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.

Nineteen Proofs There Are Infinite Primes. Nineteen sketches of different proofs there are infinitely primes, each shortened to be readable in about nineteen seconds each.

Lifting the Exponent. A very short handout on lifting the exponent, followed by some problems.

Graph Theory. A handout for an introductory graph theory lesson I gave in MOSC.

Angle Chasing (slides) (problem set). Slides and a corresponding problem set on angle chasing. Material heavily based on Chapter 1 of Euclidean Geometry for Mathematical Olympiads.

Synthetic Trigonometry. 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.

Compass and Ruler. A light problem set on compass-and-ruler constructions, as well as constructions with other tools.

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

Constructions. An experimental problem set on geometry problems that become easier after constructing something.

Hall’s Marriage Theorem. Discusses example problems, followed by a problem set. Knowledge on graph theory assumed.

Pascal’s Theorem. Briskly sets up the projective plane and discusses example problems, followed by a problem set.

Crossing Numbers. No prerequisites, but knowledge of graph theory is useful, and so is familiarity with reading proofs. Goes from a light overview to the crossing number inequality.

Non-Standard MMC Problems. 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.

Image: Pascal’s Theorem.

Expected capture time and throttling number for cop versus gambler.

J. Geneson, C. J. Quines, E. Slettnes, and S. Tsai.

From MIT PRIMES-USA 2018.

Variations on the cop and robber game on graphs.

E. Slettnes, C. J. Quines, S. Tsai, and J. Geneson.

From CrowdMath 2017: Graph Algorithms and Applications.

Bounds on metric dimension for families of planar graphs.

C. J. Quines and M. Sun.

Second Prize, Mathematics, ISEF 2017.

Bounds on metric dimension for families of planar graphs. Slides for a talk I was asked to give about one of the papers I co-authored.

2018–19 in Review. My top ten favorite problems from Philippine high school math contests this year, and a review of the problems in each contest. Has some insight in setting problems for competitions.

Spelling Out Numbers. A recreational problem set on numbers and their spelled out forms.

Talasalitaang Pangsipnayan. An English-Filipino mathematics glossary I compiled.

Image: Talasalitaang Pangsipnayan.