Math

Notes

Linear Algebra

I am much more partial to edition 2 than edition 3 of Axler for some reason. Perhaps it is because it feels more concise, or there is less wanton “put everything in a box” formatting. But either way, anything that relies on Axler will be referencing ed. 2, not ed. 3.

• Linear Algebra, in a nutshell
• Additional exercises to Linear Algebra Done Right, ed. 2

Abstract Algebra

• An Abstract Algebra Primer

  This is a medium-length (110 pages) introduction to abstract algebra. Intuition is emphasized, fully formalizing arguments takes a back seat, the theory is extremely streamlined (so many important and interesting ideas are omitted). Errata here.

• The Jordan-Holder Theorem

Category Theory

• Why should you care about category theory?

Formal Logic

Mostly based on CMU’s 21-300 Basic Logic course.

• Inductive Structures
• Unique Readability
• Propositional Formulae

Miscellaneous

• A proof of the Principle of Inclusion-Exclusion

  These are notes from my Fall 2023 AIME class that I decided to publicly share.

Math contests

Much of this is extremely old. During my undergrad, I was also involved in CMIMC (but have not written much about it online).

Recommendations

• Math contest advice

  Warning: this is extremely old; I graduated high school in 2023 and have not seriously thought about (high school) math contests since.

• Mock Contests

  A list of mock contests that I’ve written for and mock contests that I personally recommend.

• OTIS

  Evan Chen’s olympiad program.

Reflections

• Contest Report for Summer MAT 2022 (TeX)

• Contest Report for Summer MAT 2021 (TeX)

  A report on the first year of the MAT, which ran online.