Download#

Download the most recent draft of Napkin. Or download the cover art image.

You can also see all generated files, including a folder with each individual part.

Project Status#

Following semver, the version number 1.6 indicates the addition of a few new chapters (and many typo fixes), as well as a pretty cover artwork. Nonetheless, there are several chapters scheduled but not yet written, and many chapters still lack problems or solutions.

See link above for the most recent draft. You can also view the source code on GitHub; the most recent version is automatically compiled from that source.

I would highly appreciate any corrections, suggestions, or comments. The best way to propose changes is to submit a pull request on GitHub. Alternatively, for longer discussion or general action items, submit an issue on GitHub.

Description#

The Napkin project is a personal exposition project of mine aimed at making higher math accessible to high school students. The philosophy is stated in the preamble:

I’ll be eating a quick lunch with some friends of mine who are still in high school. They’ll ask me what I’ve been up to the last few weeks, and I’ll tell them that I’ve been learning category theory. They’ll ask me what category theory is about. I tell them it’s about abstracting things by looking at just the structure-preserving morphisms between them, rather than the objects themselves. I’ll try to give them the standard example Gp, but then I’ll realize that they don’t know what a homomorphism is. So then I’ll start trying to explain what a homomorphism is, but then I’ll remember that they haven’t learned what a group is. So then I’ll start trying to explain what a group is, but by the time I finish writing the group axioms on my napkin, they’ve already forgotten why I was talking about groups in the first place. And then it’s 1PM, people need to go places, and I can’t help but think:

Man, if I had forty hours instead of forty minutes, I bet I could actually have explained this all.

This book is my attempt at those forty hours.

This project has evolved to more than just forty hours.

PDF’s for individual parts#

You can also see an auto-generated table of contents as text.

You can download the entire PDF. Nonetheless, if you need a per-part PDF, you can use the ones below; though note hyperlinks that span across parts will obviously not work. If you want the figures, check all generated files.

There’s also a flowchart by chapter number (rather than part number).

• Frontmatter

1. Starting Out
2. Basic Abstract Algebra
3. Basic Topology
4. Linear Algebra
5. More on Groups
6. Representation Theory
7. Quantum Algorithms
8. Calculus 101
9. Complex Analysis
10. Measure Theory
11. Probability (TO DO)
12. Differential Geometry
13. Riemann Surfaces
14. Algebraic NT I: Rings of Integers
15. Algebraic NT II: Galois and Ramification Theory
16. Algebraic Topology I: Homotopy
17. Category Theory
18. Algebraic Topology II: Homology
19. Algebraic Geometry I: Classical Varieties
20. Algebraic Geometry II: Affine Schemes
21. Set Theory I: ZFC, Ordinals, and Cardinals
22. Set Theory II: Model Theory and Forcing
23. Appendix