{"id":1183,"date":"2023-07-17T17:14:41","date_gmt":"2023-07-17T17:14:41","guid":{"rendered":"https:\/\/website.prod.unilu.spikeseed.cloud\/fstm-en\/study-programs\/master-en-enseignement-secondaire-mathematiques\/programme\/"},"modified":"2025-06-13T11:54:53","modified_gmt":"2025-06-13T09:54:53","slug":"programme","status":"publish","type":"study-programs","link":"https:\/\/www.uni.lu\/fstm-en\/study-programs\/master-en-enseignement-secondaire-mathematiques\/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=\"7a0555bc-a313-4195-8598-4d1d90f49bbe\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button 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<\/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\/iStock-899619542-scaled.jpg\"\n                srcset=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/iStock-899619542-300x200.jpg 300w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/iStock-899619542-1024x683.jpg 1024w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/iStock-899619542-768x512.jpg 768w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/iStock-899619542-1536x1024.jpg 1536w, https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2023\/07\/iStock-899619542-2048x1365.jpg 2048w\"\n                style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&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 MSE-M activities account for 120 ECTS, grouped as follows:<br>&#8211; Pillar I: Mathematics-Specific Professional Competence (60 ECTS)<br>&#8211; Pillar II: Didactic Competence (20 ECTS)<br>&#8211; Pillar III: General Professional Competence (20 ECTS).<br>&#8211; Internships in schools (six weeks in total), and a Master thesis (20 ECTS).<br><strong>New students are requested to take the <a href=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2024\/08\/Summer-Refresher-2024.pdf\">Refresher Courses<\/a><a href=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/4\/2024\/06\/Summer-Refresher-2024.pdf\"> <\/a>scheduled before the start of the first semester.<\/strong><\/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\/master-en-enseignement-secondaire-mathematiques\/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=\"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-d9aa63fd-4d11-442c-841a-e92b16042ee3\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-d9aa63fd-4d11-442c-841a-e92b16042ee3\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-d9aa63fd-4d11-442c-841a-e92b16042ee3\"\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 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               <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-27a5654f-8943-465d-b93d-650032ebae01\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-27a5654f-8943-465d-b93d-650032ebae01\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-27a5654f-8943-465d-b93d-650032ebae01\"\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-44b503e3-b2db-49db-82cc-acd7a8224c03\"\n                data-bs-toggle=\"tab\"\n                data-bs-target=\"#tabpanel-44b503e3-b2db-49db-82cc-acd7a8224c03\"\n                role=\"tab\"\n                aria-controls=\"tabpanel-44b503e3-b2db-49db-82cc-acd7a8224c03\"\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            <\/ul>\n<\/div>\n<div class=\"tab-content\">\n    <section\n    id=\"tabpanel-d9aa63fd-4d11-442c-841a-e92b16042ee3\"\n    aria-labelledby=\"tab-d9aa63fd-4d11-442c-841a-e92b16042ee3\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Math\u00e9matiques, Semestre 1 (2025-2026 Winter)<\/h3>\n    \n<div id=\"accordion-module-69d3d943e3625\" 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-69d3d943e3664\"\n        >\n            <span class=\"accordion__title\">\n                Commutative Algebra                <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                            8                        <\/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_MAT_GM-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-69d3d943e3664\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Commutative Algebra<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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> 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                            Learn the concepts of commutative algebra in relation to applications in algebraic number theory, algebraic geometry and other fields of mathematics.                        <\/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 successful students possesses deepened and extended knowledge of the topics treated in Commutative Algebra.                    <\/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>In number theory one is naturally led to study more general numbers than just the classical integers and, thus, to introduce the concept of integral elements in number fields. The rings of integers in number fields have certain very beautiful properties (such as the unique factorisation of ideals) which characterise them as Dedekind rings. Parallelly, in geometry one studies affine varieties through their coordinate rings. It turns out that the coordinate ring of a curve is a Dedekind ring if and only if the curve is non-singular (e.g. has no self-intersection).<\/p><p>With this in mind, we shall work towards the concept and the characterisation of Dedekind rings. Along the way, we shall introduce and demonstrate through examples basic concepts of algebraic geometry and algebraic number theory. Moreover, we shall be naturally led to treat many concepts from commutative algebra.<br>Depending on the previous knowledge of the audience, the lecture will cover all or parts of the following topics:<\/p><p>(1) General concepts in the theory of commutative rings<br><\/p><ul><li>rings, ideals and modules<\/li><li>Noetherian rings<\/li><li>tensor products<\/li><li>localization<\/li><li>completion<\/li><li>dimension<\/li><\/ul><p>(2) Number rings<\/p><ul><li>integral extensions<\/li><li>ideals and discriminants<\/li><li>Noether&#8217;s normalisation theorem<\/li><li>Dedekind rings<\/li><li>unique ideal factorisation<\/li><\/ul><p>(3) Plane Curves<\/p><ul><li>affine space<\/li><li>coordinate rings and Zariski topology<\/li><li>Hilbert&#8217;s Nullstellensatz<\/li><li>resultant and intersection of curves<\/li><li>morphisms of curves<\/li><li>singular points <\/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>Combined evaluation (final exam and continuous evaluation)<br><\/p><br><p><br>First session<br><\/p><br><ol><br><li>A mark for continuous assessment, counting 40% of the final mark<\/li><br><li>A mark for the end-of-course exam, counting 60% of the final mark.<\/li><br><\/ol><br><p>The mark for the continuous assessment is the arithmetic mean of the marks for three supervised exercises. In the case of a justified absence, a supervised exercise is replaced by an oral exam. <\/p><br><p><br>Retake exam<br>Oral exam<\/p><br>Absence plan\u00a0<br><br>In the case of a justified absence, a supervised exercise is replaced by an oral exam.<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>Note \/ Literature \/ Bibliography<br><br><br><\/p><br><ul><br><li>Lecture notes, exercise sheets (available on Moodle)<\/li><br><li>E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry<\/li><br><li>Dino Lorenzini. An Invitation to Arithmetic Geometry, Graduate Studies in Mathematics, Volume 9, American Mathematical Society<\/li><br><li>M. F. Atiyah, I. G. Macdonald. Introduction to Commutative Algebra, Addison-Wesley Publishing Company.<\/li><br><\/ul><br><br><br><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-69d3d943e3683\"\n        >\n            <span class=\"accordion__title\">\n                Probability: theory and models                <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                            MA_DS-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-69d3d943e3683\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Probability: theory and models<\/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> MA_DS-31<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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>At the end of the course, a student should be familiar with the basic concepts of probability theory (event, random variables, distributions) and master the tools that allow him or her to make calculations (calculations of expectations, variances, distributions etc).\u00a0<\/li><br><li>The student should also be able to master the law of the large numbers as well as the central limit theorem.\u00a0<\/li><br><li>He or she must be able to calculate limit distributions of some sequence of random variables by means of the Delta method and Slutsky\u2019s lemma.\u00a0<\/li><br><li>Given an integral, the student should also be able to provide a probabilistic approximation of it and assess the probability of error.\u00a0\u00a0<\/li><br><li>The student should be able to provide a qualitative and quantitative analysis of some random phenomena which are modeled by Markov chains.\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>The first part of the course introduces the basic concepts and tools associated with Probability Theory.\u00a0<\/p><ul><li>What is an event, the probability of an event, a random variable?<\/li><li>What are the main notations associated with probability theory?<\/li><li>What is a law or a distribution?\u00a0<\/li><li>The main probability distributions: Bernoulli, binomial, Poisson, uniform, exponential, Cauchy, Gaussian. What random phenomena do they model?\u00a0<\/li><li>What is a density with respect to the Lebesgue measure? What is a density with respect to the counting measure?\u00a0<\/li><li>What is the distribution of a random variable?<\/li><li>What is the expectation (or mean) of a random variable? How can we interpret it?\u00a0<\/li><li>What is the variance of a random variable?<\/li><li>How to calculate the probability that a random variable belongs to a set from its distribution? How to calculate the expectation of a function of a given random variable from its distribution?\u00a0<\/li><li>What is a distribution function? What are its properties? What link densities and distribution functions?\u00a0<\/li><li>What are the quantiles of a real-valued random variable? What are the median and quartiles of a random variable?<\/li><li>The main inequalities: the Markov inequality, the Bienaym\u00e9-Tchebychev inequality, the Jensen inequality.<\/li><li>What does it mean that two random variables are independent? What is the density of a pair of independent random variables? How to generalize to n independent random variables?\u00a0<\/li><li>What is a random vector? What are the marginal distributions? How to calculate them?<\/li><li>How to calculate the distributions of random variables (from distribution functions, change of variables)<\/li><li>What does it mean that a sequence of random variables converges almost surely? In probability? In distribution? What are the connections between these convergence modes?<\/li><li>What is Law of large numbers? What is the Monte Carlo method for calculating integrals?<\/li><li>What is the central limit theorem? What is the Delta method and Slutsky\u2019s lemma?<\/li><\/ul><p>In the second part of the course, we study Markov Chains with values in a finite or countable space. We see the following concepts and tools.<\/p><ul><li>What is a Markov chain? A transition matrix? An invariant measure?<\/li><li>What is a recurrent state?\u00a0 A transient state? How can we classify the states?\u00a0<\/li><li>What is a stopping time? What the strong Markov property?\u00a0<\/li><li>What is the Ergodic Theorem?\u00a0<\/li><\/ul><p>We show how these notions can be used to study random walks, the gambler\u2019s ruin and the spread of pandemics (among others examples).<\/p>\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                        First session<br><br>Combined assessment (end of course assessment + continuous assessment).<br>Midterm exam and a final exam during the exam season.<br>Retake exam<br>For those of you who are retaking the exam, the final grade will be an oral exam which is organized during the exam season.\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>Note &#8211; Literatur<br><\/p><br><p>Measure Theory, Probability, and Stochastic Processes<br>Jean-Fran\u00e7ois Legall, SPRINGER<\/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-69d3d943e3692\"\n        >\n            <span class=\"accordion__title\">\n                Functional Analysis                <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                            F1_MA_MAT_MMCS2-2                        <\/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-69d3d943e3692\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Functional Analysis<\/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> F1_MA_MAT_MMCS2-2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                                <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 aim of the course is to provide students with efficient tools to study linear operators between infinite dimensional vector spaces. In particular, this class will deal with normed vector spaces, Banach and Hilbert spaces, with bounded linear operators on normed vector spaces, fundamental principles such as Fourier analysis, Lebesgue integral, Han-Banach Theorem, Uniform Boundedness Principle or Closed Graph Theorem, and with spectral theory of compact (self-adjoint) linear operators.\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 will acquire a solid understanding of functional analysis, its fundamental results and basic techniques. In particular, students will understand applications to measure theory, Fourier theory, and the spectral theorem for (unbounded) operators. Students will know the relevance of a theorem, its underlying motivation and a precise idea of its proof. Hopefully, students will demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from functional analysis.\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                        Functional analysis aims to study infinite-dimensional spaces of functions and features of linear operators on these spaces. Though, from the point of view of Mathematics, functional analysis has its own interest, it plays a crucial role in many related areas, in particular in Physics, Engineering or Finance. Roughly speaking, most \u201creal-life problems\u201d involve non-linear partial differential equations with infinite-dimensional solution spaces of functions (or distributions). This course provides Master students with the basic tools and the fundamental results to develop skills to solve such problems.                    <\/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 modality for the first session<br><\/p><br><ul><br><li>Written test on week of October 28, duration 1 hour, 30% of the final grade,<\/li><br><li>Final written exam (scheduled by the administration), 60% of the final grade,<\/li><br><li>Written homework (problems to be determined), 10% of the final grade.<\/li><br><\/ul><br><p><br>Exam modality for the retake exam<br>Retake exam (scheduled by the administration) will be in written form.<\/p><br><p><br>Absence<br>A make-up will be possible only for an unavoidable reason supported by a proof.<\/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>Introductory Functional Analysis with Applications, by Erwin Kreyszig.<br>Functional Analysis, Spectral Theory and Applications, by Manfred Einsiedler and Thomas Ward.<br>An Introduction to Fourier Analysis, by Russell L. Herman                    <\/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-69d3d943e369f\"\n        >\n            <span class=\"accordion__title\">\n                Riemann 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                            8                        <\/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_MAT_GM-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-69d3d943e369f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Riemann Surfaces<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-13<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                                <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                            Understand and be able to use and apply the key notions related to Riemann surfaces: definitions, key examples, maps between Riemann surfaces, integration on Riemann surfaces, divisors and meromorphic functions, algebraic curves and the Riemann-Roch theorem.\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                        At the end of the course the students should have a basic understanding of what Riemann surfaces are and how they can be studied from different points of view, especially the complex and topological one. They should be able to understand and solve simple problems involving the material from the 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                        Riemann surfaces lie at the crossroads of many fields of research of modern mathematics: topology, complex and algebraic geometry, number theory and harmonic analysis, among others.\u00a0<br>The course will cover the basic notions of the theory, starting from the definition of a complex manifold, and move on to the classification of Riemann surfaces via the study of their divisors. This will allow the students to acquire familiarity with some ubiquitous tools from complex geometry, such as the Riemann-Roch theorem.\u00a0<br>We will put some focus on examples along the way. If time allows, we will see how some constructions from the complex analytic theory can be reinterpreted in the language of modern algebraic geometry, bridging the gap between the two worlds, and we will touch some more advanced topics that could inspire the students\u2019 further work.<br>The course will mostly follow the first chapters of the book by R. Miranda, Algebraic curves and Riemann surfaces.\u00a0<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>Combined evaluation (final exam and continuous evaluation)<\/p><br><p><br>First session<br><br>Weekly exercise will be provided and the students will be asked to present some of them orally. This will provide for continuous evaluation that will make up for 1\/3 of the grade. The remaining 2\/3 will be given by the result of a final oral exam.<\/p><br>Retake exam\u00a0<br><br>Students who fail the exam can do a retake exam at the end of the following semester.<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>Note \/ Literature \/ Bibliography<br><br><br><\/p><br><ul><br><li>Rick Miranda, Algebraic Curves and Riemann Surfaces.<\/li><br><li>Martin Schlichenmaier, An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces.<\/li><br><li>Wilhelm Schlag, A concise course in complex analysis and Riemann surfaces<\/li><br><li>Curtis McMullen, Courses notes, Complex analysis and Riemann surfaces (available online)<\/li><br><li>J. Jost, Compact Riemann surfaces<br>The above texts are available either online or on a-z.lu. More references will be provided during the course.<\/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-69d3d943e36ac\"\n        >\n            <span class=\"accordion__title\">\n                Partial Differential Equations I                <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                            F1_MA_MAT_GM-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-69d3d943e36ac\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Partial Differential Equations I<\/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> F1_MA_MAT_GM-3<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                                <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 goal of the course it to get acquainted with Partial differential equations (PDE) as a powerful tool for modeling problems in science, providing functional analytic techniques in order to deal with PDE.                        <\/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:\u00a0<\/p><br><ul><br><li>Apply methods of Fourier Analysis to the discussion of constant coefficient differential equations<\/li><br><li>Work freely with the classical formulas in dealing with boundary value problems for the Laplace equation<\/li><br><li>Prove acquaintance with the basic properties of harmonic functions (maximum principle, mean value property) and solutions of the wave equation (Huygens property)<\/li><br><li>Solve Cauchy problems for the heat and the wave equations<\/li><br><li>Give a pedagogic talk for peers on a related topic\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                        Fourier transform, the classical equations, spectral theory of unbounded operators, distributions, fundamental solutions.                    <\/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 exam                    <\/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>Literatur<br><\/p><br><ol><br><li>Rudin: Functional analysis<\/li><br><li>Jost: Postmodern analysis<\/li><br><li>Folland: Introduction to partial differential equations.<\/li><br><li>Reed-Simon: Methods of mathematical physics I-IV<\/li><br><\/ol>                    <\/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-69d3d943e36ba\"\n        >\n            <span class=\"accordion__title\">\n                Scientific Python                <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                            1                        <\/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_MAT_MMCS2-4                        <\/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-69d3d943e36ba\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Scientific Python<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_MMCS2-4<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                                <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>Introduction<\/li><br><li>Getting started<\/li><br><li>Basics of Python<\/li><br><li>Array computations with numpy<\/li><br><li>Array computations with numpy (cont.)<\/li><br><li>Plotting with matplotlib<\/li><br><li>Tabular data manipulation with pandas<\/li><br><li>Tabular data manipulation with pandas (cont.)<\/li><br><li>Writing good quality and robust Python code<\/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                        First session<br><p>You should feel comfortable writing basic scientific programs in Python, and be able to participate fully in future courses that require an element of programming.<\/p><br><p><br>Retake exam<br>Retake exam not possible, course must be retaken.<\/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                        This course covers the basics of scientific programming with Python. It is aimed at people who have done some programming before, perhaps on an undergraduate course, but need a refresher before starting their Masters or Doctoral degrees at the University.<br>https:\/\/jhale.github.io\/scientific-python\/\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                        A coursework will be distributed at the end of the class. To pass the course and receive the ECTS credits you must complete the coursework.                    <\/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-69d3d943e36c7\"\n        >\n            <span class=\"accordion__title\">\n                The mathematics of networks: theory and algorithms                <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                            MA_DS-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-69d3d943e36c7\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> The mathematics of networks: theory and algorithms<\/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> MA_DS-8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                                <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>On successful completion of the course the students should be able to<\/p><br><ul><br><li>understand the relevance of the topics covered in the course for their applications,<\/li><br><li>master the proofs of the main results of the course,<\/li><br><li>solve problems using the toolkit developed in the course<\/li><br><li>be autonomous in learning in the field of Graph Theory.<\/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>Through a presentation of selected topics, the course aims to be an introduction to graph theory, its applications and its algorithmic aspects. It is designed as a self-contained course and focused on problems pertaining to Data Science. <\/p><p>Possible topics for the course include, but are not limited to<\/p><ul><li>Graphs and digraphs, degree and the degree sequence algorithm<\/li><li>Connectedness, distance, shortest paths and connected components algorithms<\/li><li>Graph matching problems and algorithms<\/li><li>Elements of algebraic graph theory and PageRank algorithm<\/li><li>Graph traversal algorithms<\/li><li>Trees and applications<\/li><li>Minimum spanning tree algorithms<\/li><li>Network flow, min cut \u2013 max flow theorem and Ford\u2013Fulkerson algorithm<\/li><li>Centrality and betweness measures<\/li><li>Cluster analysis<\/li><li>Random Graphs<\/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><\/p>Written exam and homework, and possibly algorithm implementation project during the semester.\u00a0\u00a0<br>Retake exam\u00a0<br>Writen exam<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>Note \/ Literature \/ Bibliography<br><\/p><br><ul><br><li>R. Diestel, Graph Theory, Springer, 2017<\/li><br><li>D. Jungnickel, Graphs, Networks and algorithms, Springer 2017<\/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-69d3d943e36d4\"\n        >\n            <span class=\"accordion__title\">\n                Elementary mathematics from a higher viewpoint I                <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_MA_MAT_GM-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-69d3d943e36d4\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Elementary mathematics from a higher viewpoint I<\/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_MA_MAT_GM-33<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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> 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                        Les \u00e9tudiant\u00b7e\u00b7s vont revisiter leurs connaissances des math\u00e9matiques de fin de secondaire. En parall\u00e8le, ils\u00b7elles aborderont ces sujets sous un angle nouveau, gr\u00e2ce \u00e0 leur ma\u00eetrise des math\u00e9matiques de niveau sup\u00e9rieur. Les \u00e9tudiant\u00b7e\u00b7s du MSE-M Master devront \u00eatre capable de r\u00e9pondre aux questions possibles de leur futur\u00b7e\u00b7s \u00e9l\u00e8ves.                    <\/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                        Le cours explorera les th\u00e9matiques des math\u00e9matiques de fin de secondaire sous un angle plus abstrait. Les concepts universitaires seront utilis\u00e9s pour revisiter les math\u00e9matiques du secondaire et pour approfondir la th\u00e9orie derri\u00e8re chaque formule. Des questions de compr\u00e9hension et des liens entre diff\u00e9rents sujets seront \u00e9galement abord\u00e9s.<br>Attention: les th\u00e9matiques abord\u00e9es sont divis\u00e9es en deux groupes et sont trait\u00e9es en alternance chaque ann\u00e9e.<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                        Exam modalities for the first session<br>3 midterms (50% of the final mark) and 1 written exam in january (50 % of of the final mark).<br>Exam modalities for the retake exam<br>1 written exam (100 % of final mark)<br>Absence plan<br>if justified absent during midterms, an oral exam will be organised about the same material, if justified absence during the written exam, an oral exam will take place                    <\/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-69d3d943e36e1\"\n        >\n            <span class=\"accordion__title\">\n                Student project 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                            F1_MA_MAT_GM-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-69d3d943e36e1\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Student project 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> F1_MA_MAT_GM-7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 1<\/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                \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 project the student should be able to:<\/p><br><ul><br><li>analyse complex tasks<\/li><br><li>propose solution strategies,<\/li><br><li>break up a longer project into subsequent steps,<\/li><br><li>apply a variety of methods in one project,<\/li><br><li>present a task and its solution in a scientific way.<\/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                        The ability to work on a project, either individually or as part of a team, is one of the key skills expected of a mathematician, in and outside academia. The Student Project offers the student the opportunity to improve this skill by allowing them to work on a well-defined and well chosen project, either individually or as a team, under the guidance of a researcher.<br>The Student Project consists of project work that is carried out under the supervision of a researcher. The work is either individual or group work. At the beginning of the project, supervisor and student(s) define tasks to be carried out by the student(s), corresponding to the volume of 100 working hours (4 ECTS) for each student. The student(s) need to submit the planned topic to the course responsible for approval at the latest on 15 October (Student Project 1,3) or 15 March (Student Project 2). The project outcome is a pdf document written by the student(s). Additional outcomes (such as computer code, images, videos) can be asked for. The required outcome has to be handed in on Moodle at the latest on 31 December (Student Project 1,3) or 31 May (Student Project 2). The project file will undergo an automatic plagiarism and AI check.<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 marked for their project work.<br>In the case of a retake exam, a new project has to be done. The retake can be done with other supervisors.<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<br>Depends on the project.                    <\/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-69d3d943e36ee\"\n        >\n            <span class=\"accordion__title\">\n                Student seminar 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                            1                        <\/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_MAT_GM-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-69d3d943e36ee\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Student seminar 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 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                        <p>On successful completion of the Student Seminar 1, the students should be able to:<\/p><br><ul><br><li>Acquire good insight into a field by means of individual work<\/li><br><li>Deliver a mathematical lecture on a topic of their choice<\/li><br><li>Share their knowledge with others<\/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                        Every participant chooses a supervisor among the academic staff of the Department of Mathematics or among the instructors of the Master in Mathematics and, jointly with the supervisor, a topic for a talk.<br>The audience of the talk consists at least of the participants of the Student Seminar 1, the supervisor and one other academic staff member of the Department of Mathematics (e.g. the supervisor of another talk). The duration of the talk is 40 minutes (time for questions included).                    <\/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 evaluation is based on the quality of the talk delivered by the student                    <\/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>Depends on the subject and is communicated by the chosen supervisor                    <\/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-69d3d943e36fb\"\n        >\n            <span class=\"accordion__title\">\n                Applied Didactics I &amp; III: Didactics of 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                            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                            F1_SECEDUC-32                        <\/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-69d3d943e36fb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Applied Didactics I &amp; III: Didactics of Geometry<\/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> F1_SECEDUC-32<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 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> 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                            One aim is training the participants in formulating definitions, theorems, and counterexamples, while refreshing their notions of geometry that is accessible to school pupils. Parallel to that we will discuss the recommendations provided by didacticians for teaching geometry in schools most effectively.                        <\/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 participants will refresh their knowledge of geometry and will have revisited school mathematics from a higher viewpoint. They will also have learned didactical approaches tailored to this subject.                    <\/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 is about geometry that is taught in schools or that is taught to school pupils that train for mathematical competitions.\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>First session<br><\/p><br><ul><br><li>30% presentation<\/li><br><li>70% written exam<\/li><br><\/ul><br>Retake exam\u00a0<br><ul><li>Written exam<\/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>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note \/ Literature \/ Bibliography<br><\/p><br><p>We will access to literature in English, French, and German. The literature will include books and articles of Geometry and Didactics of geometry, plus online references. The up-to-date list of references will be made available on 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-69d3d943e3708\"\n        >\n            <span class=\"accordion__title\">\n                Internship in a secondary school I                <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                            0                        <\/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_SECEDUC-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-69d3d943e3708\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Internship in a secondary school I<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 0<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_SECEDUC-17<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 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                \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                        Validated in S2<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-69d3d943e3715\"\n        >\n            <span class=\"accordion__title\">\n                Applied Didactics II: Pr\u00e9paration de le\u00e7ons de 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                            F1_SECEDUC-16                        <\/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-69d3d943e3715\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Applied Didactics II: Pr\u00e9paration de le\u00e7ons de 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> F1_SECEDUC-16<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 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 la conception de situations d&#8217;apprentissage.                        <\/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, les \u00e9tudiants devront \u00eatre capables de concevoir des s\u00e9quences d&#8217;apprentissage structur\u00e9es et coh\u00e9rentes en math\u00e9matiques, en s&#8217;appuyant sur une formulation claire et mesurable des objectifs d&#8217;apprentissage. Ils devront ma\u00eetriser diverses techniques de questionnement leur permettant de stimuler efficacement la r\u00e9flexion des \u00e9l\u00e8ves et \u00eatre capables d&#8217;int\u00e9grer des strat\u00e9gies de diff\u00e9renciation p\u00e9dagogique adapt\u00e9es dans leurs le\u00e7ons, assurant ainsi un enseignement qui r\u00e9pond aux besoins vari\u00e9s des apprenants.<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                        <p>Ce cours est con\u00e7u comme une pr\u00e9paration essentielle au stage pratique pour les futurs enseignants de math\u00e9matiques. Il vise \u00e0 d\u00e9velopper les comp\u00e9tences n\u00e9cessaires \u00e0 la conception et \u00e0 la mise en \u0153uvre de le\u00e7ons efficaces. Les \u00e9tudiants seront form\u00e9s aux aspects essentiels de la planification, de la didactique et de l&#8217;\u00e9valuation en math\u00e9matiques. Ils apprendront \u00e0 structurer des s\u00e9quences d&#8217;apprentissage, \u00e0 formuler des objectifs clairs, \u00e0 d\u00e9velopper des strat\u00e9gies de questionnement efficaces, et \u00e0 int\u00e9grer des m\u00e9thodes d&#8217;\u00e9valuation formative.\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>Premi\u00e8re session d\u2019examen<br><br>L&#8217;\u00e9valuation du cours combinera contr\u00f4le continu (20%) et examen final (80%). Le contr\u00f4le continu \u00e9valuera la participation en classe et les travaux r\u00e9guliers, r\u00e9alis\u00e9s individuellement ou en groupe. L&#8217;examen final comprendra une pr\u00e9paration \u00e9crite de le\u00e7ons (60% de la note finale) et une soutenance orale (20%).<\/p><br>\u00c9valuation lors d&#8217;une deuxi\u00e8me session (rattrapage)<br><br>L\u2019\u00e9valuation reposera enti\u00e8rement sur un examen final (100% de la note). Celui-ci consistera en une pr\u00e9paration \u00e9crite de le\u00e7ons (75% de la note) suivie d&#8217;une soutenance orale (25%).\u00a0<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>Note \/ Literature \/ Bibliography<br><\/p><br><ul><br><li>Astolfi, J.-P. (2024). L&#8217;erreur, un outil pour enseigner. Paris : ESF \u00c9diteur.<\/li><br><li>Barzel, B., B\u00fcchter, A., Leuders, T. (2007). Mathematik Methodik, Handbuch f\u00fcr die Sekundarstufe I und II. Cornelsen.<\/li><br><li>B\u00fcchter, A., Leuders, T. (2005). Mathematikaufgaben selbst entwickeln, Lernen f\u00f6rdern \u2013 Leistung \u00fcberpr\u00fcfen. Cornelsen.<\/li><br><li>Hattie, J. (2010). Visible Learning. Routledge.<\/li><br><li>Jonnaert, P., Vander Borght, C. (2003). Cr\u00e9er des conditions d&#8217;apprentissage. Bruxelles : De Boeck.<\/li><br><li>Leuders, T. (2020). Mathematikdidaktik (9e \u00e9dition). Cornelsen.<\/li><br><li>Leuders, T., Prediger, S. (2016). Flexibel differenzieren und fokussiert f\u00f6rdern im Mathematikunterricht. Cornelsen.<\/li><br><li>Malle, G. (1993). Didaktische Probleme der elementaren Algebra. Vieweg.<\/li><br><li>Meyer, H. (1989). Unterrichtsmethoden. I: Theorieband und II: Praxisband. Berlin: Cornelsen Scriptor.<\/li><br><li>Morissette, R. (2002). Accompagner la construction des savoirs. Montr\u00e9al: Cheneli\u00e8re\/McGraw-Hill.<\/li><br><li>Rieunier, A. (2018). Pr\u00e9parer un cours. Tome 1. Applications pratiques. Paris : ESF.<\/li><br><li>Rieunier, A. (2012). Pr\u00e9parer un cours. Tome 2. Les strat\u00e9gies p\u00e9dagogiques efficaces. Paris : ESF.<\/li><br><li>Sill, H.-D. (2018). Grundkurs Mathematikdidaktik. UTB.<\/li><br><li>Sturm, R. (2016). Schritt f\u00fcr Schritt zum guten Mathematikunterricht. Klett Kallmeyer.<br><\/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-69d3d943e3722\"\n        >\n            <span class=\"accordion__title\">\n                Einf\u00fchrung in die Schulp\u00e4dagogik                <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                            F3_SECEDUC-197                        <\/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-69d3d943e3722\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Einf\u00fchrung in die Schulp\u00e4dagogik<\/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> F3_SECEDUC-197<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competences I &#8211; Forschungsfeld Schule<\/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> 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                \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><br>Die Studierenden haben gelernt:<br><\/p><br><ul><br><li>Sinn, Absicht und Realit\u00e4t von Schule unter einem historischen, p\u00e4dagogischen udn soziologischen Blickwinkel zu analysieren<\/li><br><li>Den Lehrerberuf als Profession zu verstehen<\/li><br><li>Den Zusammenhang von Bildung, Bildungszielen und Bildungspl\u00e4nen zu erkennen<\/li><br><li>Lernen als sozialen Prozess zu beschreiben<\/li><br><li>Verschiedene Ideen davon, was &#8220;guten Unterricht&#8221; ausmacht zu diskutieren<\/li><br><\/ul><br><p>\u00a0<\/p><br><p><br>Die Studierenden sind in der Lage:<br><\/p><br><ul><br><li>Professionelle Standards von Lehrerhandeln umzusetzen<\/li><br><li>Die Bedingungen des luxemburgischen Schulsystems zu analysieren und verschiedene Theorien zur Unterrichtsqualit\u00e4t und Diagnostik anzuwenden.<\/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                        Die Vorlesung &#8220;Einf\u00fchrung in die Schulp\u00e4dagogik&#8221; analysiert die (luxemburgische) Schule als eine historisch gewachsene Institution, die ganz unterschiedlichen Zwecken dient bzw. dienen soll. Dabei stehen p\u00e4dagogische, soziologische und historische Erkl\u00e4rungsans\u00e4tze im Mittelpunkt der Beschreibung schulischer Wirklichkeiten. Zudem werden der Lehrerberuf sowie die Schulentwicklung (Curricula, Bildungsziele, etc.) auf ihre professionellen Begr\u00fcndungen hin vorgestellt und hinterfragt. Die Vorlesung f\u00fchrt ebenfalls in die wichtigsten Ideen zum Thema &#8220;Lernen&#8221; und zur Unterrichtsqualit\u00e4t ein.                    <\/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                        End-of-term Assessment: Klausur.                    <\/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>Ludwig Haag, Sibylle Rahm, Hans J\u00fcrgen Apel, Werner Sacher (Hrsg.): Studienbuch Schulp\u00e4dagogik. Verlag Julius Klinkhardt 2013.\u00a0<\/li><br><\/ul><br><ul><br><li>Hanna Kiper, Hilbert Meyer, Wilhelm Topsch (Hrsg.): Einf\u00fchrung in die Schulp\u00e4dagogik. Cornelsen Verlag 2011.\u00a0<\/li><br><li>Ilona Esslinger-Hinz, Anne Sliwka (Hrsg.): Schulp\u00e4dagogik. Beltz Verlag 2011.<\/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-69d3d943e372f\"\n        >\n            <span class=\"accordion__title\">\n                Informationveranstaltung \/ R\u00e9union de rentr\u00e9e &#8211; Cours Communs                <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                            0                        <\/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                            F3_SECEDUC-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-69d3d943e372f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Informationveranstaltung \/ R\u00e9union de rentr\u00e9e &#8211; Cours Communs<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 0<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F3_SECEDUC-171<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competences I &#8211; Forschungsfeld Schule<\/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                \n                \n                \n                \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-69d3d943e373c\"\n        >\n            <span class=\"accordion__title\">\n                Workshop zum orientierenden Schulpraktikum (MES MATH)                <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                            0                        <\/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                            F3_SECEDUC-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-69d3d943e373c\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e3625\">\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> Workshop zum orientierenden Schulpraktikum (MES MATH)<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 0<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F3_SECEDUC-217<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competences I &#8211; Forschungsfeld Schule<\/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                \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>Die Studierenden &#8230;<\/p><br><ul><br><li>kennen die wichtigsten diagnostischen Instrumente der Unterrichtsbeobachtung und ihre Funktion.<\/li><br><li>reflektieren vor dem Hintergrund ihrer eigenen Schulerfahrungen, Aspekte und G\u00fctekriterien von Lehr-Lernsituationen nach Andreas Helmke.<\/li><br><li>kennen die Merkmale guten Unterrichts nach Hilbert Meyer.<\/li><br><li>kennen die Grundstruktur eines Unterrichtsentwurfs.<\/li><br><li>kennen die Grundstruktur eines Stundenverlaufplans sowie die verschiedenen Phasierungsschritte von Unterricht.<\/li><br><li>kennen die Basisformen des Lehrens und Lernens sowie g\u00e4ngige Unterrichtsmethoden und Methoden des kooperativen Lernens.<\/li><br><li>reflektieren die wesentlichen Eckpunkte und Rahmenbedingungen, die sie bei der Vorbereitung, Durchf\u00fchrung und Reflexion eigener Unterrichtsversuche beachten m\u00fcssen.<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                        <p>Das Tutorium fokussiert auf die praxisorientierte Umsetzung diagnostischer Verfahren zur Vorbereitung der Unterrichtshospitation wie auch auf Gestaltungsm\u00f6glichkeiten von Unterricht zur Vorbereitung der eigenen Unterrichtspraxis im Rahmen des orientierenden Praktikums.<\/p><p>Dar\u00fcberhinaus werden eigene Wissens- und Erfahrungsst\u00e4nde der Studierenden gemeinsam mit den das Praktikum begleitenden Lehrpersonen reflektiert, um individuelle Entwicklungsziele und Forschungsinteressen f\u00fcr das Masterstudium zu identifizieren.<\/p><p>Das Tutorium ist an das Seminar Mehrsprachigkeit im Sprach- und Fachunterricht: L&#8217;importance des diff\u00e9rents langages en math\u00e9matiques (appliqu\u00e9e au syst\u00e8me \u00e9ducatif luxembourgeois) angekoppelt. <\/p>                    <\/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>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Bibliografie:<br><\/p><br><p>Ein Reader mit Grundlagentexten wird zu Beginn des Semesters \u00fcber Moodle zur Verf\u00fcgung gestellt. <\/p>                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-23b79609-5280-485b-8354-8fa0d0d944e3\"\n    aria-labelledby=\"tab-23b79609-5280-485b-8354-8fa0d0d944e3\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Math\u00e9matiques, Semestre 2 (2025-2026 Summer)<\/h3>\n    \n<div id=\"accordion-module-69d3d943e9c2b\" 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-69d3d943e9c62\"\n        >\n            <span class=\"accordion__title\">\n                Riemannian 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                            8                        <\/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_MAT_GM-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-69d3d943e9c62\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Riemannian Geometry<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-2<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                        <p>On successful completion of the course, the student should be able to:<br><\/p><br><ul><br><li>compute with tensors, such as metrics and curvature, in coordinates or coordinate-free<\/li><br><li>demonstrate detailed knowledge of the exponential map, including criteria for completeness, conjugate points, and Jacobi fields<\/li><br><li>understand multiple interpretations of curvature, for example, as the obstruction to a local parallel framing, or how it influences the spreading of geodesics via the Jacobi equation<\/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                        This foundational Master-level course is centered around the concepts of connection on a manifold and curvature. These are investigated in further depth in the setting of Riemannian or Lorentzian metrics, where the geometry of geodesics and its relation to curvature are studied.\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>First session<br>Oral or 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>Literatur<br><br><br><\/p><br><ul><br><li>M. P. do Carmo, Riemannian Geometry, Birkh\u00e4user (1992)<\/li><br><li>B. O\u2019Neill, Semi-Riemannian Geometry with applications to Relativity, Elsevier (1983)<\/li><br><li>John M. Lee, Introduction to Smooth Manifolds (2nd edition), Springer (2012)<\/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-69d3d943e9c7e\"\n        >\n            <span class=\"accordion__title\">\n                Mathematical Statistics                 <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                            MA_DS-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-69d3d943e9c7e\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Mathematical Statistics <\/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> MA_DS-35<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                        In parametric models, a successful student should be is able to establish the main properties (consistency, asymptotic normality, etc) of the most classical estimators, provide (possibly asymptotic) confidence regions and tests between two hypotheses.\u00a0\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                        The main problems of mathematical statistics: estimation, testing, the notion of risk. Construction of confidence intervals and tests. False discovery rate. The empirical measure and its applications: the moment method, estimation by empirical quantiles, the Kolmokorov-Smirnov Test. The maximum likelihood estimator. Exponential families in one dimension. Introduction to the Bayes paradigm and elements of decision theory.                    <\/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>A partial written exam and a final written exam.<\/p><br><p><br>Retake exam<br><\/p><br>The retake\u00a0exam will consist of a written test that will be the same as that taken by other students sitting the exam\u00a0for the first time.\u00a0\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>Literatur<br><\/p><br><ul><br><li><br>For probability theory: Real Analysis and Probability, R.M. Dudley<\/li><br><li>For statistics: Mathematical Statistics, P. Bickel and K. Doksum<\/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-69d3d943e9c8b\"\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-69d3d943e9c8b\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Specialisation &#8211; Mathematics 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                            <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><br>Written exam.<\/p><br><p><br>Retake session<br><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><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-69d3d943e9c98\"\n        >\n            <span class=\"accordion__title\">\n                Advanced Graph Theory                 <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                            F1_MA_MAT_GM-16                        <\/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-69d3d943e9c98\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Advanced Graph Theory <\/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> F1_MA_MAT_GM-16<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                            <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>On successful completion of the course, the student should be able to\u00a0<\/p><br><ul><br><li>Illustrate the main results and concepts with well-chosen examples<\/li><br><li>Master the proofs and techniques of the theory\u00a0<\/li><br><li>Solve exercises related to the topics covered in class\u00a0<\/li><br><li>Give an overview of the course content, focusing on his\/her own taste and favorite topics\u00a0<\/li><br><li>Communicate his\/her own pleasure in solving mathematical problem\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>Graphs are structures that are ubiquitous in Mathematics and its applications. Through a presentation of selected topics, the course aims to be an introduction to certain modern aspects of graph theory. <br>Some basic knowledge of the concept of graphs is a prerequisite for this course.<br>According to time and taste, topics covered will be chosen among (and are not limited to) the following ones:<br><\/p><ul><li>Matching, covering and packing problems<\/li><li>Edge and vertex colorings<\/li><li>Graph polynomials<\/li><li>Ramsey theory for graphs<\/li><li>Infinite Graph Theory<\/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                        Oral exam or written exam according to number of participants<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>Literatur<br><\/p><br><ul><br><li>Reinhard Diestel. Graph Theory, 5th edition. Graduate texts in mathematics 173, Springer, 2017<\/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-69d3d943e9ca4\"\n        >\n            <span class=\"accordion__title\">\n                Algebraic Number Theory                 <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                            F1_MA_MAT_GM-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-69d3d943e9ca4\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Algebraic Number Theory <\/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> F1_MA_MAT_GM-14<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                            Introduce the students to Algebraic Number Theory. Reinforce students\u2019 understanding of commutative algebra. Upon successful completion of the course, the students will understand the basic notions of algebraic number theory and be able to solve simple problems in that area. They will have an awareness that many questions in algebraic number theory, even seemingly simple equations, give rise to a wealth of deep mathematics. More specifically, they will be able to study in detail the question which primes can be written in the form x^2 + ny^2, and solve Mordell\u2019s equation.<br><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>\u00a0<\/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>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p>1. Review of finite fields, Legendre symbol, quadratic reciprocity<\/p><p>2. Primes of the form x^2 + ny^2, Mordell\u2019s equation<\/p><p>3. Principal ideal domains and unique factorization domains, Euclidean rings<\/p><p>4.Orders and maximal orders, rings of integers, Dedekind domains, prime ideal factorisation<\/p><p>5. Class group, class number, Minkowski\u2019s theorem and finiteness<\/p><p>6. Quadratic forms, genus theory<\/p><p>7.\u00a0\u00a0Units in real quadratic fields, Pell\u2019s equation, fundamental unit, continued fraction algorithm<\/p><p>8. Dirichlet\u2019s Unit Theorem in general number fields<\/p><p>9.Statement of main results of class field theory, Hilbert class fields and ring class fields<\/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>Student Presentation (30%)<br><\/p><br><p><br>During the semester, each student gives one presentation in front of the class. The topic, to be agreed upon with the lecturer, can also be an interesting example or an exercise, but must contain at least one non-trivial argument.<br><\/p><br><p><br>Final Exam (70%)<br><\/p><br><p><br>A final written exam will assess their understanding of the course material covered in the semester.<br><\/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                        <p><br>Course notes will be provided. However, students may benefit from consulting various sources on Algebraic Number Theory. References with relevant material for this course include:<br><\/p><br><p><br>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br>Peter Stevenhagen, Number Rings, https:\/\/websites.math.leidenuniv.nl\/algebra\/ant.pdf<br><\/p><br><p><br>&#8211;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Primes of the Form x^2 + ny^2, David A. Cox, 2013, Online ISBN:9781118400722<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-69d3d943e9cb0\"\n        >\n            <span class=\"accordion__title\">\n                Algebraic Topology                 <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                            8                        <\/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_MAT_GM-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-69d3d943e9cb0\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Algebraic Topology <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-12<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                        <p>On successful completion of the course, the student should be able to:<\/p><br><ul><br><li>Explain the main definitions and results of Algebraic Topology;<\/li><br><li>Comment on new concepts;<\/li><br><li>Apply the new techniques and solve 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>Provide evidence for the mastery of the Mathematical Method.\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>Topology is a field of mathematics that deals with the fundamental properties of spaces. In the topological world, two spaces are considered identical if they can be continuously transformed into one another or more generally, if they are related by what topologists call homotopy equivalence. For example, a sphere and a pyramid are identical, as are a donut and a coffee cup\u2026 A main goal is therefore to classify spaces up to homotopy equivalence.<\/p><p>Algebraic topology uses algebraic methods to solve this and other topological problems. An important method is the search for algebraic homotopy invariants. In particular, we try to assign an algebraic object such as a group to each topological space and to prove that this group is invariant if we replace the space with a homotopy equivalent space. One of the proofs of the fundamental theorem of algebra uses an algebraic invariant.<\/p><p>The main homotopy invariants we discuss are the \u2018singular homology functor\u2019 and the \u2018homotopy functor\u2019. An amazing result called the Hurewicz isomorphism, shows that the first singular homology group and the (abelianized) first homotopy group of a space are two variants of the same information. Van Kampen&#8217;s theorem allows us to practice our understanding of category theory and to compute homotopy groups of larger spaces from those of smaller spaces from which they are constructed. The final chapter will highlight the relationship between the coverings of a space and subgroups of its first homotopy group.<\/p><p>The objective is to allow the student to familiarize himself with a very active field of mathematics, with broad applications throughout science. Beyond this goal, special emphasizes will be put on the Mathematical Method, i.e., the optimal technique to learn and apply mathematics. This method is the most important of the objectives of any study program in mathematics.<\/p><p>Fundamental concepts of homological algebra<br>Chain complexes, chain maps, chain homotopies, homology functor, connecting homomorphism, K\u00fcnneth isomorphism, simplicial and singular homology, homotopy invariance, examples and applications.<\/p><p>Homotopy groups<br>Algebra and topology (revision), first homotopy group, Hurewicz isomorphism, homotopy functor, homotopy invariance, typical examples and applications.<\/p><p>Van Kampen theorem<br>Free product with amalgamation, Van Kampen-Seifert theorem (basic, general and groupoid version), examples and applications (in particular: first homotopy group of a product and of a coproduct).<\/p>Covering space theory<br>Coverings of spaces, lifting property, coverings of groupoids, orbit categories, classifications and constructions of coverings, connections with the preceding chapters, examples and applications.<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                        Written exam\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>Literatur<br><br><br><\/p><br><ul><br><li>Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002 &#8211; Mathematics &#8211; 544 pages, ISBN-13: 978-0521795401\u00a0<\/li><br><li>Peter May, A concise course in Algebraic Topology, University of Chicago Press, 1999 &#8211; Mathematics &#8211; 243 pages, ISBN-13: 978-0226511832<\/li><br><li>Charles Weibel, An introduction to homological algebra, Cambridge studies in advanced mathematics 38, 1997, ISBN: 0-521-55987-1<\/li><br><li>Saunders Mac Lane, Categories for the Working Mathematician, Graduate Texts in Mathematics, 5(2), Springer, 1978, ISBN: 978-0-387-98403-2<\/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-69d3d943e9cbc\"\n        >\n            <span class=\"accordion__title\">\n                Partial Differential Equations II                 <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                            8                        <\/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_MAT_GM-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-69d3d943e9cbc\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Partial Differential Equations II <\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 8<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_MA_MAT_GM-15<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                            Learning tools in order to deal with PDE, understanding the interplay between local and global problems and techniques.                        <\/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                        Distributions as generalized functions continued, Sobolev spaces, elliptic regularity, elliptic operators on compact manifolds, some non-linear equations.\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                        Written exam                    <\/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>Literatur<br><\/p><br><ul><br><li>Jost: Postmodern analysis<\/li><br><li>Folland: Introduction to partial differential equations\u00a0<\/li><br><li>Reed-Simon: Methods of mathematical physics I-IV\u00a0<\/li><br><li>Aubin: Nonlinear analysis on manifolds<\/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-69d3d943e9cc7\"\n        >\n            <span class=\"accordion__title\">\n                Numerical solution of partial differential equations and applications                 <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                            F1_MA_MAT_MMCS2-7                        <\/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-69d3d943e9cc7\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Numerical solution of partial differential equations and applications <\/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> F1_MA_MAT_MMCS2-7<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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 an introduction to the numerical solution of partial differential equations (PDEs). It contains a theoretical part setting the mathematical foundations necessary for some important numerical methods used to obtain solutions to some classical PDEs, in particular the finite element method and the finite difference method.\u00a0<br>The theoretical part of the course is supported by the development of a one-dimensional Galerkin finite element code for the Poisson problem and a one-dimensional finite difference code for a scalar hyperbolic transport problem.<br>We largely follow the reference [Qua09] which is available via the National Library\u2019s Website as well as on some less official websites. In particular, we cover the contents of [Qua09, Chapters 1, 2, 3, 4, and 14].                        <\/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>A brief survey of partial differential equations<br>This chapter briefly introduces the notion of linear PDEs and their classification into elliptic, parabolic and hyperbolic equations. We mention some classical examples, mainly issued from physics and engineering, such as the transport equation, the Laplace equation, the heat equation and the wave equation.<br><\/p><p>Elements of functional analysis<br>We introduce the main notions and theoretical results of functional analysis that are extensively used in the numerical analysis of partial differential equations. We consider the Riesz representation theorem regarding representation of continuous linear forms on a Hilbert space, and we survey the notions of bilinear form, of continuous injection of a Hilbert space into another, the notion of derivative in the sense of Fr\u00e9chet, some elements of the theory of distributions, the basic properties of the Lebesgue and Sobolev spaces, and the notion of adjoint operator.<\/p><p>Elliptic equations<br>We illustrate boundary-value problems for elliptic equations (in one and several dimensions), present their variational reformulations, treat the boundary conditions and analyze their well-posedness. Several examples of physical interest are introduced, in particular the Poisson equation, starting with the one-dimensional case, for various boundary conditions. We consider some variational formulations of these problems, and then turn to the boundary-value problems associated to the Poisson equation in the two-dimensional case. We establish that under some regularity condition the weak formulation is equivalent to the strong one. For general elliptic problems, the Lax-Milgram theorem ensures that the weak formulation is well-posed.<\/p><p>The Galerkin finite element method for elliptic problems<br>We formulate Galerkin\u2019s method for the numerical discretization of elliptic boundaryvalue problems and analyze its existence, uniqueness, stability and convergence features in an abstract functional setting. We then introduce the Galerkin finite elements method, first in one dimension, and then in several dimensions.<\/p><p>The Galerkin finite element method \u2013 a numerical example<br>This section introduces students to the development of a one-dimensional Galerkin finite element solver for the Poisson problem using Python. We focus on building the solver within a provided Jupyter notebook, providing hands-on experience with the computational and algorithmic aspects of the finite element method.<\/p><p>Finite differences for hyperbolic equations<br>The aim of this final chapter is to study classical finite differences methods for approximating solutions of first-order hyperbolic equations. We start with exposing some hyperbolic equations starting with the scalar transport problem in one dimension which we analyze by the method of characteristics. We also establish an a priori estimate by the energy method. We then turn to systems of linear hyperbolic equations in one dimension and give the example of the wave equation. Then we introduce the finite difference method, together with its variants: the forward\/centered Euler scheme, the Lax-Friedrichs scheme, the Lax-Wendroff scheme, in the case of the scalar transport problem, before to move to more general cases, for which we analyze the consistency, stability, convergence, dissipation and dispersion properties of the finite difference methods.<\/p>Finite differences \u2013 a numerical example<br>This section introduces students to the development of a one-dimensional finite difference solver for a hyperbolic transport problem using Python. We focus on building the solver within a provided Jupyter notebook, providing hands-on experience with the computational and algorithmic aspects of the finite difference method.                    <\/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><br>Assessment is via coursework (30%) and final examination (70%). The due date for the coursework will be set at a later time.<\/p><br><p><br>Retake policy<br><br>Failure on the coursework can be compensated through the examination, and vice versa, as long as the final mark for the course is greater than or equal to 10.<br>In the event that the final mark is less than 10:<\/p><br><ul><br><li>The student may request a retake the examination once.<\/li><br><li>The student may not resubmit the coursework.<\/li><br><\/ul>If the final mark remains less than 10 the student has failed, and can take the entire course again in the next semester that it is offered.                    <\/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>Reference<br><br>[Qua09] Alfio Quarteroni. Numerical models for differential problems. Vol. 2. Springer, 2009.<\/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-69d3d943e9cd3\"\n        >\n            <span class=\"accordion__title\">\n                Statistical Modelling                <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                            MA_DS-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-69d3d943e9cd3\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Statistical Modelling<\/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> MA_DS-15<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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 main goal of the course is to raise awareness of model assumptions and critical thinking, and to provide a guide as to how to make reasonable modelling choices.\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                        This course will deal with two cultures of statistical modelling: top-down via a parametric model, and bottom-up via data-adaptive methods. More concretely, it will cover classical distributions and their limitations, flexible distributions allowing to model complex modern datasets, interpretable machine learning, and the difference between the two modelling cultures.\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>\u00a0<\/p><br><p><br>First session<br>Written exam on both theory and exercises for 75% of the mark, and midterm exam for 25% of the mark.<\/p><br><p><br>Retake exam<br>Written exam on both theory and exercises. The student can choose whether they wish to keep their midterm exam mark or not.<\/p><br><p>\u00a0<\/p><br><p>\u00a0<\/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><br>Literatur<br><\/p><br><ul><br><li>Ley, C., Babic, S. and Craens, D. (2021) Flexible models for complex data with applications.<\/li><br><li>Annual Review of Statistics and Its Application 8, 18.1-18.23.<\/li><br><li>Genuer, R. and Poggi, J.-M. (2020) Random Forests with R, Springer.<\/li><br><li>Kleinbaum, D.G. and Klein, M. (2012) Survival Analysis \u2013 A Self-learning Text, Springer.<\/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-69d3d943e9cdf\"\n        >\n            <span class=\"accordion__title\">\n                Student Project 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_MA_MAT_GM-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-69d3d943e9cdf\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Student Project 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_MA_MAT_GM-18<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                        <p>On successful completion of the Student Project 2, the student should be able to:<br><\/p><br><ul><br><li>analyse complex tasks,<\/li><br><li>propose solution strategies,<\/li><br><li>break up a longer project into subsequent steps,<\/li><br><li>apply a variety of methods in one project,<\/li><br><li>present a task and its solution in a scientific way.<\/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                        The student project consists of project work that is carried out under the supervision of a professor or a postdoc. The work is either individual or group work. Group work needs the explicit approval of the Study Director. At the beginning of the project, supervisor and student(s) define tasks to be carried out by the student(s), corresponding to the volume of 100 working hours (4 ECTS). The student(s) need to notify the Study Director of the project and the tasks at the latest on 15 March. The project outcome is a pdf document written by the student. Additional outcomes (such as computer code, images, videos) can be asked for. The required outcome has to be handed in on Moodle at the latest on 31 May. The project file will undergo an automatic plagiarism check.                    <\/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 marked for their project work. In the case of a retake exam, a new project has to be done. The retake can be done with other supervisors.                    <\/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-69d3d943e9ceb\"\n        >\n            <span class=\"accordion__title\">\n                Student seminar 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                            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                            F1_MA_MAT_GM-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-69d3d943e9ceb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Student seminar 2 <\/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> F1_MA_MAT_GM-19<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 2<\/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                        <p>On successful completion of the Student Seminar 2, the students should be able to:<br><\/p><br><ul><br><li>Fully benefit from seminar talks<\/li><br><li>Acquire good insight into a field by means of individual work<\/li><br><li>Give themselves lectures on specific topics<\/li><br><li>Share their knowledge with others<\/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                        Every participant chooses a supervisor among the academic staff of the Department of Mathematics and, jointly with the supervisor, a topic for a talk.<br>The audience of the talk consists at least of the participants of the seminar, the supervisor and one other academic staff member of the Department of Mathematics (e.g. the supervisor of another talk). The duration of the talk is 75 minutes (time for questions not included).<br>A typewritten version of this (these) lecture(s) is requested.<br>The students&#8217; seminar talks will take place during April and May. The exact timetable depends on the number of registered students and is made during the semester.<br>The supervisor together with the course responsible marks the students\u2019 performance and the written text.<p>\u00a0<\/p><p><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                        Continuous evaluation. The mark is based on the talk and the written text delivered by the student.<br>If a student fails, a new talk and a new text can be delivered in the following semester. A supervisor change is allowed.                    <\/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-69d3d943e9cf7\"\n        >\n            <span class=\"accordion__title\">\n                Learning and Teaching Mathematics I                <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                            F1_SECEDUC-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-69d3d943e9cf7\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Learning and Teaching Mathematics I<\/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> F1_SECEDUC-30<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 2<\/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> 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                            Amener les \u00e9tudiants \u00e0 ma\u00eetriser la conception d&#8217;\u00e9preuves math\u00e9matiques \u00e9quilibr\u00e9es, l&#8217;analyse diagnostique des erreurs des \u00e9l\u00e8ves et la formulation de feedbacks constructifs adapt\u00e9s au contexte scolaire du Luxembourg.<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                        \u00c0 l\u2019issue de ce cours, les \u00e9tudiants devront \u00eatre capables de :<br><ul><br><li>Mettre en perspective les pratiques d\u2019\u00e9valuation en analysant leurs variations g\u00e9ographiques (cultures docimologiques \u00e0 l\u2019international) et leur \u00e9volution historique (gen\u00e8se de la notation et des examens).<\/li><br><li>Se rep\u00e9rer dans le cadre l\u00e9gal et r\u00e9glementaire de l\u2019\u00e9valuation au Luxembourg, afin d\u2019appliquer correctement les crit\u00e8res de promotion, les programmes et les socles de comp\u00e9tences de l\u2019ESC et de l\u2019ESG.<\/li><br><li>Concevoir des \u00e9preuves math\u00e9matiques pr\u00eates \u00e0 l\u2019emploi, en \u00e9quilibrant les niveaux taxonomiques (de l\u2019application proc\u00e9durale au raisonnement complexe) pour couvrir l\u2019ensemble du spectre des comp\u00e9tences tout en portant une attention r\u00e9flexive \u00e0 la mise en page (clart\u00e9 des \u00e9nonc\u00e9s, structuration des consignes, hi\u00e9rarchisation de l\u2019information).<\/li><br><li>\u00c9laborer des grilles de correction crit\u00e9ri\u00e9es et des corrig\u00e9s types permettant d\u2019objectiver la notation et de minimiser les biais docimologiques (constante macabre, effet de halo,\u00a0effet de contraste) pour rendre le processus d\u2019\u00e9valuation transparent, \u00e9quitable et justifiable.<\/li><br><li>Exploiter l\u2019\u00e9valuation comme un levier d\u2019apprentissage plut\u00f4t que comme un outil de sanction, en diagnostiquant les erreurs sp\u00e9cifiques des \u00e9l\u00e8ves afin de leur fournir un feedback descriptif et constructif qui favorise leur autor\u00e9gulation et leur progression.<\/li><br><\/ul><br><p><br><br><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>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Ce cours vise \u00e0 doter les futurs enseignants de math\u00e9matiques d&#8217;une expertise critique et technique en mati\u00e8re d&#8217;\u00e9valuation. L&#8217;\u00e9tudiant passera d&#8217;une vision intuitive de la notation \u00e0 une pratique professionnelle rigoureuse, capable de mesurer les acquis r\u00e9els des \u00e9l\u00e8ves tout en soutenant leur apprentissage.                    <\/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 du cours s&#8217;articule autour d&#8217;un dispositif progressif combinant contr\u00f4le continu (50%) et examen final (50%).<br>Le\u00a0contr\u00f4le continu (50% de la note finale)\u00a0comprendra deux \u00e9valuations r\u00e9alis\u00e9es pendant le semestre :<br><ul><br><li><br>L&#8217;\u00e9valuation par les pairs (25%) :<br>\u00a0<br>Suite \u00e0 la cr\u00e9ation d&#8217;une premi\u00e8re \u00e9bauche d&#8217;\u00e9preuve (formative), chaque \u00e9tudiant analysera la proposition d&#8217;un camarade en double aveugle. Il devra lui fournir un feedback \u00e9crit d\u00e9taill\u00e9, critique et constructif, en mobilisant les concepts docimologiques vus en cours.<br><\/li><br><li><br>L&#8217;\u00e9preuve pratique sur table (25%) :<br>\u00a0<br>Lors de l\u2019avant-derni\u00e8re s\u00e9ance de cours, l&#8217;\u00e9tudiant sera mis en situation professionnelle. \u00c0 partir d&#8217;un bar\u00e8me fourni, il devra corriger une \u00e0 deux copies d&#8217;\u00e9l\u00e8ves, formuler un diagnostic pr\u00e9cis des erreurs et<br>r\u00e9diger des r\u00e9troactions favorisant l&#8217;autor\u00e9gulation.<br><\/li><br><\/ul><br>L\u2019examen final (50% de la note finale)\u00a0consistera en la remise d&#8217;un\u00a0portfolio de conception\u00a0: L&#8217;\u00e9tudiant devra soumettre la version finale et aboutie de son \u00e9preuve de math\u00e9matiques (\u00e9nonc\u00e9 et corrig\u00e9 crit\u00e9ri\u00e9),\u00a0qui repr\u00e9sentera l&#8217;\u00e9volution de son \u00e9bauche initiale. Ce travail sera accompagn\u00e9 d\u2019un essai r\u00e9flexif d\u00e9taill\u00e9 dans lequel l&#8217;\u00e9tudiant justifiera ses choix de conception (validit\u00e9, niveaux taxonomiques, \u00e9vitement des biais). Il devra \u00e9galement y analyser l&#8217;\u00e9volution de son travail, en argumentant la mani\u00e8re dont le feedback de son pair a \u00e9t\u00e9 int\u00e9gr\u00e9 (ou consciemment rejet\u00e9) pour transformer l&#8217;\u00e9bauche en cette version finale.<br>Les d\u00e9tails pratiques de ce dispositif par \u00e9tapes, le mat\u00e9riel de secours \u00e9ventuel, ainsi que les dates limites de remise seront annonc\u00e9s sur Moodle.<br>Veuillez noter que chaque absence doit \u00eatre justifi\u00e9e par email avant le d\u00e9but du cours (patrick.weber.001@uni.lu). Les absences non justifi\u00e9es devront \u00eatre compens\u00e9es avec des travaux suppl\u00e9mentaires.<br>En cas d\u2019absence pour la remise du portfolio ou\/et pour l\u2019\u00e9preuve pratique sur table, merci de fournir un certificat m\u00e9dical (si possible, on trouvera une nouvelle date pour l\u2019\u00e9preuve pratique avant la p\u00e9riode d&#8217;examen).\u00a0<br>\u00a0<br>Veuillez noter que les certificats m\u00e9dicaux doivent \u00eatre envoy\u00e9s \u00e0 Madame Marbehant (<br>rachida.seguer@uni.lu<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                        Note \/ Literatur<br><br>La liste des r\u00e9f\u00e9rences bibliographiques sera publi\u00e9e sur la page Moodle de ce cours.\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-69d3d943e9d03\"\n        >\n            <span class=\"accordion__title\">\n                Didactical Seminar I                <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                            F1_SECEDUC-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-69d3d943e9d03\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Didactical Seminar I<\/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> F1_SECEDUC-29<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 2<\/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> 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                            The students train their mathematical-didactical capacities and their collaborative attitude. They benefit from the experience and insights of the main lecturer and the guest lecturers (for example, MSE-M Alumni that provide their recommendations on how to navigate the first years within the Luxembourgish school system).                        <\/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                        The aim of reflective teaching is continuously questioning the teacher&#8217;s professional practice with the cycle of &#8220;planning, acting\/observing and reflecting\/adapting&#8221;. In this workshop, we reflect on various aspects of the teacher&#8217;s role. We address both general didactical principles and specificities of the Luxembourgish school system.                    <\/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 requested to give a presentation on a topic of school mathematics (the grade depending on their mathematical-didactical performance). Moreover, it is expected that the students take part in the training offered by Thierry Meyrath (one time participation to a Scienteens Lab workshop).                    <\/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                        Each year we focus on a different theme, and we have different guest lecturers. The literature is announced in class and is available on Moodle.                    <\/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-69d3d943e9d0e\"\n        >\n            <span class=\"accordion__title\">\n                Mehrsprachigkeit im Sprach- und Fachunterricht (MATH): L\u2019importance des diff\u00e9rents langages en math\u00e9matiques  (appliqu\u00e9e au syst\u00e8me \u00e9ducatif luxembourgeois)                <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                            F3_SECEDUC-182                        <\/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-69d3d943e9d0e\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943e9c2b\">\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> Mehrsprachigkeit im Sprach- und Fachunterricht (MATH): L\u2019importance des diff\u00e9rents langages en math\u00e9matiques  (appliqu\u00e9e au syst\u00e8me \u00e9ducatif luxembourgeois)<\/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> F3_SECEDUC-182<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Professional Competence II &#8211; Multilingualism and Heterogeneity <\/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                \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 \u00e9tudiants seront amen\u00e9s \u00e0 :<br><\/p><br><ul><br><li>Faire des r\u00e9flexions sur l\u2019utilisation d\u2019une langue et les d\u00e9finitions pr\u00e9cises des mots dans le cadre d\u2019un cours de math\u00e9matiques.<br><\/li><br><li>Etudier les diff\u00e9rences entre certains mots quand ils sont utilis\u00e9s en langue courante ou en contexte math\u00e9matique.<br><\/li><br><li>L\u2019impact de la langue d\u2019instruction sur un cours de math\u00e9matiques.<br><\/li><br><li>Etablir un dictionnaire math\u00e9matique trilingue (FR-ALL-ENG) adapt\u00e9 \u00e0 l\u2019enseignement secondaire luxembourgeois.<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                        <p>Quand on pense aux math\u00e9matiques, on pense souvent \u00e0 un tableau noir rempli de symboles obscurs et incompr\u00e9hensible aux la\u00efcs. Et pourtant, le r\u00f4le des langues n\u2019est pas sans importance en math\u00e9matiques : nous communiquons les math\u00e9matiques avec des mots du langage courant et m\u00eame si les preuves math\u00e9matiques contiennent des signes propres aux math\u00e9matiques, autour de ces signes et symboles se trouve du texte \u00e9crit en une certaine langue. Les litt\u00e9raires peuvent s\u2019en passer des math\u00e9matiques, mais les math\u00e9maticiens doivent utiliser les langues, et ceci correctement. D\u2019autant plus, que beaucoup de mots de la langue courante prennent un sens tr\u00e8s pr\u00e9cis et strict en math\u00e9matiques. L\u2019histoire se complique quand la langue d&#8217;instruction du cours de math\u00e9matiques n\u2019est pas la langue maternelle du math\u00e9maticien et\/ou de l\u2019\u00e9l\u00e8ve.<br>Ces id\u00e9es constituent le point de d\u00e9part de ce cours. Nous allons nous pencher sur trois th\u00e8mes principaux :<br><\/p><ol><li>L\u2019importance des mots en math\u00e9matiques et leur d\u00e9finition pr\u00e9cise dans leur contexte math\u00e9matique.<\/li><li>Les difficult\u00e9s et avantages des classes de math\u00e9matiques multilingues.<\/li><\/ol><p>Un dictionnaire math\u00e9matique trilingue (ou plus) adapt\u00e9 au contexte luxembourgeois.<\/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                        25% projet, 75% examen oral                    <\/div>\n                <\/li>\n                \n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-27a5654f-8943-465d-b93d-650032ebae01\"\n    aria-labelledby=\"tab-27a5654f-8943-465d-b93d-650032ebae01\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Math\u00e9matiques, Semestre 3 (2025-2026 Winter)<\/h3>\n    \n<div id=\"accordion-module-69d3d943efa0b\" 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-69d3d943efa51\"\n        >\n            <span class=\"accordion__title\">\n                Lie Algebras and Lie Groups                <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                            F1_MA_MAT_GM-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-69d3d943efa51\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Lie Algebras and Lie Groups<\/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> F1_MA_MAT_GM-20<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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 purpose of this course is to give an introduction to the theory of finite dimensional Lie groups and Lie algebras, assuming knowledge of linear algebra and differentiable topology.                        <\/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><ul><br><li>Explain the deep interrelations between Lie groups and Lie algebras, as well as the technical tools behinds these interrelations.<\/li><br><li>Simplify mathematical problems admitting symmetry Lie groups actions to problems admitting symmetry actions of their Lie algebras.<\/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                        Lie groups, Lie algebra of a Lie group, the exponential map and the Lie group-Lie algebra correspondence; the adjoint representation; structure theory and classification results, with focus on simple Lie algebras.                    <\/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>Combined evaluation (final exam and continuous evaluation)<\/p><br><p><\/p><br><ol><br><li>If justified absent during midterms, a make-up oral exam.<\/li><br><li>If justified absence during the written exam, a make-up written exam.<\/li><br><\/ol>                    <\/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                        <ol><br><li>Representation Theory by W. Fulton and J. Harris<\/li><br><li>Notes on Lie Algebras by H. Samelson<\/li><br><li>\u201cPrerequisites from Differential Geometry\u201d by Sergei Merkulov (free to download)<\/li><br><\/ol>                    <\/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-69d3d943efa72\"\n        >\n            <span class=\"accordion__title\">\n                Arithmetic 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                            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                            F1_MA_MAT_GM-22                        <\/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-69d3d943efa72\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Arithmetic Geometry <\/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> F1_MA_MAT_GM-22<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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                            <ul><br><li>Introduce students to important notions from Arithmetic Geometry<\/li><br><li>Establish links to classical mathematics, also relevant in secondary schools<\/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                        <ul><br><li>Know examples of and be able to explain the continuity of mathematics from classical problems (as taught in school) to modern research questions.<\/li><br><li>Understand the relevance of knowing modern mathematics for being able to teach an integral picture of mathematics at secondary schools.<\/li><br><li>Be able to work with mathematical notions going beyond secondary school and Bachelor level.<\/li><br><li>Master the basics of local fields and be able to compute with p-adic numbers, as generalisation of the real numbers.<\/li><br><li>Master the fundamentals of the theory of quadratic forms, be able to explain its origin in the study of conics, know and be able to apply important theorems, be able to handle examples.<\/li><br><li>Master the basics of elliptic curves, know about their classical origin, know about their application in cryptography, understand their relevance for current number theory research, know and be able to apply important theorems, be able to handle examples.<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                        This course leads from classical mathematics (real numbers, conics, \u201cclassical\u201d geometry, plane curves) to some topics in modern number theory and geometry and underlines the continuity from classical geometry (as taught in school) and classical number theory to the modern points of view.<br>It covers p-adic numbers and more generally local fields as analogues of the real numbers, quadratic forms (arising from the study of conic sections) and elliptic curves (arising from the study of certain integrals), as well as some of their relevance for modern mathematics.<br>Having their origin in the study of conics, the theory of quadratic forms is a modern theory situated in both geometry and number theory with plenty of applications. It turns out that for a full classification of quadratic forms, one needs to introduce analogues for the real numbers: the so-called p-adic numbers, or, more generally, local fields. In the first part of the lecture, the theory of quadratic forms is introduced, number theory applications are treated, p-adic numbers are dealt with, and the classification theorem is fully proved.<br>The second part of the course is concerned with elliptic curves. These are curves arising from the study of certain integrals. They are relevant in everyday life for their fundamental role in Elliptic Curves Cryptography (e.g. used in ID cards, passports). In the language of modern geometry, they are curves of genus one with a rational point. For number theory, they appear in many of the most important questions of current research, e.g. the Birch-and-Swinnerton-Dyer conjecture, which is one of the 7 Millenium Problems. In the course, elliptic curves are introduced in modern geometric language, thus introducing this language, and several important number theoretic and geometric properties are proved, such as the addition law (making them into a group, a complicated generalisation of the integers), and statements on their rational points (number theoretic \u201cDiophantine\u201d question).<br>The course will be a classical lecture, complemented by integrated exercises and contributions by the students via short talks.<br>Students from the Master in Secondary Education will be asked to focus in their contributions on how to link the topics of their lectures with High School mathematics.                    <\/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 modality: Continuous evaluation<br><\/p><br><p><br>First session<br>The mark of the course consists of the evaluation of the talk(s) (40%), the supervised exercises (40%) and the presentation of the exercises (20%).<\/p><br><p><br>Retake exam<br>The retake exam in the exam period of the next summer semester (June\/July) will be an oral exam, which counts 100% of the final mark. Partial results (e.g. on talks) will not be taken into consideration. Any retake in a winter semester implies the full participation in the lecture and all elements of its continuous assessment.<\/p><br><p><br>Absence plan\u00a0<br><br><br><\/p><br><ul><br><li>In the case of a justified absence from supervised exercises, an oral exam will be carried out.<\/li><br><li>In the case of justified absence from a talk, the talk will be rescheduled.<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>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note \/ Literature<br><\/p><br><ul><br><li>Serre: A course in arithmetic, Springer\u00a0<\/li><br><li>Silverman: The arithmetic of elliptic curves, Springer<\/li><br><li>Anni, Deo, Wiese: Lecture notes for Topics in Number Theory and Geometry, distributed during the lecture<\/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-69d3d943efa7f\"\n        >\n            <span class=\"accordion__title\">\n                Algebraic 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                            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                            F1_MA_MAT_GM-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-69d3d943efa7f\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Algebraic Geometry <\/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> F1_MA_MAT_GM-23<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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                            Gaining familiarity with the language and concepts and of algebraic geometry building on commutative algebra. Applying the general theory to concrete simple examples.\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                        We will introduce basic notions of algebraic geometry starting with Hilbert\u2019s Nullstellensatz, affine and projective varieties. We can think of an affine variety as the common zeros of a set of given polynomials in multiple variables. We will further introduce rational maps between varieties leading to the important topic of birational geometry. Finally, we will learn what a singular point of an affine variety is. Along the way, we will look at many simple and concrete examples.\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>\u00a0<\/p><br><p><br>Exam modalities: Combined evaluation (final exam and continuous evaluation)<br><\/p><br><p><br>First session<br><br>Written exam and supervised homework<\/p><br><p>\u00a0<\/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><br>Note \/ Literature \/ Bibliography\u00a0<br><\/p><br><ul><br><li><br>Robin Hartshorne, Algebraic geometry<\/li><br><li>Ravi Vakil, The rising sea<\/li><br><li>Igor Shafarevitch, Basic algebraic geometry 1<\/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-69d3d943efa8b\"\n        >\n            <span class=\"accordion__title\">\n                Gaussian processes and applications                 <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_MAT_FM-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-69d3d943efa8b\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Gaussian processes and applications <\/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_MAT_FM-9<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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 learn the basic concepts and techniques associated with Gaussian processes, that are omnipresent in modelling random phenomena (finance, physics, machine learning, statistics, etc.).<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>On successful completion of the course, the student should be able to:\u00a0\u00a0<\/p><br><ul><br><li>Explain the language, basic concepts and techniques associated with Gaussian variables, vectors, and processes<\/li><br><li>Identify, analyse, and prove relevant properties of models based on a Gaussian structure<\/li><br><li>Solve exercises involving a Gaussian structure<\/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>Gaussian random variables (characteristic function, CLT, stability properties, Stein&#8217;s lemma)<\/li><li>Gaussian random vectors (definition, characteristic function, existence, uniqueness in law, multivariate CLT, density, Hermite polynomials)<\/li><li>Gaussian random processes (definition, modifications, uniqueness in law, function of positive type, existence, Brownian motion, continuity)<\/li><li>Fractional Brownian motion (definition, existence, H\u00f6lder regularity)<\/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>Written exam during the exam period (January\/February).<\/p><br><p><br>Retake exam<br>Written exam\u00a0during the exam period July).<\/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>Will be discussed in class                    <\/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-69d3d943efa97\"\n        >\n            <span class=\"accordion__title\">\n                Data Science                 <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_MAT_GM-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-69d3d943efa97\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Data Science <\/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_MAT_GM-24<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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 successful candidate will understand the fundamental theoretical concepts of data science and be able to work with real data. The aim is to contribute to data-driven AI as outlined in the German government&#8217;s AI strategy paper.                        <\/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><ul><br><li>Explain and apply basic theoretical concepts on selected aspects of data science.<\/li><br><li>Develop appropriate solutions in the scope of a data science towards a data-driven AI<\/li><br><li>Consolidate acquired competences in the subject area<\/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                        In this course, the term \u2018data\u2019 is seen centric and we will look at data from different perspectives in order to serve a data-driven AI. We will discuss selected aspects of Data Preparation and Preprocessing, Data Statistics, Data Security, Data Privacy, Data Management, Big and Small Data, Data Retrieval, Data Visualization, and Data Analytics. In the project part, each participant contributes to a public poster workshop, in which the results of the project has to be shown.\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>\u00a0<\/p><br><p><br>Poster Workshop Attendance and Presentation of the project and final report<br><\/p><br><p><br>First session<br>50% written report + 50% presentation of the project results as poster at the AICaf\u00e9 2025:\u00a0<br>The candidate will participate in the AICaf\u00e9 2025 \u2013 AI Competition (4 December 2025, 18h00 \u2013 21h00, Cercle Cit\u00e9 Luxembourg, Auditoire Cit\u00e9) and show the project work in the field of a Data-driven AI. This is a mandatory examination requirement.<\/p><br><p><br>Retake exam<br>Retakes are offered in Summer. Candidates who wish to do are pleased to get in contact with Prof. Schommer.<\/p><br><p>\u00a0<\/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><br>Note \/ Literature \/ Bibliography\u00a0<br><\/p><br><ul><br><li>Elmasri, Navathe: Fundamentals of Database Systems. Pearson Addison Wesley. 2006.<\/li><br><li>Han, Kamber: Data Mining \u2013 Concepts and Techniques. Morgan Kaufmann. 2011.<\/li><br><li>Manning, Raghavan, Sch\u00fctze: Introduction to Information Retrieval. Cambridge University Press.<br>Ware: Information Visualization. Morgan Kaufmann. 2012.<\/li><br><li>Witten, Kamber: Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann.<\/li><br><li>Aggarwal, Yu: Privacy-Preserving Data Mining \u2013 Models and Algorithms. Springer. 2008.<\/li><br><li>Marz: Big Data: Principles and best practices of scalable realtime data systems. Manning. 2015.<br>as well as different articles, reports, and journals contributions.<\/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-69d3d943efaa3\"\n        >\n            <span class=\"accordion__title\">\n                Elementary mathematics from a higher viewpoint II                <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_MA_MAT_GM-32                        <\/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-69d3d943efaa3\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Elementary mathematics from a higher viewpoint II<\/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_MA_MAT_GM-32<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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                        Les \u00e9tudiant\u00b7e\u00b7s vont revisiter leurs connaissances des math\u00e9matiques de fin de secondaire. En parall\u00e8le, ils\u00b7elles aborderont ces sujets sous un angle nouveau, gr\u00e2ce \u00e0 leur ma\u00eetrise des math\u00e9matiques de niveau sup\u00e9rieur. Les \u00e9tudiant\u00b7e\u00b7s du MSE-M Master devront \u00eatre capable de r\u00e9pondre aux questions possibles de leur futur\u00b7e\u00b7s \u00e9l\u00e8ves.                    <\/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                        Le cours explorera les th\u00e9matiques des math\u00e9matiques de fin de secondaire sous un angle plus abstrait. Les concepts universitaires seront utilis\u00e9s pour revisiter les math\u00e9matiques du secondaire et pour approfondir la th\u00e9orie derri\u00e8re chaque formule. Des questions de compr\u00e9hension et des liens entre diff\u00e9rents sujets seront \u00e9galement abord\u00e9s.<br>Attention: les th\u00e9matiques abord\u00e9es sont divis\u00e9es en deux groupes et sont trait\u00e9es en alternance chaque ann\u00e9e.                    <\/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>3 midterms (50% of the final mark) and 1 written exam in january (50 % of of the final mark).<br>Exam modalities for the retake exam<br>1 written exam (100 % of final mark)<br>Absence plan<br>if justified absent during midterms, an oral exam will be organised about the same material, if justified absence during the written exam, an oral exam will take place<\/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-69d3d943efaaf\"\n        >\n            <span class=\"accordion__title\">\n                Student Project 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                            F1_MA_MAT_GM-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-69d3d943efaaf\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Student Project 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> F1_MA_MAT_GM-25<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Specialisation &#8211; Mathematics 3<\/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                        <p>On successful completion of the Student Project 1 (or 3) the student should be able to:<\/p><br><ul><br><li>analyse complex tasks,<\/li><br><li>propose solution strategies,<\/li><br><li>break up a longer project into subsequent steps,<\/li><br><li>apply a variety of methods in one project,<\/li><br><li>present a task and its solution in a scientific way.<\/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                        The ability to work on a project, either individually or as part of a team, is one of the key skills expected of a mathematician, in and outside academia. The Student Project offers the student the opportunity to improve this skill by allowing them to work on a well-defined and well chosen project, either individually or as a team, under the guidance of a researcher.<br>The Student Project consists of project work that is carried out under the supervision of a researcher. The work is either individual or group work. At the beginning of the project, supervisor and student(s) define tasks to be carried out by the student(s), corresponding to the volume of 100 working hours (4 ECTS) for each student. The student(s) need to submit the planned topic to the course responsible for approval at the latest on 15 October (Student Project 1,3) or 15 March (Student Project 2). The project outcome is a pdf document written by the student(s). Additional outcomes (such as computer code, images, videos) can be asked for. The required outcome has to be handed in on Moodle at the latest on 31 December (Student Project 1,3) or 31 May (Student Project 2). The project file will undergo an automatic plagiarism and AI check.<br><p>\u00a0<\/p><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>First session<br>The students are marked for their project work. In the case of a retake exam, a new project on the same or a different topic has to be done.\u00a0<\/p><br><p><br>Retake exam<br>The retake can be done with a different supervisor.<\/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-69d3d943efabb\"\n        >\n            <span class=\"accordion__title\">\n                Applied Didactics I &amp; III: Didactics of 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                            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                            F1_SECEDUC-32                        <\/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-69d3d943efabb\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Applied Didactics I &amp; III: Didactics of Geometry<\/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> F1_SECEDUC-32<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 3<\/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> 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                            One aim is training the participants in formulating definitions, theorems, and counterexamples, while refreshing their notions of geometry that is accessible to school pupils. Parallel to that we will discuss the recommendations provided by didacticians for teaching geometry in schools most effectively.                        <\/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 participants will refresh their knowledge of geometry and will have revisited school mathematics from a higher viewpoint. They will also have learned didactical approaches tailored to this subject.                    <\/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 is about geometry that is taught in schools or that is taught to school pupils that train for mathematical competitions.\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>First session<br><br><\/p><br><ul><br><li>30% presentation<\/li><br><li>70% written exam<\/li><br><\/ul><br>Retake exam\u00a0<br><ul><li>Written exam<\/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>Note<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        <p><br>Note \/ Literature \/ Bibliography<br><\/p><br><p>We will access to literature in English, French, and German. The literature will include books and articles of Geometry and Didactics of geometry, plus online references. The up-to-date list of references will be made available on 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-69d3d943efac8\"\n        >\n            <span class=\"accordion__title\">\n                Applied Didactics IV &#8211; Evaluation methods and supporting mathematics learning                <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                            F1_SECEDUC-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-69d3d943efac8\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Applied Didactics IV &#8211; Evaluation methods and supporting mathematics learning<\/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> F1_SECEDUC-19<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 3<\/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                            Les questions et la taxonomie de Bloom\/Anderson Krathwohl, les probl\u00e8mes de compr\u00e9hension, ainsi que les moments cl\u00e9s d&#8217;une le\u00e7on ou d&#8217;un apprentissage sont abord\u00e9s.\u00a0<br>La planification d&#8217;une le\u00e7on ou d&#8217;une s\u00e9quence de le\u00e7ons, ainsi que l&#8217;\u00e9valuation formative et sommative sont \u00e9galement au coeur du cours.                        <\/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>Avoir conscience que chaque choix didactique influence toujours l&#8217;enseignement et l&#8217;apprentissage des contenus qui en d\u00e9coulent.\u00a0<\/li><br><li>\u00catre en mesure de formuler des questions ciblant diff\u00e9rents niveaux taxonomiques.\u00a0<\/li><br><li>Anticiper les \u00e9ventuels probl\u00e8mes de compr\u00e9hension des \u00e9l\u00e8ves.\u00a0<\/li><br><li>Identifier les moments cl\u00e9s d&#8217;une le\u00e7on ou d&#8217;un apprentissage.\u00a0<\/li><br><li>Planifier une s\u00e9quence de le\u00e7ons comprenant une introduction, des activit\u00e9s, des transitions, des moments consacr\u00e9s aux \u00e9l\u00e8ves, des exemples, des exercices, ainsi que les questions \u00e0 poser et les r\u00e9ponses attendues des \u00e9l\u00e8ves.\u00a0<\/li><br><li>Formuler des questions adapt\u00e9es \u00e0 une \u00e9valuation de type formatif ou sommatif.\u00a0<\/li><br><li>Planifier une le\u00e7on de mani\u00e8re \u00e0 ce que les objectifs d&#8217;apprentissage puissent \u00eatre atteints de plusieurs mani\u00e8res diff\u00e9rentes.<\/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>Pr\u00e9sentation des le\u00e7ons et diverses m\u00e9thodes d&#8217;introduction ;\u00a0<\/li><li>Utilisation de la taxonomie de Bloom\/Anderson &amp; Krathwohl ;\u00a0<\/li><li>Analyse des exercices et des feuilles de travail ; Introduction aux diff\u00e9rents types de temps consacr\u00e9s aux \u00e9l\u00e8ves ;\u00a0<\/li><li>Pr\u00e9paration des le\u00e7ons, mettant l&#8217;accent sur le cycle inf\u00e9rieur et moyen : Comment proc\u00e9der ? Bonnes pratiques : Public cible ;\u00a0<\/li><li>Importance du sujet pour les \u00e9l\u00e8ves ;\u00a0<\/li><li>Objectifs \u00e0 atteindre ;\u00a0<\/li><li>Mat\u00e9riel disponible\/\u00e0 utiliser ;\u00a0<\/li><li>M\u00e9thodes p\u00e9dagogiques ;\u00a0<\/li><li>Outils techniques, visualisation, applications, jeux ;\u00a0<\/li><li>R\u00e9flexion ;\u00a0<\/li><li>Introductions et rappels ;\u00a0<\/li><li>Encha\u00eenements et transitions ;\u00a0<\/li><li>Types de questions \u00e0 poser et utilisation de la taxonomie ;\u00a0<\/li><li>Moments cl\u00e9s ;\u00a0<\/li><li>Exercices ;<\/li><li>\u00c9valuation : objectifs, m\u00e9thodes, types et fr\u00e9quence ;\u00a0<\/li><li>Ressources ; Probl\u00e8mes et cons\u00e9quences des choix didactiques ;\u00a0<\/li><li>Pr\u00e9paration au stage de janvier.<\/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><br>Exam modalities for the first session: Combined assessment (contr\u00f4le continue et examen final sous forme de remise d&#8217;un dossier avec pr\u00e9sentation et d\u00e9fense orale du dossier)<br><\/p><br><p><br>Session de rattrapage<br><br>Exam modalities for the retake exam: remise d&#8217;un dossier<\/p><br>Absence plan\u00a0<br>pour les contr\u00f4les continus\/ absences lors d&#8217;un cours: me contacter au plus tard avant le d\u00e9but du cours pour la remise du dossier: une prolongation peut \u00eatre obtenue sous condition de pouvoir fournir un certificat m\u00e9dical pour la d\u00e9fense orale: une date alternative peut \u00eatre trouv\u00e9e sous\u00a0<br>condition de pouvoir fournir un certificat m\u00e9dical.                    <\/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><br><\/p><br><ul><br><li>Barzel, B., B\u00fcchter, A., Leuders, T. (2007), Mathematik Methodik, Handbuch f\u00fcr die Sekundarstufe I und II, Cornelsen<\/li><br><li>Hattie, J. (2010), Visible Learning, Routledge<\/li><br><li>Leuders, T. (2020), Mathematikdidaktik (9e \u00e9dition), Cornelsen<\/li><br><li>Leuders, T., Prediger, S. (2016), Flexibel differenzieren und fokussiert f\u00f6rdern im Mathematikunterricht, Cornelsen<\/li><br><li>Malle, G. (1993), Didaktische Probleme der elementaren Algebra, Vieweg<\/li><br><li>Padberg, F., Wartha, S. (2017), Didaktik der Bruchrechnung (5e \u00e9dition), Springer<\/li><br><li>Sill, H.-D. (2018), Grundkurs Mathematikdidaktik, utb.<\/li><br><li>Sturm, R. (2016), Schritt f\u00fcr Schritt zum guten Mathematikunterricht, Klett Kallmeyer <\/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-69d3d943efad5\"\n        >\n            <span class=\"accordion__title\">\n                Allgemeine Didaktik II                  <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                            F3_SECEDUC-188                        <\/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-69d3d943efad5\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Allgemeine Didaktik II  <\/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> F3_SECEDUC-188<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competence III &#8211; Forschungsfeld Schule<\/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                                <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>Die Studierenden &#8230;<\/p><br><p>&#8230; haben Grundlagen zu Tiefenstrukturen des Unterrichtens, insbesondere der kognitiven Aktivierung und der kognitiven Unterst\u00fctzung, erarbeitet.<\/p><br><p>&#8230; verf\u00fcgen \u00fcber ein anwendungsbezogenes Konzeptrepertoire aus den Bereichen P\u00e4dagogische Diagnostik und Evaluation.<\/p><br><p>&#8230; haben Transferm\u00f6glichkeiten vor dem Hintergrund der je eigenen Praktikumserfahrungen reflektiert und auf Basis ihrer individuellen Entwicklungsziele und Forschungsinteressen weiterentwickelt.<\/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>Description<\/strong><\/h5>\n                    <\/header>\n                    <div class=\"list-highlighted__body\">\n                        Der Workshop dient der Vertiefung p\u00e4dagogischer Grundlagen und didaktischer Konzepte im Enseignement Secondaire und damit der Erweiterung und Adaption von Gestaltungsm\u00f6glichkeiten der Unterrichtspraxis im Rahmen des vertiefenden Praktikums. Ein besonderer Schwerpunkt liegt dabei auf den individuellen Entwicklungszielen und Forschungsinteressen der Studierenden.<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>20% Aktive Teilnahme an Seminar und Schulpraktikum<\/p><br><p>20% Zwischenpr\u00fcfung in Form einer Klausur<\/p><br><p>20% Abschlusspr\u00e4sentation im Rahmen des Praktikumsfeedbacks<\/p><br><p>40% Praktikumsportfolio<\/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-69d3d943efae2\"\n        >\n            <span class=\"accordion__title\">\n                Einf\u00fchrung in die P\u00e4dagogische Psychologie                <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                            F3_SECEDUC-129                        <\/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-69d3d943efae2\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Einf\u00fchrung in die P\u00e4dagogische Psychologie<\/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> F3_SECEDUC-129<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competences III &#8211; Mehrsprachigkeit und Heterogenit\u00e4t<\/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                            <ul><br><li>Ein (P\u00e4dagogisch-) Psychologisches Fundament f\u00fcr angehende Lehrerinnen und Lehrer zur Verf\u00fcgung stellen<\/li><br><li>Unterricht aus seiner psychologischen Perspektive analysieren<\/li><br><li>Prozesse wissenschaftlichen Erkenntnisgewinns und seiner Bedeutung f\u00fcr die Berufspraxis nachvollziehbar machen<\/li><br><li>Zum eigenst\u00e4ndigen Denken und professionellem Handeln anregen<\/li><br><li>Typische Mythen und Fehlkonzepte in Bezug auf Lernen und Unterricht aus psychologischer Sicht hinterfragen und ggf. korrigieren<\/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                        Die Vorlesung f\u00fchrt ein in Gegenstand und Methode der (P\u00e4dagogischen) Psychologie als empirische Wissenschaft und ihrer Bedeutung f\u00fcr angehende LehrerInnen.\u00a0 Insbesondere die P\u00e4dagogische Psychologie, aber auch die Allgemeine, Differentielle, Entwicklungs- und Sozialpsychologie tragen bei zum Verst\u00e4ndnis menschlichem Erleben und Verhalten in Kontexten der Erziehung, der Bildung und des (formalen) Lernens (bzw. Unterrichtens). Vorgestellt und diskutiert werden zun\u00e4chst allgemeine Inhalte und Methoden der Psychologie als empirischer Wissenschaft, allgemeine Lernvoraussetzungen (z.B. Informations-verarbeitung, Lernmotivation), Aspekte der Unterrichtsgestaltung (z.B. Klassenf\u00fchrung), Aspekte der sozialen Interaktion (z.B. Freundschaft, Bullying), psychologische Besonderheiten des Lehrerberufs (z.B. Lehrerpers\u00f6nlichkeit, Burnout) sowie verschiedene Aspekte p\u00e4dagogisch-psychologischer Diagnostik (z.B. ausgew\u00e4hlte Lernst\u00f6rungen wie ADHS). Dabei werden sowohl empirische Originalstudien als auch empirisch fundierte Interventionsans\u00e4tze zur Illustration vertiefend besprochen. Zudem werden Fallbeispiele und \u00dcbungen besprochen und durchgef\u00fchrt.<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                        Schriftliche Klausur                    <\/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>Bibliografie<br>Grundlagenliteratur (d.h. online verf\u00fcgbar und pr\u00fcfungsrelevant, spez. Kap.)<br><\/p><br><ul><br><li>Fritz, A., Hussy, W. Tobinski, D. (2018). P\u00e4dagogische Psychologie. M\u00fcnchen: Reinhardt\/UTB.<\/li><br><li>Fromm, M. (2017). Lernen und Lehren: Psychologische Grundlagen f\u00fcr Lehramtsstudierende. M\u00fcnster: Waxmann.<\/li><br><li>G\u00f6tz, T. (2017, Hrsg.). Emotion, Motivation und selbstreguliertes Lernen. Paderborn: Sch\u00f6ningh\/UTB.<\/li><br><li>Imhoff, M. (2013). Psychologie f\u00fcr Lehramtsstudierende. Berlin: Springer.<\/li><br><li>Kunter, M. Trautwein, U. (2013). Psychologie des Unterrichts. Paderborn: Sch\u00f6ningh\/UTB.<\/li><br><li>Wild, E. M\u00f6ller, J. (2015, Hrsg.). P\u00e4dagogische Psychologie. Berlin: Springer.<\/li><br><li>Wisniewski, B. (2019). Psychologie f\u00fcr die Lehrerbildung. Bad Heilbrunn: Klinkhardt\/UTB.<\/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-69d3d943efaef\"\n        >\n            <span class=\"accordion__title\">\n                Teaching Children with Special Educational Needs                <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                            F3_SECEDUC-51                        <\/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-69d3d943efaef\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d943efa0b\">\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> Teaching Children with Special Educational Needs<\/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> F3_SECEDUC-51<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> General Competences III &#8211; Mehrsprachigkeit und Heterogenit\u00e4t<\/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                        This course aims to deepen student&#8217;s knowledge and understanding of special educational needs. It provides students with insights into the latest research about the learning processes of children with specific learning difficulties like dyslexia, developmental language disorder or autism spectrum disorder. It will also equip future teachers with strategies to teach children with special educational needs or other learning challenges more effectively.                    <\/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                        Over the years, research has informed the scientific and the educational community about how children&#8217;s learning processes can be affected by neurologically-based difficulties. These specific learning difficulties can interfere with the learning of basic skills such as reading, writing, maths or language learning. They can also affect higher level skills such as organisation, time planning, abstract reasoning, long- or short-term memory, and attention. It is important for teachers to understand the impact that specific learning difficulties have on children&#8217;s learning. To this end, the course will combine relevant theory with best practice.\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                        Exam\/Presentation                    <\/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><\/p><br>\u00a0<br><ul><br><li>Beck I., Mackeown M. Kucan L. (2013). Bringing Words to Life: Robust Vocabulary Instruction. New York: Guilford.<\/li><br><li>Carroll, J.M., Bowyer-Crane, C., Duff, F., Hulme, C., Snowling, MJ.\u00a0 (2011). Effective intervention for language and literacy in the early years.\u00a0 Oxford: Wiley-Blackwell.<\/li><br><li>Hulme C. Snowling M. (2009). Developmental Disorders of Language Learning and Cognition. Oxford UK: Wiley Blackwell. Chapter 2 3<\/li><br><li>Purpura, D. J., Ganley, C. (2014). Working memory and language: Skill-specific or domain-general relations to mathematics? Journal of Experimental Child Psychology, 122, 104-121.<\/li><br><li>Purpura, D. J., Napoli, A. R., Wehrspann, E. A., Gold, Z. S. (in press). Causal connections between mathematical language and mathematical knowledge: A dialogic reading intervention. Journal of Research on Educational Effectiveness.<\/li><br><li>Purpura, D. J., Reid, E. E. (2016). Mathematics and language: Individual and group differences in mathematical language skills in young children. Early Childhood Research Quarterly, 26, 259-268.<\/li><br><li>Purpura, D. J., Schmitt, S. A., Ganley, C. M. (2017). Foundations of mathematics and literacy: The role of executive functioning components. Journal of Experimental Child Psychology, 153, 15-34.<\/li><br><li>Sims, D. M., Purpura, D. J., Lonigan, C. J. (2012). The relation between inattentive and hyperactive\/impulsive behaviors and early mathematics skills. Journal of Attention Disorders. doi:10.1177\/1087054712464390.<\/li><br><\/ul><br>Snowling, M. J., Hulme, C. (2011). Evidence\u2010based interventions for reading and language difficulties: Creating a virtuous circle. British Journal of Educational Psychology, 81(1), 1-23.                    <\/div>\n                <\/li>\n                \n            <\/ul>\n        <\/div>\n    <\/div>\n<\/div>    <\/div><\/div><\/section>\n<section\n    id=\"tabpanel-44b503e3-b2db-49db-82cc-acd7a8224c03\"\n    aria-labelledby=\"tab-44b503e3-b2db-49db-82cc-acd7a8224c03\"\n    class=\"tab-panel fade hidden is-hidden\"\n>\n    <div class=\"wp-block-unilux-blocks-course-offer\">\n    <h3>Course offer for Math\u00e9matiques, Semestre 4 (2025-2026 Summer)<\/h3>\n    \n<div id=\"accordion-module-69d3d94401145\" 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-69d3d9440119a\"\n        >\n            <span class=\"accordion__title\">\n                Didactical Seminar II                <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                            F1_SECEDUC-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-69d3d9440119a\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d94401145\">\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> Didactical Seminar II<\/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> F1_SECEDUC-33<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 4<\/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                \n                \n                \n                \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-69d3d944011c6\"\n        >\n            <span class=\"accordion__title\">\n                Learning and Teaching Mathematics II                <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                            F1_SECEDUC-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-69d3d944011c6\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d94401145\">\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> Learning and Teaching Mathematics II<\/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> F1_SECEDUC-34<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 4<\/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                            Amener les \u00e9tudiants \u00e0 ma\u00eetriser la conception<br>d&#8217;\u00e9preuves math\u00e9matiques \u00e9quilibr\u00e9es, l&#8217;analyse diagnostique des erreurs des<br>\u00e9l\u00e8ves et la formulation de feedbacks constructifs adapt\u00e9s au contexte scolaire<br>du Luxembourg.<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                        <p>\u00c0 l\u2019issue de ce cours, les \u00e9tudiants devront \u00eatre capables de :<\/p><br><ul><br><li>Mettre en perspective les pratiques d\u2019\u00e9valuation en analysant leurs variations g\u00e9ographiques (cultures docimologiques \u00e0 l\u2019international) et leur \u00e9volution historique (gen\u00e8se de la notation et des examens).<\/li><br><li>Se rep\u00e9rer dans le cadre l\u00e9gal et r\u00e9glementaire de l\u2019\u00e9valuation au Luxembourg, afin d\u2019appliquer correctement les crit\u00e8res de promotion, les programmes et les socles de comp\u00e9tences de l\u2019ESC et de l\u2019ESG.<\/li><br><li>Concevoir des \u00e9preuves math\u00e9matiques pr\u00eates \u00e0 l\u2019emploi, en \u00e9quilibrant les niveaux taxonomiques (de l\u2019application proc\u00e9durale au raisonnement complexe) pour couvrir l\u2019ensemble du spectre des comp\u00e9tences tout en portant une attention r\u00e9flexive \u00e0 la mise en page (clart\u00e9 des \u00e9nonc\u00e9s, structuration des consignes, hi\u00e9rarchisation de l\u2019information).<\/li><br><li>\u00c9laborer des grilles de correction crit\u00e9ri\u00e9es et des corrig\u00e9s types permettant d\u2019objectiver la notation et de minimiser les biais docimologiques (constante macabre, effet de halo,\u00a0effet de contraste) pour rendre le processus d\u2019\u00e9valuation transparent, \u00e9quitable et justifiable.<\/li><br><li>Exploiter l\u2019\u00e9valuation comme un levier d\u2019apprentissage plut\u00f4t que comme un outil de sanction, en diagnostiquant les erreurs sp\u00e9cifiques des \u00e9l\u00e8ves afin de leur fournir un feedback descriptif et constructif qui favorise leur autor\u00e9gulation et leur progression.<\/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                        Ce cours vise \u00e0 doter les futurs enseignants de math\u00e9matiques d&#8217;une expertise critique et technique en mati\u00e8re d&#8217;\u00e9valuation. L&#8217;\u00e9tudiant passera d&#8217;une vision intuitive de la notation \u00e0 une pratique professionnelle rigoureuse, capable de mesurer les acquis r\u00e9els des \u00e9l\u00e8ves tout en soutenant leur apprentissage.                    <\/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 du cours s&#8217;articule autour d&#8217;un dispositif progressif combinant contr\u00f4le continu (50%) et examen final (50%).<br>Le\u00a0contr\u00f4le continu (50% de la note finale)\u00a0comprendra deux \u00e9valuations r\u00e9alis\u00e9es pendant le semestre :<br><ul><br><li><br>L&#8217;\u00e9valuation par les pairs (25%) :<br>\u00a0<br>Suite \u00e0 la cr\u00e9ation d&#8217;une premi\u00e8re \u00e9bauche d&#8217;\u00e9preuve (formative), chaque \u00e9tudiant analysera la proposition d&#8217;un camarade en double aveugle. Il devra lui fournir un feedback \u00e9crit d\u00e9taill\u00e9, critique et constructif, en mobilisant les concepts docimologiques vus en cours.<br><\/li><br><li><br>L&#8217;\u00e9preuve pratique sur table (25%) :<br>\u00a0<br>Lors de l\u2019avant-derni\u00e8re s\u00e9ance de cours, l&#8217;\u00e9tudiant sera mis en situation professionnelle. \u00c0 partir d&#8217;un bar\u00e8me fourni, il devra corriger une \u00e0 deux copies d&#8217;\u00e9l\u00e8ves, formuler un diagnostic pr\u00e9cis des erreurs et<br>r\u00e9diger des r\u00e9troactions favorisant l&#8217;autor\u00e9gulation.<br><\/li><br><\/ul><br>L\u2019examen final (50% de la note finale)\u00a0consistera en la remise d&#8217;un\u00a0portfolio de conception\u00a0: L&#8217;\u00e9tudiant devra soumettre la version finale et aboutie de son \u00e9preuve de math\u00e9matiques (\u00e9nonc\u00e9 et corrig\u00e9 crit\u00e9ri\u00e9),\u00a0qui repr\u00e9sentera l&#8217;\u00e9volution de son \u00e9bauche initiale. Ce travail sera accompagn\u00e9 d\u2019un essai r\u00e9flexif d\u00e9taill\u00e9 dans lequel l&#8217;\u00e9tudiant justifiera ses choix de conception (validit\u00e9, niveaux taxonomiques, \u00e9vitement des biais). Il devra \u00e9galement y analyser l&#8217;\u00e9volution de son travail, en argumentant la mani\u00e8re dont le feedback de son pair a \u00e9t\u00e9 int\u00e9gr\u00e9 (ou consciemment rejet\u00e9) pour transformer l&#8217;\u00e9bauche en cette version finale.<br>Les d\u00e9tails pratiques de ce dispositif par \u00e9tapes, le mat\u00e9riel de secours \u00e9ventuel, ainsi que les dates limites de remise seront annonc\u00e9s sur Moodle.<br>Veuillez noter que chaque absence doit \u00eatre justifi\u00e9e par email avant le d\u00e9but du cours (patrick.weber.001@uni.lu). Les absences non justifi\u00e9es devront \u00eatre compens\u00e9es avec des travaux suppl\u00e9mentaires.<br>En cas d\u2019absence pour la remise du portfolio ou\/et pour l\u2019\u00e9preuve pratique sur table, merci de fournir un certificat m\u00e9dical (si possible, on trouvera une nouvelle date pour l\u2019\u00e9preuve pratique avant la p\u00e9riode d&#8217;examen).\u00a0<br>\u00a0<br>Veuillez noter que les certificats m\u00e9dicaux doivent \u00eatre envoy\u00e9s \u00e0 Madame Marbehant (<br>rachida.seguer@uni.lu<br>).\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-69d3d944011dc\"\n        >\n            <span class=\"accordion__title\">\n                Internship in secondary school II                <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                            0                        <\/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_SECEDUC-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-69d3d944011dc\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d94401145\">\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> Internship in secondary school II<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 0<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_SECEDUC-20<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Didactics &#8211; Mathematics 4<\/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                \n                \n                \n                \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-69d3d944011f2\"\n        >\n            <span class=\"accordion__title\">\n                Master Thesis                <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                            20                        <\/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_SECEDUC-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-69d3d944011f2\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d94401145\">\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> Master Thesis<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 20<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F1_SECEDUC-28<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Master Thesis &#8211; Mathematics<\/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> 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                \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 Master Thesis, the students should be able to:<br><\/p><br><ul><br><li>Organize a comprehensive literature review<\/li><br><li>Discuss and communicate scientific ideas<\/li><br><li>Approach mathematical problems efficiently and identify appropriate theories or conceptual techniques<\/li><br><li>Discover original mathematics<\/li><br><li>Verify results and apply them<\/li><br><li>Write mathematical texts that are consistent with the tradition<\/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                        The Master Thesis in mathematics consists of the definition of a research project, the detailed explanation of research articles and\/or monographs aimed at a mathematics audience, as well as of potential further developments of these. The project, which should contain parts of original mathematics, will be designed to suit the individual objectives of the students, to deepen their competence in a selected field of mathematics, and to open a door towards mathematical research.                    <\/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                        Supervisor, director of studies                    <\/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                        Admission to the Master Thesis will be granted only to students who acquired at least 75 ECTS credit points during the first three semesters of the Master&#8217;s program (in a well-founded case, an exception to this rule might be decided by the study director).                    <\/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-69d3d94401209\"\n        >\n            <span class=\"accordion__title\">\n                Professionell Auftreten: Communication rh\u00e9torique pour enseignants                <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                            1                        <\/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                            F3_SECEDUC-231                        <\/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-69d3d94401209\" class=\"accordion__collapse collapse\" data-bs-parent=\"#accordion-module-69d3d94401145\">\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> Professionell Auftreten: Communication rh\u00e9torique pour enseignants<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Number of ECTS:<\/span> 1<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Course code:<\/span> F3_SECEDUC-231<\/li>\n                            <li><span class=\"text-dark font-heading font-bold\">Module(s):<\/span> Module 4.3 : General Professionnal Competence IV &#8211; FHSE<\/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                \n                \n                \n                \n                \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 MSE-M activities account for 120 ECTS, grouped as follows:<br \/>\n&#8211; Pillar I: Mathematics-Specific Professional Competence (60 ECTS)<br \/>\n&#8211; Pillar II: Didactic Competence (20 ECTS)<br \/>\n&#8211; Pillar III: General Professional Competence (20 ECTS).<br \/>\n&#8211; Internships in schools (six weeks in total), and a Master thesis (20 ECTS).<br \/>\nNew students are requested to take the Refresher Courses scheduled before the start of the first semester.<\/p>\n","protected":false},"author":34,"featured_media":1179,"parent":1182,"menu_order":0,"template":"","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"Master en Enseignement secondaire - 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