# Discrete mathematics

## Summary

Study of structures and concepts that do not require the notion of continuity. Graph theory, or study of general countable sets are some of the areas that are covered by discrete mathematics. Emphasis will be laid on structures that the students will see again in their later studies.

## Content

- Elementary Combinatorics, counting.
- Graphs, Trees.
- Partially ordered sets, Set systems.
- Generating functions.
- Probabilistic method.
- Linear Algebra method.

## Keywords

Combinatorics, graphs, set systems

## Learning Prerequisites

## Required courses

Linear algebra, Analysis

## Learning Outcomes

By the end of the course, the student must be able to:

- Analyze discrete structures
- Formulate main theorems of the course
- Solve typical combinatorial problems
- Prove main results of the course

## Transversal skills

- Use a work methodology appropriate to the task.

## Teaching methods

Ex cathedra lecture with exercises in the classroom.

## Expected student activities

Solving homework problems

## Assessment methods

Weekly graded homeworks count as 40% of the final grade

Written exam counts as 60% of the final grade.

## Resources

## Bibliography

Discrete Mathematics: Elementary and Beyond (L. Lovasz, J. Pelikan, K. Vesztergombi), Combinatorics: Set Systems etc. (B. Bollobas), Invitation to Discrete Mathematics (J. Matousek, J. Nesetril).

## Ressources en bibliothèque

- Combinatorics : set systems, hypergraphs, families of vectors and combinatorial probability / Bollobás
- Invitation to Discrete Mathematics / Matousek
- Invitation aux mathématiques discrètes / Matousek
- Discrete Mathematics: Elementary and Beyond / Lovasz

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Discrete mathematics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks