Teacher(s)

Saerens Marco;

Language

French

Prerequisites

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.

Main themes

Set theory

• 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

Logic

• Introduction to the logic of the proposals
• Introduction to the logic of predicates
• Prove methods
• Mathematical induction
• Notions of Boolean Algebra

Introduction to number theory

• 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

Combinatorial mathematics

• counting
• permutations
• arrangements
• Recurrence relations
• Solutions of recurrence equations

Introduction to graph theory

• 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

Aims

At the end of this learning unit, the student is able to :
1	Given the learning outcomes of the "Bachelor in Engineering" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes: S1.I1, S1.G1 S2.2 Students who have successfully completed this course will be able to: Use the terminology of functions, relationships and together well and perform related operations when the context requires it Explain the basic structure of the main proof techniques (direct proof, counterexample, proof by the absurd, induction, recurrence) Apply the various proof techniques in a convincing way by selecting the most adapted to the problem posed Analyze a problem to determine the underlying recurrence relationships Calculate counts, permutations, arrangements on sets as part of an application. Modeling various real-world problems encountered in computer science using the appropriate forms of graphs Explain the problem of the shortest path in a graph and apply classical algorithms to solve this problem

Teaching methods

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.

Evaluation methods

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.

Online resources

On Moodle

Bibliography

Rosen K., Discrete mathematics and its applications, 8th edition, 2019. Mc Graw Hill.

Teaching materials

• Slide du cours
• Mathématiques discrètes de K. Rosen

Faculty or entity

INFO