Basic counting: sum rule, product rule, selection problems, occupancy problems, binomial coefficients, Stirling numbers

Generating functions: ordinary and exponential generating functions, applications to counting

Recurrences: Fibonacci numbers, derangements, the method of characteristic roots, solving recurrences with generating functions

Principle of inclusion-exclusion

Pigeonhole principle, non-constructive proofs, parity arguments.

Introduction to graph theory: quick overview of fundamental concepts, connectedness, graph coloring, trees; Cayley’s theorem on the number of trees

Brief introduction to Ramsey theory