MATH-260(a) / 4 crédits
Enseignant: Viazovska Maryna
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.
- Elementary Combinatorics, counting.
- Graphs, Trees.
- Partially ordered sets, Set systems.
- Generating functions.
- Probabilistic method.
- Linear Algebra method.
Combinatorics, graphs, set systems
Linear algebra, Analysis
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
- Use a work methodology appropriate to the task.
Ex cathedra lecture with exercises in the classroom.
Expected student activities
Solving homework problems
Weekly graded homeworks count as 40% of the final grade
Written exam counts as 60% of the final grade.
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
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Discrete mathematics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines