Math Competitions

I help out with a variety of math competitions, mostly in Canada. I've proposed problems to HMMT and the CMO. I've also been a trainer for past Canada IMO camps / delegations.

Math Competition Handouts

Here are some of my past math competition handouts. These are all olympiad handouts, with difficulty labelled by peppers (🌶 being IMO 1 level, 🌶 🌶 🌶 being IMO 2-3 level). For some general advice, see my Math Competition Resource List. There are definitely typoes in these handouts, so if you have any questions feel free to email me.

Geometry

• Computability (🌶 🌶 🌶): techniques on how to reduce geometry problems to a computation, as well as how to think with a "computable" mindset.
• Funky Conditions (🌶 🌶 🌶): if you've ever seen geometry problems with weird conditions and you think those problems are impossible, this may be a good handout for you.
• Integer Polynomials (🌶 🌶): some standard techniques on olympiad number theory, as well as some theory on algebraic numbers.
• Inversion (🌶): a standard inversion handout with some emphasis on orthogonal circles. Heavily based off of Evan Chen's EGMO chapter 8, so maybe you're better off reading that.
• Isogonalities (🌶 🌶): some theory including the Isogonal line lemmas as well as quadrilateral isogonal conjugates.
• Möbius Transformations (🌶 🌶 🌶): introduction to fractional linear (Möbius) transformations, and how to view them as a super-powered generalization of inversion.
• Spiral Similarities and Ratios (🌶 🌶): my hallmark handout. The central thesis is that combining spiral similarities with length ratios gives a very powerful and versatile tool.
• Spiral Similarities and Linearity (🌶 🌶 🌶): a beefed up version of the previous handout which also discusses linear moving points.

Number Theory

• Orders, Groups, and Fields (🌶 🌶 🌶): a supersonic introduction to group and field theory for the young olympiad mind.
• Size and Asymptotics (🌶 🌶): some practice with proving that "big" \neq "small" because "big" > "small". In fact, we even practice showing that "really big" \neq "really small" because "really big" >> "really small"!