Instructor:  Dr. Dezsõ MIKLÓS  COA (and Dr. Attila SALI  COB)
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. Since the number of students preregistering for the course is well above 20 we've introduced 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).