erkenntnisse zustande kommen. Dabei werden wir sehen, wie die moderne Mathematik immer noch stark von alten Vorbildern beeinflusst wird. Paradigmatische Beispiele hierf\u00fcr liefern die axiomatisch-deduktive Methode und die Konstruktionen mit Zirkel und Lineal.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>Assidu\u00eft\u00e9 en particulier travail sur les probl\u00e8mes pos\u00e9s et r\u00e9daction d\u2019un m\u00e9moire personnel ; <br>aktive Teilnahme insbesondere Bearbeitung von \u00dcbungsaufgaben und schriftliche Ausarbeitung.\u00a0<\/p><br><p>Themen f\u00fcr BA-Thesen werden im zentralen Themenpool bekannt gegeben.\/<br>Des sujets pour des th\u00e8ses de BA sont propos\u00e9s cf. le pool central des th\u00e8mes.<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><\/p><br><p>Textes et probl\u00e8mes \u00e0 travailler d\u00e9pos\u00e9s sur Moodle\u00a0<br>Die zu bearbeitenden Texte und Aufgaben sind in Moodle zug\u00e4nglich.\u00a0<\/p><br><p><br>Literature<br><\/p><br><p>Une bibliographie sera d\u00e9pos\u00e9e sur Moodle .<\/p>Voici \u00e0 titre indicatif quelques titres : Amy Dahan Jeanne Peiffer, Une histoire des math\u00e9matiques. Routes et d\u00e9dales, Points Seuil, Paris, 1986<ul><li>Amy Dahan\/Jeanne Peiffer, Wege und Irrwege. Eine Geschichte der Mathematik, Birkh\u00e4user, Basel, 1994.\u00a0<\/li><li>Euclide, Les \u00e9l\u00e9ments (beaucoup d\u2019\u00e9ditions num\u00e9ris\u00e9es sont disponibles en ligne) &#8211; Euklid, Die Elemente (verschiedene Ausgaben sind im Internet zug\u00e4nglich).<\/li><\/ul>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b636a\"\n        >\n            <span class=\"accordion__title\">\n                Logiciels math\u00e9matiques                 <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            3                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-13                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b636a\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Logiciels math\u00e9matiques <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-13<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            The first part of the course will cover the basics of the LaTeX markup language.<br>We will see how to use it to write a mathematical text, such as lecture notes or a Thesis, and to prepare slides for a presentation.<br>In the second part we will focus on SageMath and other mathematical software to carry out computations. We will also briefly talk about computational complexity and how to write more efficient code.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The student who completes the course will be able to use the LaTeX markup language to write documents and prepare slide-based presentations and to use SageMath and other mathematical software to carry out computations.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>LaTeX [1] is a markup language to write and format documents of any type. It is particularly well-suited for scientific documents, but it can be used for any type of document, including books, CVs and even presentation slides.<br>It can be used together with a graphical front-end (such as TexMaker, TexStudio, Overleaf&#8230;) to immediately see the pdf output. The main advantage over a more classical word processor such as Microsoft Word, besides a much better support for writing mathematical formulas and theorems, is that in LaTeX &#8220;What you see is what you mean&#8221; [2]: by typing commands instead of visually changing the appearence of the text, the &#8220;compiler&#8221; will always try to produce an output that is faithful to what the user indicated, so the user does not have to manually adjust the result after every major modification.<br>SageMath [3] is a free and open-source Mathematical software system which builds on top of many existing: NumPy, SciPy, matplotlib, Sympy, Pari\/GP, GAP, R and many more. Thanks to it, all the features all these languages can be accessed from a common python-based interface.<br>In practice, the SageMath &#8220;language&#8221; is almost identical to python, but it provides a complete set of libraries to deal with many mathematical objects and computations.<\/p><ol><li>https:\/\/en.wikipedia.org\/wiki\/LaTeX<\/li><li>https:\/\/en.wikipedia.org\/wiki\/WYSIWYM<\/li><li>https:\/\/www.sagemath.org\/<\/li><\/ol><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>The evaluation of the course will be based Quiz and Final project.\u00a0<br><\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note<br><\/p><br><p><br>https:\/\/doc.sagemath.org\/html\/en\/tutorial\/index.html<br><\/p><br><p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6377\"\n        >\n            <span class=\"accordion__title\">\n                Math\u00e9matiques exp\u00e9rimentales 3                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            4                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-46                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6377\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> Math\u00e9matiques exp\u00e9rimentales 3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-46<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.1-b<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> No<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            <p>Learn and use in a practical context mathematical notions beyond the content of other courses. Develop programing skills. Discover a research-oriented aspect of mathematics and participate in research projects.<\/p>                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Students who have successfully followed this unit will have learned and been able to use in a practical context mathematical notions beyond the content of other courses. They will have developed their programing skills, and discovered a research-oriented aspect of mathematics and, in some cases, participated in research projects.                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Les \u00e9tudiants suivant ce module prendront part, seuls ou en groupes de 2 ou 3, \u00e0 un projet de math\u00e9matiques exp\u00e9rimentales qui comportera une partie importante de programmation sur ordinateur et qui fera appel aux notions math\u00e9matiques enseign\u00e9es jusqu&#8217;au semestre 2. L&#8217;encadrement est assur\u00e9 par un enseignant de l&#8217;Unit\u00e9 de Math\u00e9matiques. Il n&#8217;y aura pas de contrainte horaire particuli\u00e8re pour participer \u00e0 ce module: un calendrier de suivi sera \u00e9tabli en d\u00e9but de semestre entre l&#8217;enseignant et le (les) \u00e9tudiant(s) concern\u00e9s.<br>La liste des projets disponibles peut \u00eatre consult\u00e9e sur http:\/\/math.uni.lu\/eml. Le nombre de places pour participer \u00e0 ce module \u00e9tant limit\u00e9, les \u00e9tudiants int\u00e9ress\u00e9s sont pri\u00e9s de participer \u00e0 la r\u00e9union de pr\u00e9sentation qui leur sera propos\u00e9e, puis de se faire connaitre dans les deux jours qui suivent. S&#8217;il y a plus de personnes int\u00e9ress\u00e9es que de places disponibles, le seul crit\u00e8re retenu sera l&#8217;excellence du dossier. <p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>L&#8217;\u00e9valuation consistera en la r\u00e9daction d&#8217;un m\u00e9moire de projet (contenant entre autre le code et son explication, un r\u00e9sum\u00e9 des math\u00e9matiques utilis\u00e9es, une discussion des r\u00e9sultats exp\u00e9rimentaux obtenus quand c&#8217;est le cas, &#8230;) et sa d\u00e9fense pendant une soutenance orale.<br><\/p><br><p>Retake: un nouveau projet doit etre fait<\/p>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\u00a0<\/p>Support \/ Arbeitsunterlagen \/ Support\u00a0:<br>sera mis \u00e0 disposition au d\u00e9but du projet<br>Litt\u00e9rature \/ Literatur \/ Literature\u00a0:<br>sera communiqu\u00e9e au d\u00e9but du projet <p>\u00a0<\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>            \n<div class=\"accordion__item\">\n    <h4 class=\"accordion__header\">\n        <button\n                type=\"button\"\n                class=\"accordion__button collapsed\"\n                aria-expanded=\"false\"\n                data-bs-toggle=\"collapse\"\n                data-bs-target=\"#accordion-panel-6a13f623b6385\"\n        >\n            <span class=\"accordion__title\">\n                M\u00e9moire                <span class=\"accordion__data\">\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">ECTS credits:<\/span>\n                        <span class=\"accordion__data__value\">\n                            12                        <\/span>\n                    <\/span>\n                    <span class=\"accordion__data__item\">\n                        <span class=\"accordion__data__name\">Course code:<\/span>\n                        <span class=\"accordion__data__value\">\n                            BA_MATH_GEN-50                        <\/span>\n                    <\/span>\n                <\/span>\n            <\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down icon--lg\"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\"><\/use><\/svg>        <\/button>\n    <\/h4>\n\n    <div id=\"accordion-panel-6a13f623b6385\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-6a13f623b625e\">\n        <div class=\"accordion__body p-0\">\n            <ul class=\"list-highlighted\">\n                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Details<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <ul>\n                            <li><span class=\"text-dark font-heading font-bold\">Course title:<\/span> M\u00e9moire<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 12<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> BA_MATH_GEN-50<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 6.2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Language:<\/span> FR, EN<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Mandatory:<\/span> Yes<\/li>\n                        <\/ul>\n                    <\/div>\n                <\/li>\n\n                <!--<li class=\"list-highlighted__item items-start\">-->\n                <!--    <header class=\"list-highlighted__header\">-->\n                <!--        <h5 class=\"text-18\"><strong>--><!--<\/strong><\/h5>-->\n                <!--    <\/header>-->\n                <!--    <div class=\"list-highlighted__body\">-->\n                <!--        <div class=\"speaker-group\">-->\n                <!--            -->                <!--        <\/div>-->\n                <!--    <\/div>-->\n                <!--<\/li>-->\n\n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Objectives<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>\n                            Teaching of students to work independently, to get the ability to extract the important information individually, and present his\/her ideas in the written form clearly and cleanly.                        <\/p>\n                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Course learning outcomes<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The students are expected to master a difficult subject which goes beyond the content of teaching at the bachelor level.<br><br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Each bachelor project (&#8220;m\u00e9moire&#8221;) is a special case. Bachelor projects involve typically reading, understanding, and explaining in the written form parts of a more advanced book or even a research article, or some other educational\/research activity such as computer implementation, vizualisation of mathematical objects, etc. At the end of the semester each student present its work during 15min and then answer to the questions of the committee during 15min.                    <\/div>\n                <\/li>\n                \n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Assessment<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        The bachelor projects have to be submitted before the deadline which is announced to students in the beginning of the corresponding semester. Evaluations are done jointly by all supervisors and members of the DMATH on the basis of the \u2018\u2019m\u00e9moire\u2018\u2019\u00a0 and of the oral presentation.<br>                    <\/div>\n                <\/li>\n                \n                                <li class=\"list-highlighted__item items-start\">\n                    <header class=\"list-highlighted__header\">\n                        <h5 class=\"text-18\"><strong>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Note \/ Literature \/ Bibliography is advised by a supervisor.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<\/div>\n<\/div><\/section>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The Bachelor in Mathematics at the 8xav福利导航 of Luxembourg offers the following programme:<\/p>\n<p>Year 1 introduces analysis, algebra and geometry, alongside optional courses: didactics, computer science or physics.<\/p>\n<p>Year 2 adds probability &amp; statistics to further analysis and algebra. Optional courses help with professional orientation.<\/p>\n<p>Year 3 combines a mobility semester, optional courses (number theory, numerical analysis, Markov chains, etc.) and a supervised report on a specific subject.<\/p>\n","protected":false},"author":276,"featured_media":0,"parent":1104,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Bachelor in Mathematics","uluxPrePostTitle":"","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"study_program_identifiers":"BA_MATH_GEN__F1_BA_MATH_GEN__F1_BA_MATH","override_seo_title":false},"type-of-studies":[],"teaching-languages":[],"field-of-interest":[],"organisation":[],"authorship":[276,281],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - 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