Handouts

Here are some math handouts that I have written, at the Olympiad and competition level.

High school:
Inellipses (SDMC Cauchy 11/11/2017)
mod p^k (SDMC Cauchy 12/2/2017)
Polynomials (SDMC Cauchy 11/5/2016)
Quadratic Residues (SDMC Cauchy 9/26/2018)
Vieta in Action (SDMC Gauss/Cauchy 10/26/2024)

Middle school:
Inequalities (SDMC Euler 12/14/2024)

Errata

• Quadratic Residues: Problem 11 should instead be modulo any integer not divisible by 32.

Expository notes

Here are some math notes for expository talks that I have given.

Extremal Graph Theory (SDMC Special Talk 1/4/2020): An introduction to extremal numbers of graphs.
Incidence Geometry: Based on Chapter 7 of Larry Guth's Polynomial Methods in Combinatorics.
Partial Symmetries: Based on Chapter 9 of Larry Guth's Polynomial Methods in Combinatorics.

Slides

Here are some slides from virtual math circle talks that I gave at the San Diego Math Circle.

High school:
Abstract Algebra (vSDMC Gauss/Cauchy 4/25/2020)
Arrow's Theorem (vSDMC Gauss/Cauchy 4/18/2020)
Discrete Fourier Transform (vSDMC Gauss/Cauchy 5/2/2020)

Middle school:
Poker Probabilities (vSDMC Euler 3/28/2020)
Proving Irrationality (vSDMC Euler 6/20/2020)