Here are all of my 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. You can also view handouts categorized by subject on the main handouts page.
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.
A very short handout on lifting the exponent, followed by some problems.
A handout for an introductory graph theory lesson I gave in the Philippine Math Olympiad Summer Camp.
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.
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.
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.
Discusses example problems, followed by a problem set. Some basic knowledge about graph theory assumed.
Briskly sets up the projective plane and discusses example problems using Pascal’s theorem, followed by a problem set.
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.
An article on mathematical investigations. The intended audience are Philippine high school students, in view of the planned curriculum change.
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 light-hearted problem set on compass-and-ruler constructions, as well as constructions with other tools. Best not to take it too seriously.
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.
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.