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 preemptively 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 $a^2+b^2+c^2=1$ for positive real numbers $a$, $b$, $c$. Find the minimum possible value of $S = a^2b + b^2c + c^2a$.

The wrong solution I keep seeing goes like so:

Nonsense solution: By AM-GM, the minimum value of $S$ is $S\ge 3\text{exception 25:}$

A while ago someone asked me how COVID had affected the students I worked with. I replied that, on average, the pandemic had tripled my students’ productivity.

And I’m gonna brag about it like the proud teacher I am.

Couple Thanksgiving presents for y’all:

Errata List now on GitHub

The list of errata is now version controlled on GitHub: vEnhance/egmo-book-errata. So now you can actually see a changelog of the ocean of typos as they come in.

Shout-out to the crew working on the Japanese translation of the book for finding way more errors than I will ever care to admit (I didn’t count, but it’s probably in the 200-300 ballpark).

Automatically Generated EGMO Solutions Treasury (AGEST)

I took a snapshot my database entries for sourced problems in EGMO. It turns out that I have many written up already, so we now have something of a solutions manual for about half the problems or so. Since I like idiotic names, I dubbed it the Automatically Generated EGMO Solutions Treasury.

You can download it here: web.evanchen.cc/textbooks/AGEST.pdf

Some people have asked me why I anti-recommend JavaScript for beginners on my website FAQ. This post will try to give a few reasons why.

Some notes:

• I’m referring to base JS. I like TypeScript a lot for example (it’s high on my tier list of programming languages for beginners). And I know about eslint, but you asked me about recommendations for beginners, and I think beginners shouldn’t have to worry about setting up an IDE with strict linting until after they can write a for loop by themselves without screwing up.
• I have multi-file projects in mind. I don’t have a problem with using inline JavaScript for tiny 20-line snippets of code embedded in a webpage.
• I’m an amateur programmer. Professional programming is a different ball game.

Weak typing

I’m clumsy. I make many more mistakes than the average programmer. The other day …

don’t ask why it just came in my head

Quandary

So you have a fair coin that you found on the ground,
or at least that’s what everyone says.
But on each of N times that you’ve tossed it around,
you see every flip has been heads.

For which value of N should you start to suspect
that the coin isn’t actually fair?
For which values of N can you firmly declare
that the tails side is not even there?

By popular request, Twitch Solves ISL is renewed for a second season which will begin on Friday, 18 November 2022.

As in the past, streams will start at 8:00pm Eastern time on Friday nights, and last 1-4 hours depending on how much coffee I drank that morning.

I’ve scheduled 26 episodes for the second season to follow anime standards; this will last up through the spring semester of MIT, around May 2023.

That said, my holiday plans are to-be-determined so things are likely to change around a bit around the end of December or early January. The stream scheduled for 13 January 2023 is also likely to be modified due to the 2023 Mystery Hunt, which I’m nominally on the organizing team for (though I’m only helping a little bit this year).

Tune in! https://twitch.tv/vEnhance :)

To all my loyal viewers —

After two years, 480 hours, and 102 episodes of Twitch Solves ISL, I’ve finally decided that it’s time for me to take a hiatus from my weekly Friday night streams. So, episode 102 will be the end of Season 1.

To answer the obvious question: I’m definitely open to having a Season 2, although it will probably have to wait until after the summer (as I will be away from my stream setup then), and it probably won’t last 100 episodes. Between now and then, I might also sporadically stream video game sessions if I’m in the mood for it, so if you come by Friday night, you might get to watch me play through something from my Steam library.

I’d like to thank all my viewers and 1800 followers on Twitch, for being such a great audience all …

信言不美，美言不信。

I get a lot of questions that are so general that there is no useful answer I can give, e.g., “how do I get better at geometry?”. What do you want from me? Go do more problems, sheesh.

These days, in my instructions for contacting me, I tell people to be as specific as possible e.g. including specific problems they recently tried and couldn’t solve. Unsurpisingly the same kind of people who ask me a question like that are also not the kind of people who read instructions, so it hasn’t helped much. 😛

But it’s occurred to me it’s possible to take this too far. Or maybe more accurately, it’s always better to ask a specific question, but sometimes the best answer will still be “go do more problems, sheesh”.

Here’s a metaphorical example …

I went and took the idea in I switched to point-based problem sets one step further this year. Now the OTIS-WEB page looks like this:

Makes it feel a bit more rewarding to complete problem sets, I think. Also gives me the chance to plant Easter eggs everywhere, which is always a lot of fun ;)

If you want to see how this is done, the source is up on GitHub.

This is a pitch for a new text that I’m thinking of writing. I want to post it here to solicit opinions from the general community before investing a lot of time into the actual writing.

Summary

There are a lot of students who ask me a question isomorphic to:

How do I learn to write proofs?

I’ve got this on my Q&A. For the contest kiddos out there, it basically amounts to saying “read the official solutions to any competition”.

But I think I can do better.

Requirements

Calling into question the obvious, by insisting that it be “rigorously proved”, is to say to a student, “Your feelings and ideas are suspect. You need to think and speak our way.”

Now there is a place for formal proof in mathematics, no question. But that place is not a student’s first introduction to mathematical argument. At …