Napkin v1.5 (and more)

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.

recent-flowchart

You can download the latest version from the usual page, or directly from https://usamo.files.wordpress.com/2019/02/napkin-v15-20190220.pdf. 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:

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

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.)