Finally, if you attempt to read this without working through a significant number of exercises (see §0.0.1), I will come to your house and pummel you with [Gr-EGA] until you beg for mercy. It is important to not just have a vague sense of what is true, but to be able to actually get your… Continue reading On choosing exercises
Category: Pedagogy
MOHS hardness scale
There's a new addition to my olympiad problems and solutions archive: I created an index of many past IMO/USAMO/USA TST(ST) problems by what my opinions on their difficulties are. You can grab the direct link to the file below: https://evanchen.cc/upload/MOHS-hardness.pdf In short, the scale runs from 0M to 50M in increments of 5M, and every… Continue reading MOHS hardness scale
Understanding with System 1
Math must be presented for System 1 to absorb and only incidentally for System 2 to verify. I finally have a sort-of formalizable guideline for teaching and writing math, and what it means to "understand" math. I've been unconsciously following this for years and only now managed to write down explicitly what it is that… Continue reading Understanding with System 1
MOP should do a better job of supporting its students in not-June
Up to now I always felt a little saddened when I see people drop out of the IMO or EGMO team selection. But actually, really I should be asking myself what I (as a coach) could do better to make sure the students know we value their effort, even if they ultimately don't make the… Continue reading MOP should do a better job of supporting its students in not-June
Undergraduate Math 011: a firsT yeaR coursE in geometrY
tl;dr I parodied my own book, download the new version here. People often complain to me about how olympiad geometry is just about knowing a bunch of configurations or theorems. But it recently occurred to me that when you actually get down to its core, the amount of specific knowledge that you need to do… Continue reading Undergraduate Math 011: a firsT yeaR coursE in geometrY
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
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
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 