The objective of this EU is to deepen the concepts of analysis seen at the science terminal and to improve the computational skills of students. Complex numbers, derivability, primitive calculation, study of usual reciprocal functions, polynomials, as well as first and second order ordinary differential equations, linear and with constant coefficients are discussed.

Teaching language

FRANÇAIS / FRENCH

Content: 1) Real numbers (upper and lower bound, absolute value, integer part, axiomatic of R, intervals, density of rational and irrational numbers)2) Real sequences: monotonicity, convergence (with epsilon), inductive and adjacent sequences, Cauchy sequences, Bolzano-Weierstrass theorem, arithmetic and geometric sequences. 3) Real functions (limit with Epsilon, delta), continuity, image of a compact and non compact interval through a continuous function, uniform continuity, Heine's theorem, bijections, homeomorphisms, lipschitzian functions. 4) Derivation of real functions: definition, Rolle's theorem, Mean value theorem, local extrema, Taylor-Lagrange and Taylor-Young formula, limited developments and application to local extrema.

Teaching language

FRANÇAIS / FRENCH

The learning outcomes of the "méthodologie des mathématiques" course are designed to acquire the mathematical method based on the unambiguous definition of notions, the formulation of conjectures, the formulation of mathematical propositions and their demonstration using logic from more basic propositions, going back to the axioms. To do this, learning and mastering the language of mathematics is fundamental (speech, syntax, objects, variables). This course aims to allow the acquisition of the basic elements of this language by its implementation in simple demonstrations addressing basic but new concepts that will be seen in class. Topics include naïve set theory, applications, binary relations, natural integers and groups. At the end of this course the students will be able to independently demonstrate simple original propositions concerning these notions. This course is built around three modalities: the lecture, the tutorials, and the personal work. These revolve around the elements transmitted in class and in Tds but also with the help of other educational resources, including self-correcting exercises.

Teaching language

FRANÇAIS / FRENCH

The course of Linear Algebra consists of three chapters. The first chapter defines the vector spaces, the bases, and introduces the notion of dimension.Then we deal with linear applications: kernel, image, rank, projectors. The last chapter is about matrices: their links to linear applications, base change, and linear systems.

Teaching language

FRANÇAIS / FRENCH

This module is the very first computer science course of the degree and is intended for students who do not necessarily have experience in computer science. Its main objective is to introduce the fundamental bases of imperative programming (values, types, variables, conditionals, loops), as well as the basics of algorithmics (list manipulation, strings). The support language is Python.

Teaching language

FRANÇAIS / FRENCH

This module is intended for students who already have some experience of computer science in general, and in Python programming in particular (especially students who have followed the NSI speciality in ``première'' or ``terminale'' in high school). It emphasizes accompanied problem solving, and requires autonomy, curiosity and perseverance for students. The module is divided into four or five sequences, each of which consists of the presentation of a problem, its resolution by the students and the presentation of the work done in the form of a short document, generally accompanied by a Python program. This course shares the main learning objectives of Algorithms and Programming 1 (AP1): basic concepts of imperative programming and the Python language, elementary algorithms (especially list traversal), creation of readable and structured programs. The theoretical part of the course will be based on a common evaluation with the one of AP1.

Teaching language

FRANÇAIS / FRENCH

This course is the continuation of Algorithms and Programming 1 (AP1) from the first semester. It builds on the notions previously introduced to study new and more advanced ones. In particular, the notions of recursive programming and complexity are covered. Some classical backtracking algorithms, searching, and sorting will also be introduced.

Teaching language

FRANÇAIS / FRENCH

This module is intended for students who already have some experience with the specific algorithmic topics covered in Algorithms and Programming 2 (AP2). It may be of particular interest to students who have taken the NSI speciality in ``terminale'' in high school. Like the APP1 module, it emphasizes accompanied problem solving, and requires autonomy, curiosity and perseverance from the students. The module is divided into four or five sequences, each consisting of the presentation of a problem, its resolution by the student, and the presentation of the work done in the form of a short document, generally accompanied by a Python program. This teaching shares the main learning objectives of the AP2 module: recursion, complexity, searching and sorting algorithms, stacks, queues, implicit graph traversal. The theoretical part will be based on a common evaluation with the AP2 module.

Teaching language

FRANÇAIS / FRENCH

Teaching language

FRANÇAIS / FRENCH

This module is an initiation to the creation and to the programming of web pages. After a brief description of the mechanisms by which the internet works, the focus will be on the study of the web and the creation of web pages. To do this, the structure of the content of a web page (HTML) will be presented first, then its appearance (CSS), and finally the dynamic modification of these (Javascript) by the user's web browser.

Teaching language

FRANÇAIS / FRENCH

This second part of the semester is devoted to introducing students to the basic concepts of how to carry out a computer science project of reasonable size from start to finish. The practical part of this module consists precisely in designing such a project in Python. Special attention will be paid to communication and presentation: students will have to know how to write a documentation and to present their work during a defense.

Teaching language

FRANÇAIS / FRENCH

This second part of the semester is devoted to introducing students to the basic concepts of how to carry out a computer science project of reasonable size from start to finish. The practical part of this module consists precisely in designing such a project in Python. Special attention will be paid to communication and presentation: students will have to know how to write a documentation and to present their work during a defense.

Teaching language

FRANÇAIS / FRENCH

This second semester course is a continuation of Project 1 (Pr1) taught in the first semester. Here again, students will be introduced to methods for designing a computer science project. Such a project will have to be carried out entirely. It will be based on most of the notions seen so far (Python programming, algorithms and web programming) and, if the opportunity arises, will propose a project using all of them.

Teaching language

FRANÇAIS / FRENCH

The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.

Teaching language

ANGLAIS / ENGLISH

The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.

Teaching language

ANGLAIS / ENGLISH

Déterminants, réduction des endomorphismes, espace euclidien.

Teaching language

FRANÇAIS / FRENCH

1 : Etudes des suites numériques et complexes, formules de Taylor. 2. Etude des séries numériques et complexes. 3. Intégrale de Riemann

Teaching language

FRANÇAIS / FRENCH

L'objectif du cours est d'apprendre à représenter et manipuler informatiquement les objets mathématiques de base, à effectuer des calculs algébriques et numériques en utilisant l'outil informatique, à explorer des problèmes mathématiques à l'aide de l'outil informatique, à modéliser et résoudre des problèmes pratiques en utilisant les mathématiques et l'informatique. Le cours est organisé autour d'une série de problèmes variés (ensemble de Mandelbrot, cryptographie, splines, calcul des fonctions usuelles, etc.) comportant une partie théorique et une partie pratique (programmation). Les concepts mathématiques intervenant dans ces problèmes sont les concepts de base vus en première année : arithmétique, relations binaires, nombres complexes, suites et fonctions, polynômes, algèbre linéaire, matrices, etc. La partie programmation est réalisée en Python.

Teaching language

FRANÇAIS / FRENCH

Etude des fonctions de plusieurs variables, extrema. Intégrales doubles triples, Fubini, changements de variables, courbes paramétrées

Teaching language

FRANÇAIS / FRENCH

1. Notions de convergence des suites de fonctions et propriétés des fonctions limites. 2. Séries de fonctions usuelles, séries entières, dérivation et intégration sous le signe somme. 3. Intégrales de Riemann généralisée, critères de convergence.

Teaching language

FRANÇAIS / FRENCH

TPE dans le domaine des probabilités, ou bien TPE dans le domaine des équations différentiel

Teaching language

FRANÇAIS / FRENCH

Teaching language

FRANÇAIS / FRENCH

The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.

Teaching language

ANGLAIS / ENGLISH

The teaching of English during the bachelor's degree aims to improve written and oral skills so that students become more autonomous. The aim is to be able to understand and communicate in future professional exchanges, as well as to be able to understand the scientific articles that they may encounter during their studies and/or professional lives. Throughout the bachelor's degree, English courses focus on providing an opening to different cultures in order to encourage exchanges between countries. Level groups are set up during the first semester to enable everyone to approach English courses in the best possible conditions. The emphasis is on oral participation thanks to a quality policy of the UFR which organises English courses in half groups.

Teaching language

ANGLAIS / ENGLISH