Here are all of my handouts, categorized by subject. You can also view handouts categorized by whether or not they’re for competition math. If you’re looking to prepare for math contests, you should also look at PRIME.
An explanation of Newton interpolation that I find makes it easy to remember, and its relation to the calculus of finite differences and umbral calculus in general.
The canonical decomposition of a function, as explained in Aluffi’s Algebra Chapter 0, and what I think is the correct way to explain quotienting and the first isomorphism theorem.
How I think about convex combinations, both algebraically and geometrically, why they’re named convex combinations, and their relation to Jensen’s inequality.
A handout for an introductory graph theory lesson I gave in the Philippine Math Olympiad Summer Camp.
Discusses example problems, followed by a problem set. Some basic knowledge about graph theory assumed.
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.
A light-hearted problem set on compass-and-ruler constructions, as well as constructions with other tools. Best not to take it too seriously.
A problem set on deriving the values of trigonometric functions for common angles using synthetic methods. Helpful for memorizing sin 36° and cos 75°, for example.
A problem set about angle chasing, for a class I gave in the Philippine Math Olympiad Summer Camp. Has corresponding lecture slides. Heavily based on Chapter 1 of Euclidean Geometry for Mathematical Olympiads.
Discusses some techniques in computational geometry through the proofs of some lesser-known theorems.
An experimental problem set on geometry problems that become easier after constructing something.
Briskly sets up the projective plane and discusses example problems using Pascal’s theorem, followed by a problem set.
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.
Nineteen sketches of different proofs there are infinitely primes, each shortened to be readable in about nineteen seconds each.
A very short handout on lifting the exponent, followed by some problems.
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.
An article on mathematical investigations. The intended audience are Philippine high school students, in view of the planned curriculum change.
My top ten favorite problems from Philippine high school math contests in 2018–19, and a review of the problems in each contest. Has some insight in setting problems for competitions.
A recreational problem set on numbers and their spelled out forms.
An English-Filipino mathematics glossary I compiled, aimed towards words used for math competitions. Mostly based on Maugnaying Talasalitaang Pang-Agham, edited by Gonasalo del Rosario.
Practice questions for the oral rounds, compiled for use of our math team. Has actual MMC questions and questions similar in format, mostly from NIMO.