This class will be a quick tour of some counting arguments, with an introduction to a few general methods. Here are some examples of what might be counted: lattice paths, triangulations, trees, tilings, functions, and partitions.

Is it possible to comb a cat? Will there always be a tuft or swirl of hair left uncombed? Come get your existential questions answered in this class about the hairy ball theorem. It turns out that you can't comb a hairy ball. A bit more rigorously, the hairy ball theorem is the following statement in topology: every smooth vector field on a sphere has a singular point. In this class, I will give an outline of a proof of this statement. If there is any time left, I might also talk about some fixed point theorems. Warning: there probably won't be any actual cats, I'm sorry. But there might be some inanimate substitutes to play around with.