Combinatorics I

Sets: the theorems of Sperner, Erdös-Ko-Rado, Kruskal-Katona. Graphs: Trees, chromatic number, planar graphs, extremal theorems of Turán, Kövári-Sós-Turán and Erdös-Stone. Ramsey theory. Random graphs. The Szemerédi Regularity Lemma, and applications. Algebraic and Topological methods in Combinatorics. Additive Combinatorics.

References:
BOLLOBÁS, B. – Modern Graph Theory, New York : Springer, c1998.
ALON, N., SPENCER, JOEL H. – The Probabilistic Method, 3rd ed. Hoboken, N.J.: Wiley, c2008.

* Standard program. The teacher has the autonomy to make any changes.