Math contest platitudes, v3

I think it would be nice if every few years I updated my generic answer to "how do I get better at math contests?". So here is the 2019 version. Unlike previous instances, I'm going to be a little less olympiad-focused than I usually am, since these days I get a lot of people asking… Continue reading Math contest platitudes, v3

A few shockingly linear graphs

There's a recent working paper by economists Ruchir Agarwal and Patrick Gaule which I think would be of much interest to this readership: a systematic study of IMO performance versus success as a mathematician later on. Here is a link to the working paper. Despite the click-baity title and dreamy introduction about the Millenium Prizes, the… Continue reading A few shockingly linear graphs

New oly handout: Constructing Diagrams

I've added a new Euclidean geometry handout, Constructing Diagrams, to my webpage. Some of the stuff covered in this handout: Advice for constructing the triangle centers (hint: circumcenter goes first) An example of how to rearrange the conditions of a problem and draw a diagram out-of-order Some mechanical suggestions such as dealing with phantom points… Continue reading New oly handout: Constructing Diagrams

Make training non zero-sum

Some thoughts about some modern trends in mathematical olympiads that may be concerning. I. The story of the barycentric coordinates I worry about my geometry book. To explain why, let me tell you a story. When I was in high school about six years ago, barycentric coordinates were nearly unknown as an olympiad technique. I… Continue reading Make training non zero-sum

Revisiting arc midpoints in complex numbers

1. Synopsis One of the major headaches of using complex numbers in olympiad geometry problems is dealing with square roots. In particular, it is nontrivial to express the incenter of a triangle inscribed in the unit circle in terms of its vertices. The following lemma is the standard way to set up the arc midpoints… Continue reading Revisiting arc midpoints in complex numbers

Lessons from math olympiads

In a previous post I tried to make the point that math olympiads should not be judged by their relevance to research mathematics. In doing so I failed to actually explain why I think math olympiads are a valuable experience for high schoolers, so I want to make amends here. 1. Summary In high school… Continue reading Lessons from math olympiads

Some Thoughts on Olympiad Material Design

(This is a bit of a follow-up to the solution reading post last month. Spoiler warnings: USAMO 2014/6, USAMO 2012/2, TSTST 2016/4, and hints for ELMO 2013/1, IMO 2016/2.) I want to say a little about the process which I use to design my olympiad handouts and classes these days (and thus by extension the… Continue reading Some Thoughts on Olympiad Material Design

Formal vs Functional Series (OR: Generating Function Voodoo Magic)

Epistemic status: highly dubious. I found almost no literature doing anything quite like what follows, which unsettles me because it makes it likely that I'm overcomplicating things significantly. 1. Synopsis Recently I was working on an elegant problem which was the original problem 6 for the 2015 International Math Olympiad, which reads as follows: Problem… Continue reading Formal vs Functional Series (OR: Generating Function Voodoo Magic)

New algebra handouts on my website

For olympiad students: I have now published some new algebra handouts. They are: Introduction to Functional Equations, which cover the basic techniques and theory for FE's typically appearing on olympiads like USA(J)MO. Monsters, an advanced handout which covers functional equations that have pathological solutions. It covers in detail the solutions to Cauchy functional equation. Summation,… Continue reading New algebra handouts on my website

Against the “Research vs. Olympiads” Mantra

There's a Mantra that you often hear in math contest discussions: "math olympiads are very different from math research". (For known instances, see O'Neil, Tao, and more. More neutral stances: Monks, Xu.) It's true. And I wish people would stop saying it. Every time I've heard the Mantra, it set off a little red siren… Continue reading Against the “Research vs. Olympiads” Mantra