** Syllabus:** Enumeration (permutations and combinations, the principle of inclusion-exclusion, generating functions, special counting sequences, construction of bijections, enumeration under group action). Composition of power series (the exponential formula, enumeration of trees, Lagrange inversion). Graph theory (basic concepts, network flows, matchings, algebraic graph theory, topological graph theory). Partially ordered sets (important examples, partitions into chains and antichains).

There are no specific prerequisites for this course, but prior experience with abstraction and proofs is helpful. Furthermore, the successful completion of a calculus course and an elementary algebra course (linear algebra, groups) is also helpful.

**Textbook:** Peter Cameron, Combinatorics. Topics, Techniques, Algorithms, Cambridge University Press, 1994, ISBN 0-521-45761.

Cristian Lenart, Department of Mathematics, ES 118, SUNY at Albany