Combinatorics

This is a first course in combinatorics. One of the most fundamental things humans do is count, and combinatorics is the art of counting. More specifically, combinatorics is the study and enumeration of various kinds of naturally arising mathematical structures. The course will introduce many of the basic objects of combinatorics: sets, subsets, functions, partitions, and permutations. At the same time, the course will introduce a number of techniques for analyzing these kinds objects—e.g., the Pigeonhole principle, the principle of inclusion-exclusion, double counting, induction, and generating functions.