About five years ago I wrote a blog post warning that I thought it was a bad idea to design math olympiads to be completely untrainable, because I think math olympiads should be about talent development rather than just talent identification, yada yada yada. So now I want to say the other direction: I also… Continue reading Brianchon is fair game
Category: Mathematics
New handout: Intro to Proofs for the Morbidly Curious
Downloadable at https://web.evanchen.cc/handouts/NaturalProof/NaturalProof.pdf. I don't know why I thought to write this, but it's been bugging me for a year or two now that I've never seen the answer to "what is a proof" written out quite this way. So here you go. It's a bit weird for me to be writing an article that… Continue reading New handout: Intro to Proofs for the Morbidly Curious
Everything I need is on the ground
For me the biggest difference between undergraduate math and PhD life has been something I've never seen anyone else talk about: it's the feeling like I could no longer see the ground. To explain what this means, imagine that mathematics is this wide tower, where you start with certain axioms as a foundation, and then… Continue reading Everything I need is on the ground
A common type-error on the OTIS application
There's a common error I keep seeing on OTIS applications, so I'm going to document the error here in the hopes that I can pre-emptively dispel it. To illustrate it more clearly, here is a problem I made up for which the bogus solution also gets the wrong numerical answer: Problem: Suppose $latex {a^2+b^2+c^2=1}&fg=000000$ for… Continue reading A common type-error on the OTIS application
Circular optimization
This post will mostly be focused on construction-type problems in which you're asked to construct something satisfying property $latex {P}&fg=000000$. Minor spoilers for USAMO 2011/4, IMO 2014/5. 1. What is a leap of faith? Usually, a good thing to do whenever you can is to make ``safe moves'' which are implied by the property $latex… Continue reading Circular optimization
Hard and soft techniques
In yet another contest-based post, I want to distinguish between two types of thinking: things that could help you solve a problem, and things that could help you understand the problem better. Then I'll talk a little about how you can use the latter. (I've talked about this in my own classes for a while… Continue reading Hard and soft techniques
Napkin v1.5 (and more)
Careful readers of my blog might have heard about plans to have a second edition of Napkin out by the end of February. As it turns out I was overly ambitious, and (seeing that I am spending the next week in Romania) I am not going to make my self-imposed goal. Nonetheless, since I did… Continue reading Napkin v1.5 (and more)
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 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
Power Overwhelming 