mathbabe

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