Lectures (chosen among the following topics)
1) Sets, relations and functions. Algorithms and their complexity. Mathematical induction. Permutations and k-permutations, binomial coefficients and combinatorial identities. Inclusion and exclusion principle.
2) Recurrence relations. Applications, constructions and solving recurrence relations. Generating functions.
3) Pigeon-hole principle and its applications.
4) graphs and introduction to graph theory.
5) Communication networks, shortest/widest path, network flows, bipartite graphs, trees and spanning trees. Searching trees, algorithms. Bridges and articulations, Vertex and Edge-connectivit, blocks.
Oriented and weighted graphs, networks and flows, cuts and max-flown min-cut theorem.
6) Planar and non planar graphs.
7) Main coding theory problem. Equivalence of codes, necessary and sufficient conditions of the existence of (n, M, d) - codes, Hamming bound, perfect codes.
8) Finite fields and vector spaces Orthogonal Latin squares, projective planes.
9) Codes and Latin squares. Latin squares and mutually orthogonal Latin squares.
10) Introduction to combinatorial designs. Symmetric designs, Application in coding theory.
11) Steiner triple systems. Constructions and relation to graph decompositions.
During the semester each student prepares one or two projects.
1) Sets, relations and functions. Algorithms and their complexity. Mathematical induction. Permutations and k-permutations, binomial coefficients and combinatorial identities. Inclusion and exclusion principle.
2) Recurrence relations. Applications, constructions and solving recurrence relations. Generating functions.
3) Pigeon-hole principle and its applications.
4) graphs and introduction to graph theory.
5) Communication networks, shortest/widest path, network flows, bipartite graphs, trees and spanning trees. Searching trees, algorithms. Bridges and articulations, Vertex and Edge-connectivit, blocks.
Oriented and weighted graphs, networks and flows, cuts and max-flown min-cut theorem.
6) Planar and non planar graphs.
7) Main coding theory problem. Equivalence of codes, necessary and sufficient conditions of the existence of (n, M, d) - codes, Hamming bound, perfect codes.
8) Finite fields and vector spaces Orthogonal Latin squares, projective planes.
9) Codes and Latin squares. Latin squares and mutually orthogonal Latin squares.
10) Introduction to combinatorial designs. Symmetric designs, Application in coding theory.
11) Steiner triple systems. Constructions and relation to graph decompositions.
During the semester each student prepares one or two projects.