Instructor:  Dr. Dezsõ MIKLÓS
Text: handouts and Miklós Bóna: A walk through combinatorics

Topics:

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

Introductory graph theory ( quick overview of 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.  This is the more advanced course out of the two COM1 courses, basically adviced for those having some earlier experience with combinatorics.
This course will only have a quick introduction into graph theoryl, so those taking graph theory are suggested to take this course..
In case the number of students registering for the two combo courses  will be below 15 we'll join the two combinatorics courses.