{"id":36,"date":"2023-08-24T13:31:43","date_gmt":"2023-08-24T11:31:43","guid":{"rendered":"https:\/\/www.uni.lu\/life-fr\/?page_id=36"},"modified":"2026-01-13T10:25:00","modified_gmt":"2026-01-13T09:25:00","slug":"mathematiques","status":"publish","type":"page","link":"https:\/\/www.uni.lu\/life-fr\/scienteens-lab\/ateliers\/mathematiques\/","title":{"rendered":"Math\u00e9matiques"},"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=\"04f7e347-4070-4894-8c64-89c93996622e\">\n    <nav id=\"secondary-navigation\" role=\"navigation\" aria-label=\"Secondary menu\" class=\"secondary-nav\">\n        <button class=\"secondary-nav__button btn btn-solid--primary w-full\" aria-expanded=\"false\" aria-controls=\"secondary-navigation__list\" title=\"The selected page is Accueil\" type=\"button\">\n            <span class=\"btn__name mr-auto\">Accueil<\/span>\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n                <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-down\" \/>\n            <\/svg>\n        <\/button>\n\n        <ul id=\"secondary-navigation__list\" class=\"secondary-nav__list\">\n            <li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/life-fr\/scienteens-lab\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Accueil<\/span>\n    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focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Notre \u00e9quipe<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/life-fr\/scienteens-lab\/nous-soutenir\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Nous soutenir<\/span>\n    <\/a>\n<\/li>\n<li class=\"secondary-nav__item\">\n    <a href=\"https:\/\/www.uni.lu\/life-fr\/scienteens-lab\/contact\/\" target=\"\" rel=\"noreferrer noopener\" class=\"secondary-nav__link \">\n        <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--xs\">\n            <use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\" \/>\n        <\/svg>\n        <span class=\"secondary-nav__name\">Contacts<\/span>\n    <\/a>\n<\/li>\n        <\/ul>\n    <\/nav>\n<\/div>\n<!-- end SecondaryNavigationMirror --><\/div><\/section>\n\n\n\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<div class=\"wp-block-columns is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h1 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"mathematiques\"\n    >\nMath\u00e9matiques<\/h1>\n\n\n\n<p>Le Scienteens Lab propose cinq ateliers de math\u00e9matiques pour les classes du secondaire. Ils portent sur la th\u00e9orie des graphes, les probabilit\u00e9s, la cryptographie, la classification et la mod\u00e9lisation. La plupart de ces ateliers sont destin\u00e9s aux \u00e9l\u00e8ves \u00e2g\u00e9s de 16 \u00e0 19 ans. Ils se d\u00e9roulent sur le campus de Belval, sous la supervision de l&rsquo;\u00e9quipe du Scienteens Lab. Chaque atelier est d\u00e9crit ci-dessous. Vous pouvez \u00e9galement avoir un aper\u00e7u de ces ateliers gr\u00e2ce \u00e0 une courte vid\u00e9o.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"thumbnail  wp-block-unilux-blocks-thumbnail-video\">\n    <div class=\"card bg-theme p-0\">\n        <div class=\"card__container p-0\">\n            <div class=\"card__body p-0\">\n                <iframe \n            src=\"https:\/\/www.youtube.com\/embed\/fSM8BsLqy1U\" \n            title=\"YouTube video player\" frameborder=\"0\" \n            allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" \n            style=\"object-position: 50% 50%; aspect-ratio: 16\/9; object-fit: cover; width: 100%;\"\n            allowfullscreen data-cookieconsent=\"ignore\">\n            <\/iframe>                            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n<div class=\"wp-block-unilux-blocks-spacer is-spacer-size-md\"><\/div>\n\n\n<div class=\"wp-block-unilux-blocks-accordion accordion accordion--theme accordion-standard\" data-reference=\"a062ce1a-70e5-43c3-a5be-969b8d1d37e3\" data-accordion-type=\"standard\"><div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-fc818803-18c2-40b7-9760-31f1ef184b33\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-fc818803-18c2-40b7-9760-31f1ef184b33\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-fc818803-18c2-40b7-9760-31f1ef184b33\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>1. <strong>G\u00e9rer le hasard ? Gr\u00e2ce aux lois de probabilit\u00e9 !<\/strong><\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-fc818803-18c2-40b7-9760-31f1ef184b33\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-fc818803-18c2-40b7-9760-31f1ef184b33\"\n        data-bs-parent=\"[data-reference=&quot;a062ce1a-70e5-43c3-a5be-969b8d1d37e3&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Cet atelier propose une introduction \u00e0 la th\u00e9orie des probabilit\u00e9s et pr\u00e9sente aux \u00e9l\u00e8ves les concepts et les notions math\u00e9matiques sous-jacentes. Des exercices pratiques que les participants peuvent effectuer par eux-m\u00eames les aident \u00e0 mieux comprendre comment aborder les calculs de probabilit\u00e9. Au moyen d\u2019exemples sp\u00e9cifiques, ils d\u00e9couvrent comment les concepts abord\u00e9s peuvent aider \u00e0 prendre une d\u00e9cision, par exemple dans le domaine de la m\u00e9decine.<\/p>\n\n<p>L\u2019atelier couvre entre autres :<\/p>\n\n<ul class=\"ulux-list\">\n<li class=\"ulux-list-item\">des notions de base (exp\u00e9rience al\u00e9atoire, variable al\u00e9atoire, loi de probabilit\u00e9)<\/li>\n\n\n\n<li class=\"ulux-list-item\">l\u2019\u00e9preuve de Bernoulli et la loi binomiale<\/li>\n\n\n\n<li class=\"ulux-list-item\">la loi g\u00e9om\u00e9trique<\/li>\n\n\n\n<li class=\"ulux-list-item\">la probabilit\u00e9 conditionnelle<\/li>\n\n\n\n<li class=\"ulux-list-item\">des exemples et applications de la th\u00e9orie des probabilit\u00e9s<\/li>\n<\/ul>\n\n<p>Cet atelier est accessible \u00e0 partir de la classe de 3<sup>e<\/sup>&nbsp;.<br>L&rsquo;atelier est con\u00e7u pour \u00eatre flexible et le rythme est adapt\u00e9 en fonction du niveau de chaque classe.<br>Il existe sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30) ou d\u2019une demi-journ\u00e9e (3-4h).<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-e611ef53-0c1b-497e-9a00-ba5f444d616c\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-e611ef53-0c1b-497e-9a00-ba5f444d616c\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-e611ef53-0c1b-497e-9a00-ba5f444d616c\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>2. <strong>Trouver le chemin le plus court ? Gr\u00e2ce \u00e0 la th\u00e9orie des graphes !<\/strong><\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-e611ef53-0c1b-497e-9a00-ba5f444d616c\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-e611ef53-0c1b-497e-9a00-ba5f444d616c\"\n        data-bs-parent=\"[data-reference=&quot;a062ce1a-70e5-43c3-a5be-969b8d1d37e3&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Pendant cet atelier, les \u00e9l\u00e8ves d\u00e9couvrent la th\u00e9orie des graphes et apprennent comment diff\u00e9rents concepts th\u00e9oriques sont utilis\u00e9s pour mod\u00e9liser et r\u00e9soudre des probl\u00e8mes de la vie courante, par exemple dans la logistique et la planification d\u2019itin\u00e9raire. Les \u00e9l\u00e8ves peuvent participer activement au travers de plusieurs exercices pratiques et ont l\u2019opportunit\u00e9 de tester eux-m\u00eames les concepts pr\u00e9sent\u00e9s pendant l\u2019atelier.<\/p>\n\n<p>L\u2019atelier aborde entre autres :<\/p>\n\n<ul class=\"ulux-list\">\n<li class=\"ulux-list-item\">le probl\u00e8me des sept ponts de K\u00f6nigsberg<\/li>\n\n\n\n<li class=\"ulux-list-item\">les graphes Eul\u00e9riens et semi-Eul\u00e9riens<\/li>\n\n\n\n<li class=\"ulux-list-item\">les graphes pond\u00e9r\u00e9s<\/li>\n\n\n\n<li class=\"ulux-list-item\">l\u2019algorithme de Dijkstra pour trouver le chemin le plus court<\/li>\n\n\n\n<li class=\"ulux-list-item\">le probl\u00e8me du voyageur de commerce<\/li>\n\n\n\n<li class=\"ulux-list-item\">l\u2019algorithme PageRank de Google<\/li>\n\n\n\n<li class=\"ulux-list-item\">des applications de la th\u00e9orie des graphes dans la vie quotidienne<\/li>\n<\/ul>\n\n<p>Cet atelier est accessible \u00e0 partir de la classe de 4<sup>e<\/sup>.<br>Il existe sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30) ou d\u2019une demi-journ\u00e9e (3-4h).<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-08d18fb2-531f-4ece-9f59-7c9916dfffc8\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-08d18fb2-531f-4ece-9f59-7c9916dfffc8\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-08d18fb2-531f-4ece-9f59-7c9916dfffc8\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>3. <strong>Garder un secret ? Gr\u00e2ce \u00e0 la th\u00e9orie des nombres !<\/strong><\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-08d18fb2-531f-4ece-9f59-7c9916dfffc8\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-08d18fb2-531f-4ece-9f59-7c9916dfffc8\"\n        data-bs-parent=\"[data-reference=&quot;a062ce1a-70e5-43c3-a5be-969b8d1d37e3&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Cet atelier de math\u00e9matiques permet aux lyc\u00e9ens de d\u00e9couvrir comment la th\u00e9orie des nombres est utilis\u00e9e pour s\u00e9curiser les communications. Au travers d\u2019exercices pratiques, comme le d\u00e9codage d\u2019un message crypt\u00e9 avec une roue de d\u00e9codage, les \u00e9l\u00e8ves d\u00e9couvrent comment fonctionne les algorithmes utilis\u00e9s en cryptographie et la th\u00e9orie des nombres sous-jacente.<\/p>\n\n<p>Les \u00e9l\u00e8ves aborderont diff\u00e9rents concepts math\u00e9matiques&nbsp;:<\/p>\n\n<ul class=\"ulux-list\">\n<li class=\"ulux-list-item\">la division euclidienne<\/li>\n\n\n\n<li class=\"ulux-list-item\">le plus grand diviseur commun (PGCD)<\/li>\n\n\n\n<li class=\"ulux-list-item\">l&rsquo;algorithme d&rsquo;Euclide \u00e9tendu<\/li>\n\n\n\n<li class=\"ulux-list-item\">le petit th\u00e9or\u00e8me de Fermat<\/li>\n\n\n\n<li class=\"ulux-list-item\">l&rsquo;algorithme RSA<\/li>\n<\/ul>\n\n<p>Si les enseignants souhaitent pr\u00e9parer leurs classes avant l&rsquo;atelier, du mat\u00e9riel p\u00e9dagogique portant sur les notions importantes sera fourni.&nbsp;(voir l&rsquo;onglet Pr\u00e9requis pour plus de d\u00e9tails)<\/p>\n\n<p>Cet atelier est accessible \u00e0 partir de la classe de 3<sup>e<\/sup>&nbsp;.<br>L&rsquo;atelier est con\u00e7u pour \u00eatre flexible et le rythme est adapt\u00e9 en fonction du niveau de chaque classe.<br>Il existe uniquement sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30).<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-24251c6e-c7b7-4f1e-8abb-296c6254a130\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-24251c6e-c7b7-4f1e-8abb-296c6254a130\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-24251c6e-c7b7-4f1e-8abb-296c6254a130\"\n        >\n            <span class=\"accordion__title\">\n                                4. Comment les math\u00e9maticiens classifient-ils les objets ?            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-24251c6e-c7b7-4f1e-8abb-296c6254a130\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-24251c6e-c7b7-4f1e-8abb-296c6254a130\"\n        data-bs-parent=\"[data-reference=&quot;a062ce1a-70e5-43c3-a5be-969b8d1d37e3&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Le concept de classification des objets, leur regroupement en diff\u00e9rentes cat\u00e9gories selon certains crit\u00e8res, joue un r\u00f4le important dans de nombreuses sciences. En biologie, par exemple, les organismes vivants sont classifi\u00e9s sur la base de caract\u00e9ristiques communes et de leur histoire \u00e9volutive. En math\u00e9matiques, il en va de m\u00eame et de nombreux math\u00e9maticiens s&rsquo;int\u00e9ressent \u00e0 la classification des objets math\u00e9matiques.<\/p>\n\n<p>Cet atelier pr\u00e9sente le concept de classification et illustre son importance en math\u00e9matiques. \u00c0 l&rsquo;aide d&rsquo;exemples tels que les nombres, les graphes ou les formes g\u00e9om\u00e9triques, les \u00e9l\u00e8ves d\u00e9couvrent comment les objets math\u00e9matiques peuvent \u00eatre classifi\u00e9s et apprennent comment utiliser certaines propri\u00e9t\u00e9s dites invariantes pour distinguer les objets.<\/p>\n\n<p>Cet atelier convient aux \u00e9l\u00e8ves \u00e0 partir de la 3e.<br>Il existe uniquement sous la forme d\u2019une demi-journ\u00e9e (3-4h). <\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n                    id=\"5-la-modelisation-mathematique-optimisation-lineaire-dynamique-des-populations\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-eed0a40e-d6c0-4d45-8c5e-61c4234ea1ad\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-eed0a40e-d6c0-4d45-8c5e-61c4234ea1ad\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-eed0a40e-d6c0-4d45-8c5e-61c4234ea1ad\"\n        >\n            <span class=\"accordion__title\">\n                                5. La mod\u00e9lisation math\u00e9matique : optimisation lin\u00e9aire &amp; dynamique des populations            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-eed0a40e-d6c0-4d45-8c5e-61c4234ea1ad\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-eed0a40e-d6c0-4d45-8c5e-61c4234ea1ad\"\n        data-bs-parent=\"[data-reference=&quot;a062ce1a-70e5-43c3-a5be-969b8d1d37e3&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Cet atelier donne aux \u00e9l\u00e8ves un aper\u00e7u de la mod\u00e9lisation math\u00e9matique et leur montre comment des probl\u00e8mes r\u00e9els peuvent \u00eatre mod\u00e9lis\u00e9s et r\u00e9solus gr\u00e2ce aux math\u00e9matiques. Il est divis\u00e9 en deux parties.<\/p>\n\n<p>Au cours de la premi\u00e8re partie, les \u00e9l\u00e8ves apprennent comment formuler un probl\u00e8me d\u2019optimisation lin\u00e9aire et comment un probl\u00e8me \u00e0 deux variables peut \u00eatre r\u00e9solu graphiquement. Ils d\u00e9couvrent ensuite l\u2019algorithme du simplexe qui peut \u00eatre utilis\u00e9 lorsqu&rsquo;il y a plus de deux variables.<br><br>La deuxi\u00e8me partie est consacr\u00e9e \u00e0 la mod\u00e9lisation des processus de croissance et traite en particulier le mod\u00e8le SIR qui permet de mod\u00e9liser la propagation d\u2019une \u00e9pid\u00e9mie dans une population donn\u00e9e.<\/p>\n\n<p>L\u2019atelier aborde entre autres :<\/p>\n\n<ul class=\"ulux-list\">\n<li class=\"ulux-list-item\">des exemples de probl\u00e8mes d\u2019optimisation lin\u00e9aire<\/li>\n\n\n\n<li class=\"ulux-list-item\">la r\u00e9solution graphique d\u2019un probl\u00e8me \u00e0 deux variables (\u00e0 l\u2019aide de GeoGebra)<\/li>\n\n\n\n<li class=\"ulux-list-item\">l\u2019algorithme du simplexe<\/li>\n\n\n\n<li class=\"ulux-list-item\">la croissance lin\u00e9aire, exponentielle et logistique<\/li>\n\n\n\n<li class=\"ulux-list-item\">le mod\u00e8le SIR et son impl\u00e9mentation dans GeoGebra<\/li>\n<\/ul>\n\n<p>Cet atelier est accessible \u00e0 partir de la classe de 3<sup>e<\/sup>.<br>Il existe sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30) ou d\u2019une demi-journ\u00e9e (3-4h).<br>Les classes qui viennent pour une demi-journ\u00e9e doivent choisir entre les deux parties de l\u2019atelier (optimisation ou dynamique des populations).<\/p>\n\n<p>Pour la partie sur l\u2019algorithme du simplexe, il est utile que les \u00e9l\u00e8ves aient d\u00e9j\u00e0 des connaissances sur les syst\u00e8mes d\u2019\u00e9quations lin\u00e9aires.<\/p>\n        <\/div>\n    <\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<ul class=\"wp-block-unilux-blocks-custom-buttons btn-list justify-center\"><li class=\"wp-block-unilux-blocks-custom-button\"    aria-disabled=\"false\"\n    >\n    <a\n        role=\"link\"\n        aria-disabled=\"false\"\n                    href=\"https:\/\/booking.scienteenslab.lu\/fr\/teachers\/mathematics_for_classes\/\"\n                target=\"_blank\"\n        class=\"btn btn--primary\"\n            >R\u00e9server un atelier<\/a>\n<\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n<div class=\"wp-block-unilux-blocks-spacer is-spacer-size-md\"><\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><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\/29\/2023\/08\/ScLab_Website_Mathematics_SmallPic_1-scaled.jpg\"\n                    style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 16\/9; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><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\/29\/2023\/08\/ScLab_Website_Mathematics_SmallPic_2.jpg\"\n                    style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: cover; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 16\/9; object-fit: cover; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure><\/div>\n<\/div>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p><\/p>\n<\/div><\/section>\n\n\n\n<section class=\"py-0 wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<h3 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"informations-pratiques-pour-tous-les-ateliers-de-mathematiques\"\n    >\nInformations pratiques pour tous les ateliers de math\u00e9matiques<\/h3>\n\n\n\n<div class=\"wp-block-unilux-blocks-accordion accordion accordion--theme accordion-standard\" data-reference=\"3b355f31-40ae-4e1f-a730-8ed8fcc2cddb\" data-accordion-type=\"standard\"><div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-91860d32-ba37-4f09-8cce-95483997b239\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-91860d32-ba37-4f09-8cce-95483997b239\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-91860d32-ba37-4f09-8cce-95483997b239\"\n        >\n            <span class=\"accordion__title\">\n                                <strong><strong>Quelles classes peuvent participer ?<\/strong><\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-91860d32-ba37-4f09-8cce-95483997b239\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-91860d32-ba37-4f09-8cce-95483997b239\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Tous les ateliers de math\u00e9matique sont destin\u00e9s \u00e0 des classes allant de la 3<sup>e<\/sup>\u00a0\u00e0 la 1<sup>\u00e8re<\/sup>\u00a0(niveaux du syst\u00e8me scolaire luxembourgeois), c&rsquo;est-\u00e0-dire des \u00e9l\u00e8ves \u00e2g\u00e9s de 16 \u00e0 19 ans.<\/p>\n\n<p>L&rsquo;atelier 2 (th\u00e9orie des graphes) peut aussi convenir aux classes de 4<sup>e<\/sup>&nbsp;.<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-35d0b927-bae1-4571-8984-128174bb6b96\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-35d0b927-bae1-4571-8984-128174bb6b96\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-35d0b927-bae1-4571-8984-128174bb6b96\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>Langues<\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-35d0b927-bae1-4571-8984-128174bb6b96\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-35d0b927-bae1-4571-8984-128174bb6b96\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Les ateliers de math\u00e9matiques se d\u00e9roulent en luxembourgeois, fran\u00e7ais, allemand ou anglais.<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-d1c51550-53e0-4c54-b80e-c2da52096b73\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-d1c51550-53e0-4c54-b80e-c2da52096b73\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-d1c51550-53e0-4c54-b80e-c2da52096b73\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>Horaires<\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-d1c51550-53e0-4c54-b80e-c2da52096b73\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-d1c51550-53e0-4c54-b80e-c2da52096b73\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Les ateliers 1, 2 et 5 (Lois de probabilit\u00e9s, Th\u00e9orie de graphes et Mod\u00e9lisation) existent sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30) ou d\u2019une demi-journ\u00e9e (3-4h). L&rsquo;atelier 3 (Th\u00e9orie des nombres) existe uniquement sous la forme d\u2019une journ\u00e9e compl\u00e8te (6h30). L&rsquo;atelier 4 (Classification) existe uniquement sous la forme d\u2019une demi-journ\u00e9e (3-4h). <\/p>\n\n<p>Les ateliers sur la journ\u00e9e se d\u00e9roulent de 9h \u00e0 15h30 avec une pause d\u00e9jeuner d\u2019une heure. Pendant la pause d\u00e9jeuner, les \u00e9l\u00e8ves peuvent manger au restaurant universitaire ou dans les restaurants situ\u00e9s sur le campus et dans Belval Plaza. Les horaires de la pause repas doivent \u00eatre respect\u00e9s afin que les activit\u00e9s de l\u2019apr\u00e8s-midi puissent reprendre \u00e0 l\u2019heure.<\/p>\n\n<p>Les classes qui viennent pour une demi-journ\u00e9e peuvent choisir l\u2019heure de d\u00e9marrage qui leur convient le mieux (choix effectu\u00e9 au moment de l\u2019inscription).<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-e4f67dcf-459b-42e5-bab2-cfc8d00be7ee\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-e4f67dcf-459b-42e5-bab2-cfc8d00be7ee\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-e4f67dcf-459b-42e5-bab2-cfc8d00be7ee\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>L<\/strong>ieu            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-e4f67dcf-459b-42e5-bab2-cfc8d00be7ee\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-e4f67dcf-459b-42e5-bab2-cfc8d00be7ee\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Les ateliers de math\u00e9matiques se d\u00e9roulent \u00e0 la Maison du Savoir sur le Campus Belval.<\/p>\n\n<p>Si vous venez en voiture ou en car, prenez l\u2019A4 et suivez-la jusqu\u2019au bout, puis suivez les panneaux vers \u00ab Belval \u00bb. Sur le campus, il n\u2019y a malheureusement aucun panneau indiquant le chemin jusqu\u2019au b\u00e2timent de la Maison du Savoir. Veuillez utiliser le plan ci-dessous pour vous y rendre.<\/p>\n\n<p>Si vous venez en train, descendez \u00e0 la gare de \u00ab Belval Universit\u00e9 \u00bb. Notre b\u00e2timent se trouve \u00e0 environ 10 minutes de marche de la gare. Plusieurs bus peuvent \u00e9galement vous amener jusqu\u2019au Campus de Belval.<\/p>\n<figure class=\"wp-block-dev4-reusable-blocks-image  object-fit--contain\">\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\/29\/2023\/08\/2023-08_BelvalMap_ScLab_MSA.jpg\"\n                    style=\"object-position: 50.00% 50.00%; font-family: &quot;object-fit: contain; object-position: 50.00% 50.00%;&quot;; aspect-ratio: 1\/1; object-fit: contain; width: 100%;\"\n        loading=\"lazy\"\n\/>    <\/figure>        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-79f2eb29-a3af-44f3-8cbb-4203ce7bd2c4\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-79f2eb29-a3af-44f3-8cbb-4203ce7bd2c4\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-79f2eb29-a3af-44f3-8cbb-4203ce7bd2c4\"\n        >\n            <span class=\"accordion__title\">\n                                <strong><strong>Pr\u00e9requis<\/strong><\/strong>            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-79f2eb29-a3af-44f3-8cbb-4203ce7bd2c4\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-79f2eb29-a3af-44f3-8cbb-4203ce7bd2c4\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>Pour l&rsquo;atelier 3 (Garder un secret ? Gr\u00e2ce \u00e0 la th\u00e9orie des nombres !), si vous souhaitez pr\u00e9parer la classe avant l&rsquo;atelier, vous pouvez rappeler ou introduire les notions suivantes :<\/p>\n\n<p>a) Division euclidienne (division avec reste) et algorithme d&rsquo;Euclide (pour la division, aussi voir les cas avec un dividende\/diviseur n\u00e9gatif).<\/p>\n\n<p>b) Le plus grand diviseur commun (PGCD) de 2 nombres entiers et le th\u00e9or\u00e8me de Bachet-B\u00e9zout qui donne le plus grand diviseur commun de 2 nombres entiers comme une combinaison lin\u00e9aire.<br>Par exemple 3 = pgcd(6, 15) = -12*6 + 5*15. Une telle combinaison lin\u00e9aire peut \u00eatre obtenue avec l&rsquo;algorithme d&rsquo;Euclide \u00e9tendu.<\/p>\n\n<p>c) D\u00e9finition d&rsquo;un nombre premier.<\/p>\n\n<p>d) Les r\u00e8gles de base de l&rsquo;exponentiation.<\/p>\n\n<p>Du mat\u00e9riel p\u00e9dagogique portant sur ces notions sera fourni aux enseignants.<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"accordion__item  wp-block-unilux-blocks-accordion-item\">\n    <h3 class=\"accordion__header\"\n        >\n        <button\n            type=\"button\"\n            id=\"accordion-labelledby-36ba3ce8-aea9-462f-942f-f1373ec5b7c2\"\n            class=\"accordion__button collapsed\"\n            aria-expanded=\"false\"\n            aria-controls=\"accordion-panel-36ba3ce8-aea9-462f-942f-f1373ec5b7c2\"\n            data-bs-toggle=\"collapse\"\n            data-bs-target=\"#accordion-panel-36ba3ce8-aea9-462f-942f-f1373ec5b7c2\"\n        >\n            <span class=\"accordion__title\">\n                                <strong>Certificat<\/strong> de participation            <\/span>\n\n            <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-down \"><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    <\/h3>\n    <div id=\"accordion-panel-36ba3ce8-aea9-462f-942f-f1373ec5b7c2\"\n        class=\"accordion__collapse collapse\"\n        aria-labelledby=\"accordion-labelledby-36ba3ce8-aea9-462f-942f-f1373ec5b7c2\"\n        data-bs-parent=\"[data-reference=&quot;3b355f31-40ae-4e1f-a730-8ed8fcc2cddb&quot;]\"\n    >\n        <div class=\"accordion__body \">\n            \n<p>\u00c0 la fin d&rsquo;un atelier, chaque \u00e9l\u00e8ve re\u00e7oit un certificat attestant de sa participation.<\/p>\n        <\/div>\n    <\/div>\n<\/div><\/div>\n<\/div><\/section>\n\n\n<section class=\"section section wp-block-unilux-blocks-quick-link-discover-section\">\n    <div class=\"container xl:max-w-screen-xl\">\n        \n<h2 class=\"has-text-align-left wp-block-unilux-blocks-heading\"        id=\"a-decouvrir\"\n    >\n\u00c0 d\u00e9couvrir<\/h2>\n\n<ul class=\"wp-block-unilux-blocks-quick-link-discover quick-link-list\">\n<li class=\"wp-block-unilux-blocks-quick-link-discover-item\">\n    <a\n                    href=\"https:\/\/www.uni.lu\/life-fr\/scienteens-lab\/ateliers\/biologie\/\"\n                    class=\"quick-link\"\n            target=\"\"\n    >\n            <span class=\"quick-link__container\">\n                <span class=\"quick-link__text\">\n                    Biologie                <\/span>\n                <svg aria-hidden=\"true\" focusable=\"false\" class=\"icon icon-outline icon--arrow-right \"><use xlink:href=\"https:\/\/www.uni.lu\/wp-content\/themes\/unilux-theme\/assets\/images\/icons\/icons-outline.svg#icon--arrow-right\"><\/use><\/svg>            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