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
- Combinatorial counting
- Double-counting, 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
- 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.