The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
- Set notations and operations
- Binary relations between sets: applications and link with functions in analysis
- Cardinality of a set (finite and infinite) and notion of inclusion-exclusion
- Equivalence, equivalence classes
- Introduction to the logic of the proposals
- Introduction to the logic of predicates
- Prove methods
- Mathematical induction
- Notions of Boolean Algebra
- Natural integer numbers, principle of recurrence, prime numbers, etc.
- Euclidean division, representation in a base, modulo arithmetic, representation of the integers in the computer
- Gcd, Euclid's algorithm
- Basic notions of cryptography
- Recurrence relations
- Solutions of recurrence equations
- Oriented and non-oriented graphs and their matrix representations
- Bipartite graphs and matching problems
- Paths on a graph and Eulerian / Hamiltonian circuits
- Planar graphs and coloring
- Problems of shorter path
- Ranking of the nodes of a graph: PageRank
At the end of this learning unit, the student is able to :
Given the learning outcomes of the "Bachelor in Engineering" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes:
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.About 30 hours of lectures, on-site or remotely depending on the situation.
A mandatory project/case study on the implementation of an algorithm.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.A mandatory project/case study that counts for 2 out of 20 points. If the project report is not done (no report submitted), the student will not be allowed to pass the exam.
A written exam organized in session counting for 18 out of 20 points. Organized on-site or remotely, depending on the health situation.
- Slide du cours
- Mathématiques discrètes de K. Rosen