With Christmas Day, here are some announcements about my work that will possibly interest readers of this blog. OTIS V Applications Applications for OTIS V are open now, so if you are an olympiad contestant interested in working with me during the 2019-2020 school year, here is your chance. I'm hoping to find 20-40 students… Continue reading Some things Evan is working on for 2019
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
A trailer for p-adic analysis, second half: Mahler coefficients
In the previous post we defined $latex {p}&fg=000000$-adic numbers. This post will state (mostly without proof) some more surprising results about continuous functions $latex {f \colon \mathbb Z_p \rightarrow \mathbb Q_p}&fg=000000$. Then we give the famous proof of the Skolem-Mahler-Lech theorem using $latex {p}&fg=000000$-adic analysis. 1. Digression on $latex {\mathbb C_p}&fg=000000$ Before I go on,… Continue reading A trailer for p-adic analysis, second half: Mahler coefficients
A trailer for p-adic analysis, first half: USA TST 2003
I think this post is more than two years late in coming, but anywhow... This post introduces the $latex {p}&fg=000000$-adic integers $latex {\mathbb Z_p}&fg=000000$, and the $latex {p}&fg=000000$-adic numbers $latex {\mathbb Q_p}&fg=000000$. The one-sentence description is that these are ``integers/rationals carrying full mod $latex {p^e}&fg=000000$ information'' (and only that information). The first four sections will… Continue reading A trailer for p-adic analysis, first half: USA TST 2003
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
I switched to point-based problem sets
It's not uncommon for technical books to include an admonition from the author that readers must do the exercises and problems. I always feel a little peculiar when I read such warnings. Will something bad happen to me if I don't do the exercises and problems? Of course not. I'll gain some time, but at… Continue reading I switched to point-based problem sets
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
An apology for HMMT 2016
Median Putnam contestants, willing to devote one of the last Saturdays before final exams to a math test, are likely to receive an advanced degree in the sciences. It is counterproductive on many levels to leave them feeling like total idiots. --- Bruce Reznick, "Some Thoughts on Writing for the Putnam" Last February I made… Continue reading An apology for HMMT 2016
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
Power Overwhelming 