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
- Discrete Mathematics: Elementary and Beyond / Lovasz
- Invitation aux mathématiques discrètes / Matousek
- Invitation to Discrete Mathematics / Matousek
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Discrete mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory