Instructor:   Dr. Attila SALI
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 (fundamental concepts, connectedness, graph coloring, 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).
 

Remark.  This is the less advanced course out of the two COM1 courses, basically adviced for those having no courses ever related to combinatorics. This course will have detailed introduction into graph theory as well, so those taking graph theory are suggested to take COM1A.
In case the number of students registering for the two combo courses  will be below 15 we'll join the two combinatorics courses.