L1 - Double Bachelor's Degree in Computer Science and Mathematics

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

The EU also introduces the basic language of polynomials.

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Introduction of the main concepts of computer systems

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

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The aim of this course is to rework certain concepts of analysis from high school, by deepening them, and by developing the practice of calculation and the interpretation of calculations.

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In this module we present the basic concepts in algorithms (notion of 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.... 

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This course aims at introducing the functional programming paradigm. First, we will talk about lambda-calculus, which is the computational model on which functional languages are based. Then, we will teach a real functional programming language, namely OCaml.

The presentation of OCaml will mainly follow the following plan:
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 the module system of OCaml, one of the main motivations of which is to group related definitions, but which also allows to introduce reusability through the system of parameterized modules (functors).

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This UE aims at working on the geometry of the plane, its objects but also the demonstrations. The UE also aims at introducing complex numbers. The parts geometry and complex numbers represent each half of the UE.

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

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

- work on mathematical demonstration

- introduction of complex numbers, geometric interpretation, calculation with complex numbers

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The aim of this course is to clarify the notions of limits of sequences and functions, to deepen the study of sequences and functions, and to study the notions of continuity and derivability of functions, as well as to introduce the main "usual" functions.

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Continuation of HAI101I, Algorithms 1

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

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This UE aims to introduce the elementary concepts of arithmetic and enumeration useful for the beginning of the degree in mathematics.

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Introduction to web application programming

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This course is a continuation of the S1 course (Algebra I) where linear algebra in R², R³ and ^Rn, matrix calculus and polynomials with real coefficients were introduced.

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

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This course follows the S1 course (Analysis I) where continuity and derivability of real functions, usual 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.

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