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.)