
We give a systematic introduction to some core
areas of combinatorics with special emphasis on links between seemingly
unrelated areas and on applications to problems in other parts of mathematics
and computer science. Some basic knowledge of linear algebra, calculus,
and familiarity with the notion of finite fields are required.
We cover the following
topics:
 Combinatorial counting
 Doublecounting, parity arguments
 The number of spanning trees
 Dilworth' theorem and extremal set theory
 Finite projective planes, latin squares
 Proofs by counting: probabilistic proofs
 Generating functions
 Partitions
 Applications of linear algebra
 Combinatorial designs
Recommended Textbooks J.
Matoušek and J. Nešetřil: Invitation to Discrete Mathematics,
Oxford University Press, 1998.
L. Lovász, J. Pelikán and K. Vesztergombi: Discrete
Mathematics, Springer, Berlin, 2003.

