Math

Handouts for math contests and other mathy things.

Write-ups and descriptions of some math projects I’ve worked on.

Lecture notes for PRIME, a two-month training program for the Philippine Mathematical Olympiad.

Past problems, answers, and reflections for the PMO, Sipnayan, Mathirang Mathibay, GMATIC.

Best Of Math

Here’s what I think are some of the best math-related things I’ve written:

Type Theory by Example

Type theory, focusing on the theory behind proof assistants, with an emphasis on examples. Prerequisites are some familiarity with logic.

Machine Learning

Machine learning, for people more used to reading math textbooks than writing code. Prerequisites are some knowledge of probability theory, and dealing with matrices and vectors.

Engineering

Engineering is finding the answer to a problem without solving it. People aren’t trying to engineer enough, so I wrote this to change that.

Four-Function Primality Testing

Here’s how to use a four-function calculator to check that 123,456,789,011 is prime in fifteen minutes. Discusses the Fermat test and the Miller-Rabin test.

Obscure Geometry Theorems

Discusses some techniques in computational geometry through the proofs of some lesser-known theorems.

Crossing Numbers

Talks about the Euler characteristic, Kuratowski’s and Wagner’s theorems, Fáry’s theorem, and the crossing number inequality. No prerequisites, but knowledge of graph theory is useful.