ECTS
30 credits
Training structure
Faculty of Science
List of courses
Algebra I Linear Systems
5 creditsCalculus CUPGE & Math
3 creditsAlgorithms 1
5 creditsReasoning and Set Theory
2 creditsFunctional programming
5 creditsEnglish S1
1 creditGeometry in the plane, space, and the complex plane
4 creditsAnalysis I Functions of one variable and sequences
5 credits
Algebra I Linear Systems
ECTS
5 credits
Training structure
Faculty of Science
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.
Calculus CUPGE & Math
ECTS
3 credits
Training structure
Faculty of Science
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.
Algorithms 1
ECTS
5 credits
Training structure
Faculty of Science
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.
Reasoning and Set Theory
ECTS
2 credits
Training structure
Faculty of Science
Functional programming
ECTS
5 credits
Training structure
Faculty of Science
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).
Geometry in the plane, space, and the complex plane
ECTS
4 credits
Training structure
Faculty of Science
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
Analysis I Functions of one variable and sequences
ECTS
5 credits
Training structure
Faculty of Science
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.