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 … Continue reading
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.
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.
Despite the click-baity title and dreamy introduction about the Millenium Prizes, the rest of the paper is fascinating, and the figures section is a gold mine. Here are two that stood out to me:
There’s also one really nice idea they had, which was to investigate the effect of getting one point less than a gold medal, versus getting exactly a gold medal. This is a pretty clever way to account for the effect of the prestige of the IMO, since “IMO gold” sounds so much better on a CV than “IMO silver” even though in any given year they may not differ so much. To my surprise, the authors found that “being awarded a better medal appears to have no additional impact on becoming a professional mathematician or future knowledge production”. I included the relevant graph below here.
The data used in the paper spans from IMO 1981 to IMO 2000. This is before the rise of Art of Problem Solving and the Internet (and the IMO was smaller back then, anyways), so I imagine these graphs might look different if we did them in 2040 using IMO 2000 – IMO 2020 data, although I’m not even sure whether I expect the effects to be larger or smaller.
(As usual: I do not mean to suggest that non-IMO participants cannot do well in math later. This is so that I do not get flooded with angry messages like last time.)
Suppose you are a math PhD student at MIT. Officially, this “costs” $50K a year in tuition. Fortunately this number is meaningless, because math PhD students serve time as teaching assistants in exchange for having the nominal sticker price waived. MIT then provides a stipend of about $25K a year for these PhD student’s living expenses. This stipend is taxable, but it’s small and you’d pay only $1K-$2K in federal taxes (about 6%).
The new GOP tax proposal strikes 26 U.S. Code 117(d) which would cause the $50K tuition waiver to also become taxable income: the PhD student would pay taxes on an “income” of $75K, at tax brackets of 12% and 25%. If I haven’t messed up the calculation, for our single PhD student this means paying $10K in federal taxes out of the same $25K stipend (about 40%).
I think a 40% tax rate for a PhD student is a bit unreasonable; the remaining $15K a year is not too far from the poverty line.
(The relevant sentence is page 96, line 20 of the GOP tax bill.)
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!
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.)