I was a senior staff member at the HCSSiM program in 2012, where I taught a workshop for the first half of the program, so 17 lectures, with my awesome junior staff Elizabeth Campolongo, Maxwell Levit, and Josh Vekhter.
I also gave a prime time theorem talk on the game of Nim.
I also wrote a bit about the tradition of Yellow Pig Day and the songs we sing every July 17th.
I also wrote a post about what is a proof and why mathematicians are trained to admit they’re wrong.
Here are the notes from the workshop:
- day 1: Notetaking algorithm, map of math, watermelon cutting problem, combinatorial arguments, induction
- day 2: More watermelons, all pigs are yellow, strong induction, notation, cross products of sets
- day 3: Equivalence relations, adding mod n, pigs-in-hole principle, gcd
- day 4: Arithmetic mod n, posets, and the complex numbers
- day 5: Modular arithmetic, cardinality, and the geometry of the complex plane
- day 6: What is a group, what is a graph, and what is the projective plane?
- day 7: The reals are uncountable, Chinese Remainder Theorem, and Dillworth’s Theorem
- day 8: More Dillworth’s Theorem, dihedral groups, and Euler’s totient function
- day 9: Cantor-Shroeder-Bernstein, homomorphisms, and Fermat and Wilson’s theorems
- day 10: Quadratic equations mod p, Cantor’s argument, and Euler characteristic of planar graphs
- day 11: Lagrange, primitive root mod p, and platonic solids
- day 12: More platonic solids and revisiting the complex plane with matrices
- day 13: Permutations, quadratic reciprocity, the alternating group, and transforming the plane
- day 14: Solving the Rubik’s Cube using group theory
- day 15: Sandpiles (Aaron Abrams’ notes)
- day 16: Degenerate and smooth cubics (Benji Fisher’s notes)
- day 17: Magic squares, the game of Set, probability functions on lattices, king chickens, the notetaking algorithm