ECTS
30 credits
Component
Faculty of Science
List of courses
Algebra I linear systems
5 creditsCalculus CUPGE & math
3 creditsAlgorithmics 1
5 creditsReasoning and Set Theory
2 creditsFunctional programming
5 creditsEnglish S1
1 creditsGeometry in the plane, space and complex plane
4 creditsAnalysis I functions of one variable and sequences
5 credits
Algebra I linear systems
ECTS
5 credits
Component
Faculty of Science
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.
Calculus CUPGE & math
ECTS
3 credits
Component
Faculty of Science
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.
Algorithmics 1
ECTS
5 credits
Component
Faculty of Science
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....
Reasoning and Set Theory
ECTS
2 credits
Component
Faculty of Science
Functional programming
ECTS
5 credits
Component
Faculty of Science
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).
Geometry in the plane, space and complex plane
ECTS
4 credits
Component
Faculty of Science
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
Analysis I functions of one variable and sequences
ECTS
5 credits
Component
Faculty of Science
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.