Topics of the classes:
- 1. Mathematical inductions, Dirichlet's box principle
(pl,
ang).
- 2. The law of multiplication, addition and the general principles of bijection
(pl,
ang).
- 3. Selection schemes (pl,
ang).
- 4. Binary sequences, dominated sequences (pl,
ang).
- 5. Combinatorial identities
(pl,
ang).
- 6. Recurrence relations (pl,
ang).
- 7. Inclusion-exclusion principle, partitions (pl,
ang).
- 8. Characteristic polynomials and generating functions (pl,
ang).
- 9. Characteristic polynomials and generating functions (part 2) (pl,
ang).
- 10. Finite fields, congruences.
- 11. Introduction to graphs.
- 12. Paths, cycles, connectivity.
- 13. Eulerian and Hamiltonian graphs.
- 14. Graph enumeration, Prüfer code.
- 15. Graphic sequences, isomorphism.