Surely everything below will have typos and errors. Please email me about any you find.
PROMYS 2022 Mincourse Notes
Some notes for talks that I gave as a PROMYS counselor.
AKS Algorithm; a proof of the validity of a polynomial-time prime-checking algorithm, along with a runtime analysis.
Constructible Polygons; the 'T-Shirt Talk' on proving (one direction, at least) of the constructbility criterion for regular polygons. (I brough a giant compass and constructed a pentagon on the chalkboard for this talk it was a lot of fun.)
Googology; some fun vignettes of absurdly big finite numbers and how we construct them.
The Polynomial Trick; some examples of Alon's "polynomial method" used to generate combinatorial bounds via polynomial vector space dimension arguments.
Stanford Class Projects
Dinitz' theorem: written as a final expository paper for Math 107 (Graph Theory).
Probabilistic Method: a crash course, originally written as a series of mini-lectures for Math75SI students. The examples range from game theory to graph theory to Euclidean geometry.
Semidirect Products: written for the WiM paper in Math 120 (Groups and Rings).