117(d): Please don’t tax PhD tuition waivers

This is a rare politics post; I’ll try to keep this short and emotion-free. If parts of this are wrong, please correct me. More verbose explanations here, here, here, here, longer discussion here.

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.)

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New algebra handouts on my website

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!

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.)