# cjquines.

## Handouts

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.

## Papers

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.

## Other

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.