Here are all of my handouts, categorized by whether or not they’re for competition math. You can view their LaTeX source files here.
A handout about using overpowered NT theorems for olympiad problems.
A handout about orbits and functional graphs, which some people call thinking about “arrows”.
A handout about chains and antichains in posets, and how to use Mirsky’s and Dilworth’s theorems on them.
A handout about turning inequalities to equalities, by adding them together, using monotonicity, or using equality cases.
A handout about using incidence matrices to solve set combinatorics problems, often using double counting.
A double counting handout specifically themed around counting pairs of things.
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.
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.
A handout about a little-known operator called parallel, its algebraic properties, and its appearances in geometry.
Notes for a Summer HSSP 2022 class aimed at high schoolers. Its ambitious goal is to cover every reference used in the Klein Four’s song, “Finite Simple Group (of Order Two)”.
Type theory, focusing on the theory behind proof assistants, with an emphasis on examples. Prerequisites are some familiarity with logic.
Talks about some neat facts about continuants, a series of polynomials related to continued fractions.
Leads up to a specific example of the Curry–Howard correspondence, a neat connection between logic and type theory.
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.
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.
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.