L1 - Double Degree in Computer Science and Mathematics

This course is an introduction to linear algebra (formalized in S2) based on intuition derived from plane and space geometry. It includes an introduction to matrix calculus.

The EU is also introducing the basic language of polynomials.

See the full page

Introduction to the main concepts of computer systems

See the full page

The theory of languages and automata belongs to the fundamental branch of computer science. In this teaching unit, we will study languages and their representation, in particular rational languages and their representation by finite-state automata.

See the full page

The aim of this EU is to revisit certain concepts from high school analysis, exploring them in greater depth and developing calculation skills and the interpretation of calculations.

See the full page

In this module, we present the basic concepts of algorithms (notion of a problem, problem instance, instance size, notion of complexity, termination, proof of validity).

The algorithms presented will focus on problems related to sorting, stacks, queues, arrays, etc. 

See the full page

See the full page

This course aims to introduce the functional programming paradigm. First, we will discuss lambda calculus, which is the computational model on which functional languages are based. Then, we will move on to teaching a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following outline:
1. Basic types, definitions.
2. Function declarations.
3. Basic data structures (tuples, lists).
4. Advanced data structures (sum types, records).
5. Exceptions.
6. Higher-order functions, iterators on lists.

If time permits, we will also look at OCaml's module system, one of the main motivations for which is to group related definitions together, but which also allows for reusability through the system of parameterized modules (functors).

See the full page

See the full page

This unit aims to cover plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The geometry and complex numbers sections each represent half of the unit.

- objects of plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical proof

- introduction to complex numbers, geometric interpretation, calculations with complex numbers

See the full page

The aim of this course is to clarify the concepts of limits of sequences and functions, to deepen the study of sequences and functions, to study the concepts of continuity and differentiability of functions, and to introduce the main "usual" functions.

See the full page

Continuation of HAI101I, Algorithms 1

See the full page

Mastery of the basics of C programming; understanding how algorithms and abstract data structures are implemented in the machine.

See the full page

This course aims to introduce the basic concepts of arithmetic and counting that are useful for beginning a bachelor's degree in mathematics.

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

See the full page

Introduction to Web Application Programming

See the full page

This follows on from EU S1 (Algebra I), which introduced linear algebra in R², R³ and^Rn, matrix calculus, and polynomials with real coefficients.

The objective is to introduce some basic concepts of algebraic structure and to deepen the study of vector spaces and linear applications, as well as polynomials.

See the full page

See the full page

This follows on from S1 (Analysis I), where continuity and differentiability of real functions, common functions, and the study of real sequences were introduced.

The objective is to continue and deepen the work on sequences and functions, and to introduce the study of numerical series.

See the full page