I am currently taking Stevo Todorcevic’s course (MAT1435HS Topics in Geometric Topology: High-Dimensional Ramsey Theory) at the University of Toronto in Spring 2014. I will be typing up notes and posting them here. Please contact me (by commenting below, or by email) to give me any feedback (typos, questions, clarifications, etc.)
(This is a talk I gave for the Canadian IMO team at their 2014 winter camp at York University on Jan 3, 2014.)
The pigeonhole principle is a remarkable combinatorial theorem that looks silly and obvious, but turns out to be quite powerful and useful, especially in the context of contest problem solving. I’m going to present a couple of statements of the pigeonhole principle, then I’ll give some broad applications of it. I’ll end off with a list of problems.