Instructor:  Dr. Dezsõ MIKLÓS (and Dr. Attila SALI, if needed)
Text: handouts

Topics:

Basic counting rules (product rule, sum rule, permutations, combinations, Pascal's triangle, occupancy problems).

Introductory graph theory (fundamental concepts, connectedness, graph coloring, trees, Cayley's theorem on the number of trees).

Generating functions (definition, operations on generating functions, applications to counting, binomial theorem,
exponential generating functions).

Recurrences (Fibonacci numbers, derangements, recurrences involving more than one sequence, the method of generating functions).

Principle of inclusion and exclusion (the principle and applications, occupancy problems with distinguishable balls and
cells, derangements, the number of objects having exactly $m$ properties).

Pigeonhole principle and Ramsey theory (Ramsey's theorem, bounds on Ramsey numbers, applications).

Symmetric combinatorial structures, block designs (definition, latin  squares, finite  projective planes).

Remark. If the number of students preregistering for the course will be around or above 20 we'll introduce two introductory combinatorics courses. They might differ a little bit in the topics covered and space of the  COA and COB. Finally COA is the course  of a bit
faster space, assuming more background of the students and omitting graph theory (which will be concurrent with COB).