Power Overwhelming - News

American Masters in Mathematics 2026

2026-03-04T13:37:00-05:00

Some of you have probably noticed that I’m helping with organizing a new contest and are asking what exactly this is. So far, I haven’t said much about it because so much is up-in-the-air (and that’s still true).

However, with the first few acceptances and registrations coming out, I’m going to post an FAQ and few quick thoughts of my own. Just to be clear, everything here is my own personal commentary and views and not those of my employer or OMEGA generally.

What is OMEGA?

OMEGA (Organization for Math Engagement and Growth in America) is a new 501(c)(3) whose ambitious long-term goal is to build great, robust math programs for thousands of students all across the USA (whether competition-like or not).

However, that is a pipe dream, because OMEGA is also about four months old and has a whopping four staff, many of which are part-time (I’m officially only working 1/3-time). Maybe OMEGA will be a big deal one day, but it certainly isn’t right now. My way of working has always been following Linus Torvalds’ advice:

Nobody should start to undertake a large project. You start with a small trivial project, and you should never expect it to get large. … So start small, and think about the details. Don’t think about some big picture and fancy design. If it doesn’t solve some fairly immediate need, it’s almost certainly over-designed.

That brings us to the next FAQ:

What is AMM?

The American Masters in Mathematics is that smallest reasonable project we could start with. It will be the first event we run from May 22 to 25, 2026 in Denver this year.

The competition itself will be fairly standard. It’ll be a proof-based, 4.5-hour, 5-problem event with each problem worth 7 points. We officially have a syllabus if you are interested, but at least for 2026 there won’t be any huge shockers here for any of you that have done math olympiad content before. The easiest problems are intended to be similar to what you see on the middle of BAMO-12; the hardest ones will be medium-hard IMO level.

But in addition to the contest itself (4.5 hours), there will be quite a lot of time for some fun events. Officially, the branding is “competition and festival”. In the program, the competition lasts 4.5 hours but the festival is something like 15 to 20 hours.

What makes AMM different?

When I pitched the idea of AMM, the basic thesis was that we should run a legit in-person proof-based event, because those are pretty rare in the USA.

To me, I think what should make AMM attractive and fill some immediate need is some combination of the following:

You write proofs and human reviewers will read what you wrote. It’s not yet another computational contest where you get graded based on just a number, so we can write better, more interesting problems.

You’ll even get a chance to talk with the reviewers briefly. I don’t want to brand this as IMO coordination, because it’s definitely not that (in particular, we don’t want to be adversarial). There are so many things TBD about how this is going to look. However, the basic premise is we’d like everyone who comes to be able to spend a few minutes getting live feedback from a mathematician about at least one of their submitted solutions.

It’s in-person. You’ll get to hang out with people, unlike USEMO. I think you’re missing out on a lot if your only interactions with like-minded peers is on Discord.

I don’t know how to say this politely, but I think it’s ridiculous to tell a high school student “you can only write a proof once you get 13+ on the AIME”. Like, hello? Anyway, if you’re sad about not getting to take USAMO this year, come to Denver. Our problems will also be cool.

I will make sure there is a puzzle hunt on Sunday. It might be a tiny mini-hunt with three puzzles and a metapuzzle (think Zelda hunt), or it might be a bit bigger, but there will be something.

Why is there a long and annoying application?

Mostly because we have no idea how we’re going to select people if we end up getting more applications than capacity (we all know AMC/AIME scores are almost worthless now). So we’re asking for a lot of information because we don’t even know what we’re looking for yet.

Please bear with us. It’s our first time too.

There’s higher math on the syllabus!?

That’s not a question, but yes, I did put it there. I understand this might be a bit controversial. But broadly speaking I want to push people to not be so confined with respect to whatever the unspoken “IMO syllabus” is. As I said in a forum post a few years back:

Certainly, there needs to be some informal boundary on exam content, so that the IMO does not degenerate into a trivia contest. However, on the other extreme, I should hope that the world’s best math students are not so inflexible that merely mentioning concavity makes them cower in fear. Change breaks the brittle.

I just think we should encourage people to learn more math. The choice of “basic algebra and analysis” is intentional because that’s the narrow bottleneck between high-school math and the modern undergraduate syllabus.

I know there’s such a thing as going too far. Affine schemes appearing in high-school problem statements is unreasonable, for example. But I don’t think some first-year algebra and analysis is going too far. So many more doors are open if you know a bit of abstract and linear algebra and real analysis. So I think the ROI is well-justified.

Are you planning to replace the MAA AMC?

I mean, that’s sure a tempting idea, but that’s not even on my radar right now. Again: start with a small trivial project, and never expect it to get large.

The AMM is just an event having its first year. I honestly already think the scope of AMM 2026 is too big and it’s stressing me out.

Where did the name come from?

During some meeting early on, I said something like “we can run our own version of the RMM, like the American Masters in Mathematics or whatever” and the name never changed after that.

How do I apply?

Go to the website and fill out the seven pages of Google Forms.

USEMO 2025 announcement

2025-09-25T13:37:00-04:00

Announcement for the USEMO 2025:

The USEMO 2025 will be held on October 25 - 26, from 12:30pm - 5:00pm ET each day.
For competitors, registration will open in early October on AoPS.
If you’d like to volunteer for grading, the signup for that is posted on the website now too. You should sign up no later than October 25 for that.

As usual, all relevant info at https://web.evanchen.cc/usemo.html.

OTIS XI Applications Out

2025-06-03T13:37:00-04:00

OTIS 2025-2026 applications are due August 1, 2025. The usual fare.

https://web.evanchen.cc/otis.html#apply

March 2025 newsflash

2025-03-14T13:37:00-04:00

Happy Pi Day! Here’s a quick summary of some recent things going on with me:

I got my PhD! (I defended my thesis last December.)

My multivariable calculus (18.02) notes are published on MIT OpenCourse Ware.

The 2025 Teammate Hunt runs from March 28 to April 6. Please check it out! (Yes, I’m on the organizing team.)

USEMO 2025 is open to all middle and high school students now (the US requirement has finally been dropped). Problem proposals are open now and are due on May 10, 2025; see the USEMO page for submission instructions.

After being in development hell for 10 years, the silly weekend project I put together in 2015 is finally up: Olympiad GeoGuessr, a dumb game where you can try to guess collinear and concyclic points from real MO diagrams. Thanks to Abdullahil Kafi for contributing a lot of the recent levels.

We’re going to call this a beta version because it hasn’t been tested much. If you play enough, you’re likely to spot some mistakes in the answer key. Please report these when you see them.

The OTIS Mock AIME is now a data set on Hugging Face for AI enthusiasts. Shrug.

More generally, you can read about my general life status at my now page.

OTIS Mock AIME 2025 & USEMO 2024 results

2024-12-06T13:37:00-05:00

Two pieces of news for high school math contest enthusiasts:

OTIS Mock AIME 2025

We’re running the OTIS Mock AIME again this year! It’ll go from December 19, 2024 to January 20, 2025.

New this year is that we’re offering two tests, I and II, and you can try either or both. However, unlike the real AIME, the two versions are intentionally different:

The OTIS Mock AIME I is going to be tough. It will definitely be harder than the actual AIME, by perhaps 2 to 4 problems. But more tangibly, it will also have significant artistic license. Problems will freely assume IMO-style background throughout the test, and intentionally stretch the boundary of what constitutes an “AIME problem”.
The OTIS Mock AIME II is meant to be more practically useful. It will adhere more closely to the difficulty and style of the real AIME. There will inevitably still be some more IMO-flavored problems, but they’ll appear later in the ordering.

We’ll post at https://web.evanchen.cc/mockaime.html. And the problems will go up on that link on the start date.

USEMO 2024 results

If you haven’t seen, the solutions and results for USEMO 2024 are posted on the archive at https://web.evanchen.cc/usemo.html now.

September newsflash

2024-09-05T13:37:00-04:00

Publicity announcements for all things Evan:

Twitch stream schedule

Twitch Solves ISL will resume on September 13, 2024 and September 20, 2024 at the usual time. Then a two-week break (because I’m traveling on both September 27 and October 4), and then continuing on Fridays for some to-be-determined number of weeks. Check the calendar.

In addition, this Sunday (September 8) at 7PM EDT [EDIT: meant Sunday! agh], by popular request from the otters, I’ll be streaming a session where I work on part of the calculation that I need for my PhD thesis. It’s not going to make any sense so I dunno why people want to see it, but give the kiddos what they want. If it goes well I might run more of them.

USEMO dates

USEMO 2024 will take place 26 October 2024 - 27 October 2024 and is open to US students, see the webpage for details. Volunteering for grading is also open, see https://web.evanchen.cc/usemo.html for details.

0xPARC’s book preview

Some of you might have noticed on my Instagram a picture of a stuffed animal reading a book with my name as one of the editors. If you’re curious, the drafts of this book (which is still a work-in-progress) are actually publicly viewable now at https://github.com/0xPARC/0xparc-intro-book. But this is a behinds-the-scene preview, so expect things to be pretty rough still at this stage.

OTIS X

OTIS X is underway, but you can still join if you want (up until April 2025 or so) by filling out a late application. See https://web.evanchen.cc/otis.html#apply for the instructions for this.

We’ll have a mock AIME this year as well, like last year, but the exact date and time are still TBD.

Galactic Puzzle Hunt 2024

GPH begins 20 September 2024: https://2024.galacticpuzzlehunt.com/. You should check it out :) I’ll be participating as well.

Napkin updates

After 10 years, the cover of the Napkin finally has an artwork piece as well! Thanks to Jenny Chu and Lanie Deng for drawing it. See https://web.evanchen.cc/napkin.html. Or download the cover art image.

New artwork for Napkin!

Also, it’s now possible to download individual parts to Napkin, closing a long-standing feature request for people who don’t want to download the entire 1000-page PDF just to see a specific chapter. See https://web.evanchen.cc/napkin.html#toc for this.

OTIS X applications are open

2024-05-06T13:37:00-04:00

The tenth year of OTIS is now accepting applications.

Due August 1, 2024 for regular deadline and April 30, 2025 for late applications.

https://web.evanchen.cc/otis.html#apply

The application and syllabus are pretty much going to be the same as in previous years; here are some of the (mostly small) changes:

I deleted the question that used to ask about past contest results because I never read the answers to it anyway.
The application problem set is one geometry problem shorter.
Problem C.1 had its description change from “Learn to code” to “Learn to code, please, I implore you” to encourage more people to not skip the problem.
Reading Comprehension answers are now all nonnegative integers who sum is six times a prime to make it harder for people to get the answers wrong when they submit a late application. (For on-time application, the Google Form actually won’t even let you submit until you get all three answers right. But I was consistently shocked at how many people managed to get wrong answers to the reading comprehension in the late application.)
The syllabus now declares that “otter” is preferred over “OTIS-er”. 🦦
Experiment announcement: starting from OTIS X, there will be a few reading units related to the undergraduate math syllabus rather than contest math. The goal for this would be to reduce the activation energy needed to get people to read through parts of Napkin or other textbooks (by baking it into the OTIS system that kids are already using) while not causing any visible changes to people who aren’t interested (because they can just ignore the new units and do other stuff). I haven’t decided exactly how I want these units to look, but if you have opinions you’d like throw at me, feel free to discuss in the comments section.

OTIS Mock AIME 2024

2023-12-22T15:00:00-05:00

This is a short advertisement announcing that the OTIS Mock AIME 2024 is out. The short version is that I wanted to give my students a chance to try their hand at problem composition, which they took enthusiastically, and from their submissions I chose 15 problems to replicate an AIME.

There’s some really nice problems on here (I have some favorites, but to avoid spoilers for people using this as a practice test, I won’t say which ones yet). You can check it out here:

https://web.evanchen.cc/mockaime.html

I expect a number of students who plan to use this test as practice for the upcoming real AIME, so I’ve set a “deadline” of January 15 and ask to avoid public discussion of spoilers before then.

Twitch & USEMO Announcement

2023-08-26T13:37:00-04:00

Twitch Solves ISL Season 3

I’ll be resuming streaming live solves of math problems this fall!

As usual, the stream runs at 5pm Pacific / 8pm Eastern on Fridays, for 2-4 hours per stream usually.

The dates of the first ten streams are currently scheduled (tentatively; these move around a lot) as:

~~Friday September 15~~ Sunday September 17 (note unusual date)
Friday September 22
Friday September 29
Friday October 27
Friday November 3
Friday November 10
Friday November 17
Friday November 24
Friday December 1
Friday December 8

The holiday era (late December / early January) is always a big toss-up, so I’m holding off on scheduling those dates until I have a bit more clarity on my plane tickets those months. We’ll also probably be continuing in the spring semester as well — keep an eye out at https://web.evanchen.cc/videos.html for updates on that.

Tune in for live streams at https://twitch.tv/vEnhance or watch past broadcasts at https://youtube.com/c/vEnhance.

USEMO 2023

I’m writing to lock in the dates for the USEMO:

Registration opens around October 2 on AoPS portal. It remains open until end-of-day October 20 or when capacity is reached.
Day I is Sat. 21 October 2023, from 12:30pm ET to 5:00pm ET.
Day II is Sun. 22 October 2023, from 12:30pm ET to 5:00pm ET.

See https://web.evanchen.cc/usemo.html for details.

New handout: Intro to Proofs for the Morbidly Curious

2023-04-30T13:37:00-04:00

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 contains “you can stop reading here” as the second sentence, but first time for everything, I guess.

Signal boost for Carina Initiatives full-time position

2023-02-23T15:40:00-05:00

The Carina Initiatives (https://carina.fund) is a friend of the math education community which has supported organizations like Art of Problem Solving, BEAM, Athemath, and others. They’re starting a math talent search organization in the United States and are looking to hire a full-time leader (salary $200K-$250K).

Passing this along in case anyone in this space might be interested in applying or knows someone who might be. The link to apply is:

https://carina-initiatives-inc.breezy.hr/p/4ff029962ddc-executive-in-residence-math-talent-search

Japanese EGMO is published!

2023-02-09T13:37:00-05:00

Another translation has arrived!

I’m happy to thank 日本評論社 and their team (Fuma Hirayama, Yuki Kumagae, Taiyo Kodama, Ayato Shukuta, among others) for making the Japanese translation a reality. As well as tripling the length of the errata PDF :)

This marks the second translation of the EGMO textbook (a Chinese translation was published a while ago as well by Harbin Institute of Technology). Both linked below:

Japanese translation at nippyo.co.jp and amazon.co.jp. ISBN-10: 4535789789 / ISBN-13: 978-4535789784.
Chinese translation at abebooks and amazon. ISBN-10: 7560395880 / ISBN-13: 978-7560395883.

Two updates on the EGMO textbook

2022-11-24T13:37:00-05:00

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

Twitch Solves ISL, Season 2

2022-11-04T11:57:00-04:00

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 :)

Ending Season 1 of Twitch Solves ISL

2022-03-11T22:11:00-05:00

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 this time. Having you all come by to support my stream means the world to me.

Until next time!

USA Special Team Selection Test Series for IMO 2021

2020-11-10T13:37:00-05:00

A lot of people have been asking me how team selection is going to work for the USA this year. This information was sent out to the contestants a while ago, but I understand that there’s a lot of people outside of MOP 2020 who are interested in seeing the TST problems :) so this is a quick overview of how things are going down this year.

This year there are six tests leading to the IMO 2021 team:

USA TSTST Day 1: November 12, 2020 (3 problems, 4.5 hours)
USA TSTST Day 2: December 10, 2020 (3 problems, 4.5 hours)
USA TSTST Day 3: January 21, 2021 (3 problems, 4.5 hours)
RMM Day 1: February 2021 (3 problems, 4.5 hours)
APMO: March 2021 (5 problems, 4 hours)
USAMO: April 2021 (2 days, each with 3 problems and 4.5 hours)

Everyone who was at the virtual MOP in June 2020 is invited to all three days of TSTST, and then the top scores get to take the latter three exams as team selection tests for the MO. Meanwhile, the RMM teams and EGMO teams are based on just the three days of TSTST.

Similar to past years, discussion of TSTST is allowed on noon Eastern time Monday after each day. That means you can look forward to the first set of three new problems coming out on Monday, November 16, and similarly for the other two days of TSTST.

To add to the hype, I’ll be doing a short one-hour-or-less Twitch stream at 8:00pm ET on Tuesday November 17 where I present the solutions to the TSTST problems of day 1. If there’s demand, I’ll probably run a review session for the other two days of TSTST, as well.

EDIT: Changed stream time to Tuesday so more people have time to try the problems.

USEMO sign-ups are open

2020-04-21T13:37:00-04:00

I’m happy to announce that sign-ups for my new olympiad style contest, the United States Ersatz Math Olympiad (USEMO), are open now! The webpage for the USEMO is https://web.evanchen.cc/usemo.html (where sign-ups are posted).

Logo for USEMO.

The US Ersatz Math Olympiad is a proof-based competition open to all US middle and high school students. Like many competitions, its goals are to develop interest and ability in mathematics (rather than measure it). However, it is one of few proof-based contests open to all US middle and high school students. You can see more about the goals of this contest in the mission statement.

The contest will run over Memorial day weekend:

Day 1 is Saturday May 23 2020, from 12:30pm ET – 5:00pm ET.
Day 2 is Sunday May 24 2020, from 12:30pm ET – 5:00pm ET.

In the future, assuming continued interest, I hope to make the USEMO into an annual tradition run in the fall.

MOHS hardness scale

2019-11-26T13:37:00-05:00

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 USAMO / IMO problem on my archive now has a rating too.

My hope is that this can be useful in a couple ways. One is that I hope it’s a nice reference for students, so that they can better make choices about what practice problems would be most useful for them to work on. The other is that the hardness scale contains a very long discussion about how I judge the difficulty of problems. While this is my own personal opinion, obviously, I hope it might still be useful for coaches or at least interesting to read about.

As long as I’m here, I should express some concern that it’s possible this document does more harm than good, too. (I held off on posting this for a few months, but eventually decided to at least try it and see for myself, and just learn from it if it turns out to be a mistake.) I think there’s something special about solving your first IMO problem or USAMO problem or whatever and suddenly realizing that these problems are actually doable — I hope it would not be diminished by me rating the problem as 0M. Maybe more information isn’t always a good thing!

Undergraduate Math 011: a firsT yeaR coursE in geometrY

2019-04-01T13:37:00-04:00

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 well in olympiad geometry is very little. In fact I’m going to come out and say: I think all the theory of mainstream IMO geometry would not last even a one-semester college course.

So to stake my claim, and celebrate April Fool’s Day, I decided to actually do it. What would olympiad geometry look like if it was taught at a typical college? To find out, I present to you the course notes for:

Undergrad Math 011: a firsT yeaR coursE in geometrY

Cover art for tr011ey.

It’s 36 pages long, title page, preface, and index included. So, there you go. It is also the kind of thing I would never want to read, and the exercises are awful, but what does that matter?

Screenshot from tr011ey.

(I initially wanted to post this file as an April Fool’s gag, but became concerned that one would not have to be too gullible to believe these were actual course notes and then attempt to work through them.)

Napkin v1.5 (and more)

2019-02-20T13:37:00-05:00

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 finish a decent chunk of what I hoped to do, I decided the perfect is the enemy of the good and that I should at least put up what I have so far.

So since this is someplace between version 1 and the (hopefully eventually) version 2, it seems appropriate to call it version 1.5. The biggest changes include a complete rewrite of the algebraic geometry chapters, new parts on real analysis and measure theory, and a reorganization of many of the earlier chapters like group theory and topology, with more examples and problems. There’s also a new chapter 0 entitled “sales pitches” which gives an advertisement for each of the parts later. The obvious gaps: the chapters on probability are yet to be written, as is some more algebraic geometry. The updated flowchart from the beginning of the book is pictured below.

Flowchart from the Napkin.

You can download the latest version from the usual page. The number of errors has doubtless increased, and corrections are comments are more than welcome.

Incidentally, this seems as good a time as any to mention two more things:

My personal website has seen some updates and re-organization, including most notably the OTIS lecture notes that I promised last Christmas, as well as my personal USAMO/IMO solutions.
Also, I now have a public Facebook page. Right now I mostly plan to use it as a mirror for this blog, but I might also find some other uses for it later. Please feel free to like me ;)

That’s all. Hope you all like it! Best wishes from the Zurich airport.

Some things Evan is working on for 2019

2018-12-25T16:37:00-05:00

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 for the next school year. Note that the application has math problems in it, unlike previous years, so you have to start early.

OTIS Lecture Series

At the same time, I realize that I will never be able to take everyone for OTIS. So I am planning to post a substantial fraction of OTIS materials for public consumption, hopefully by late January, but no promises.

Napkin 2nd edition

The Napkin is getting a second edition which, if all goes well, should come out by the end of February (but that is a big “if”). Most chapters will be mostly unchanged modulo typos, but a few big changes:

I am hoping to add a new part on measure theory with an eye towards probability applications (e.g. law of large numbers, central limit theorem, stopped martingales).
There will be a bit of real analysis / calculus now. (Not much.)
Maybe two-ish bonus chapters on other topics being added.
The earliest chapters (on algebra and topology) are being re-organized significantly, though most of the content should remain the same.
The algebraic geometry chapters on schemes are getting a major facelift, because the old ones were terrible. They will still cover roughly the same content, but in a way that makes more sense, has more examples, and has more pictures.

This means that for the first time the numbering of the chapters is going to break with the new update. This also means there will be plenty of new typos and mistakes for readers to find. I’m looking forward to it!

SPARC 2019 applications

For high school students, SPARC applications will open soon. The deadline will probably be the end of February. This year SPARC will be held in the Bay Area from July 24 to August 2.

New handout: Constructing Diagrams

2018-09-19T13:37:00-04:00

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
Some examples of computer-generated figures

Enjoy.

New algebra handouts on my website

2016-10-01T13:37:00-04:00

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, which is a compilation of various types of olympiad-style sums like generating functions and multiplicative number theory.

I have also uploaded:

English, notes on proof-writing that I used at the 2016 MOP (Mathematical Olympiad Summer Program).

You can download all these (and other handouts) from my MIT website. Enjoy!

First drafts of Napkin up!

2016-07-18T13:37:00-04:00

EDIT: Here’s a July 19 draft that fixes some of the glaring issues that were pointed out.

This morning I finally uploaded the first drafts of my Napkin project, which I’ve been working on since December 2014. See the Napkin tab above for a listing of all drafts.

Napkin is my personal exposition project, which unifies together a lot of my blog posts and even more that I haven’t written on yet into a single coherent narrative. It’s written for students who don’t know much higher math, but are curious and already are comfortable with proofs. It’s especially suited for e.g. students who did contests like USAMO and IMO.

There are still a lot of rough edges in the draft, but I haven’t been able to find much time to work on it this whole calendar year, and so I’ve finally decided the perfect is the enemy of the good and it’s about time I brought this project out of the garage.

I’d much appreciate any comments, corrections, or suggestions, however minor. Please let me know! I do plan to keep updating this draft as I get comments, though I can’t promise that I’ll be very fast in doing so.

Here’s a table of contents, in brief:

I. Basic Algebra and Topology
II. Linear Algebra and Multivariable Calculus
III. Groups, Rings, and More
IV. Complex Analysis
V. Quantum Algorithms
VI. Algebraic Topology I: Homotopy
VII. Category Theory
VIII. Differential Geometry
IX. Algebraic Topology II: Homology
X. Algebraic NT I: Rings of Integers
XI. Algebraic NT II: Galois and Ramification Theory
XII. Representation Theory
XIII. Algebraic Geometry I: Varieties
XIV. Algebraic Geometry II: Schemes
XV. Set Theory I: ZFC, Ordinals, and Cardinals
XVI. Set Theory II: Model Theory and Forcing

(I’ve also posted this on Reddit to try and grab a larger audience. We’ll see how that goes.)