The approach of this course is practical: building on the knowledge acquired in high school, the aim is to apply the basic techniques of analysis. Topics covered: Complex numbers; Common functions; Calculation of limits; Derivation and study of functions; Calculation of integrals; Solving differential equations.

Teaching language

FRANÇAIS / FRENCH

The aim of this course is to acquire the mathematical method, which is based on the unambiguous definition of concepts, the formulation of conjectures, the statement of mathematical propositions and their demonstration using logic based on more elementary propositions. To achieve this, learning and mastering the language of mathematics (discourse, syntax, objects, variables) is fundamental. In particular, this course consolidates (or introduces) the following notions: rudiments of logic (quantifiers, modes of reasoning), sets, applications, binary relations.

Teaching language

FRANÇAIS / FRENCH

Real numbers: integer part, upper bound, density of rationals and irrationals in the reals; Real sequences: basic notions, definition of the limit of a sequence, special sequences, Bolzano-Weierstrass theorem; Real functions: definition of the limit at a point, continuity, intermediate value theorem, image of an interval by a continuous function, uniform continuity, lipschitzian functions; Derivatives of real functions: definition, local extremum and critical point, Rolle's theorem, mean value theorem, Taylor formulas.

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 basics 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 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 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

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

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

Introductory electronics course.

Teaching language

FRANÇAIS / FRENCH

The course aims to introduce some elements of graph theory, combinatorics, arithmetic and their links with discrete geometry. We will focus on algebraic equations that we will solve using origametry (combinatorics of origami and folds). Geometry will be approached from the point of view of graphs but also meshes and finite differences. We will propose to use 3D representation software to address questions of topological and geometric algorithms.

Teaching language

FRANÇAIS / FRENCH

Machine learning is at the heart of many modern artificial intelligence algorithms. This course aims to present the basics of these algorithms by studying the problems of regression, classification, data partitioning and dimension reduction. In practice, the algebra and analysis notions acquired during the year will be used to study these algorithms, which will then be implemented in Python.

Teaching language

FRANÇAIS / FRENCH

This course covers in greater depth the notions of logic seen in the first semester (Peano axioms, cardinality, recursion, propositional calculus, predicate calculus). This course will also be an opportunity to discover a particular type of software called "proof assistant". These powerful tools enable you to model mathematical objects, formulate a theorem about them, interactively develop a formal proof of that theorem, and then automatically check the validity of the proof you've constructed.

Teaching language

FRANÇAIS / FRENCH

In this course, students work under supervision on mathematical problems (such as may be encountered in teaching recruitment exams, for example). It builds on the concepts covered in the year's other mathematics courses, and aims to strengthen students' reasoning and writing skills.

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.

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.

Teaching language

ANGLAIS / ENGLISH

This course is a continuation of the first-year linear algebra course. Topics covered: Symmetric group and determinants; Reduction of endomorphisms and square matrices (eigenvectors, eigenvalues, diagonalization, etc.); Bilinear algebra (bilinear forms and quadratic forms, Euclidean spaces, endomorphisms of a Euclidean space).

Teaching language

FRANÇAIS / FRENCH

This course is a continuation of the first-year analysis course. Topics covered: Reminders and supplements on comparison of sequences and Taylor expansions; Numerical series: elementary computations of sums, generalities about series, positive-term series (comparison theorems, D'Alembert's rule, Cauchy's rule, Riemann and Bertrand series), arbitrary-term series (Cauchy's criterion), series and integrals; Construction of the Riemann integral: Darboux sums, main properties of the integral, connection with integral calculus and primitive search, change of variables; Improper integrals: presentation of the problem at infinity, case of positive functions (comparison theorems), case of functions of arbitrary sign (absolute convergence, Cauchy's criterion, integration by parts).

Teaching language

FRANÇAIS / FRENCH

Basic course on groups and elementary number theory. Topics covered: Number theory: divisibility, Euclidean division, greatest common divisor, least common multiple, Euclid's algorithm, Gauss's lemma, congruence modulo n, prime numbers, decomposition into product of prime numbers, sieve of Eratosthenes, Bézout's theorem, Fermat's little theorem; Groups: definition, examples of groups, subgroups, cyclic groups, order of an element, Lagrange's theorem, group morphism, image, kernel, factorization theorem, quotient group (commutative case), Z/nZ, elementary calculus in Z/nZ

Teaching language

FRANÇAIS / FRENCH

Topics covered: Sequences of functions: different modes of convergence, theorems on uniform convergence and limit/continuity, uniform convergence and integration, uniform convergence and derivation, Dini's theorems, Weierstrass' theorem; Series of functions: different modes of convergence, theorems on uniform convergence and limit/continuity, uniform convergence and integration, uniform convergence and derivation, the zeta function; Power series: radius, operations on power series, Abel's theorem, power series expansion.

Teaching language

FRANÇAIS / FRENCH

Teaching language

FRANÇAIS / FRENCH

This course is an introduction to probability. Topics covered: probability on a finite set, counting; conditional probability, independent events; discrete random variables: definition, common distributions (Bernoulli, binomial, geometric, Poisson), expected value, variance, covariance, independence, pairs of random variables; real random variables with density: definition, cumulative distribution function, common distributions (uniform, exponential, normal), expected value, variance.

Teaching language

FRANÇAIS / FRENCH

Introductory course in programming with C (C17 standard). Topics covered: expressions, statements, functions; compilers, executables, parameters; arrays, strings, files; types, type synonyms (typedef), structures; pointers, memory, dynamic allocation; linked lists.

Teaching language

FRANÇAIS / FRENCH

Introductory course on databases, from design to use in an application context. In particular, the course covers the following topics: Modeling from a specification (entity-association diagram, relational model, choice of constraints and data types); Using a database management system (PostgreSQL) and the SQL language; Developing a dynamic web site as a proof of concept for database use; Using the Python libraries Flask (server) and Psycopg (database communication). The course also covers some of the theoretical foundations of relational databases, including relational algebra, functional dependencies, and schema normalization.

Teaching language

FRANÇAIS / FRENCH

This course introduces tools for verifying that an algorithm or a program is correct, in the sense that it produces the expected result with the announced performance. It contains both a theoretical part on algorithms (variants and invariants to show termination and correction, complexity, etc.) and an applied part on programs (statistical tests, code coverage, floating-point representation problems, etc.). In the final part, all these notions are applied to a case study: hash tables.

Teaching language

FRANÇAIS / FRENCH

This course focuses on trees and their applications. Program: hash methods; trees, binary trees; different representations of trees; traversal methods and their applications: prefix order, postfix order, infix order; applications of trees: binary search trees, Huffman encodings, heaps and priority queues; relationship between binary trees and logarithmic complexity; application to sorting algorithms: fast sort, heap sort, merge sort, complexity bounds. The notions introduced should be familiar not only from a theoretical point of view, but also from a practical point of view, through programming exercises.

Teaching language

FRANÇAIS / FRENCH

Teaching language

FRANÇAIS / FRENCH

Course objectives: Understand the role of the operating system; Know how to use the operating system; Master some of the fundamental concepts of the system: input/output, file systems and memory management; Understand the difference between libraries and system calls.

Teaching language

FRANÇAIS / FRENCH

Teaching language

FRANÇAIS / FRENCH

Digital skills are key to learning, citizenship in a digitized society and integration into the professional world. They are acquired throughout the initial training of students, from elementary school to higher education, but also throughout life, thanks to continuing education, both formal and informal. The French Education Code defines a Reference Framework of Digital Skills (Cadre de Référence des Compétences Numériques - CRCN) based on 16 skills divided into five main areas: information and data, communication and collaboration, content creation, protection and security, and the digital environment. These digital skills are certified by the PIX platform. This Teaching Unit is dedicated to the preparation and passing of the PIX certification.

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.

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.

Teaching language

ANGLAIS / ENGLISH