Due to the COVID19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
Teacher(s)
Language
French
Prerequisites
This course assumes that the student already masters notions of algebra covered by the course LINFO1112
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.
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 inclusionexclusion
 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
 counting
 permutations
 arrangements
 Recurrence relations
 Solutions of recurrence equations
 Oriented and nonoriented 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:

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”.
Teaching methods
Due to the COVID19 crisis, the information in this section is particularly likely to change.
About 30 hours of lectures, onsite or remotely depending on the situation.A mandatory project/case study on the implementation of an algorithm.
Evaluation methods
Due to the COVID19 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 onsite 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