Here you can find links to my LaTeX notes for some of the graduate classes I've taken at UCR. The idea of typing up my hand-written notes as I have started was inspired by Shane Rankin, whose notes have been a great deal of help to me. Typing up my notes gives me the chance mull over all the material we cover in class while also practicing writing in LaTeX. Even further, if people miss class, I can offer them notes that they actually have a decent chance of being able to read while also being able to hopefully provide extra insight and intuition on more difficult concepts.
As a warning, these notes are almost definitely riddled with typos, so keep an eye out for them and feel free to contact me if you find any. There shouldn't be anything so bad that with a little thinking, you'll be able to figure out what I actually meant to say, but feel free to contact me if you come across some difficulties.
Notes (Last updated: 29 March 2026)
Instructors: Part A - Dr. Carl Mautner, Part B - Dr. Jacob Greenstein, Part C - Dr. Vyjayanthi Chari
Unfortunately, Part C of these notes will not be added, as I lost my Algebra notes (along with pretty much everything else I own) in an apartment fire.
Notes (Last updated: 20 August 2025)
Instructors: Part A - Dr. Carl Mautner, Part B - Dr. Peter Samuelson, Part C - Dr. Bun Wong
Notes (Last updated: 17 July 2025)
Instructors: Part A - Dr. Agnieszka Zelerowicz, Part B - Dr. Qi Zhang, Part C - Dr. Zhenghe Zhang
I've taken a little more liberty in the organisation of these notes (Last updated: 31 August 2026) to create a narrative feel to them and put them in an order that I feel would have been more helpful for me. The core narrative of this is MATH 232 B (with MATH 232 A as interludes) and (hopefully) after that MATH 259.
Instructors: MATH 232 A - Dr. Frederick Wilhelm, MATH 232 B - Dr. Brian Collier, MATH 259 - Dr. Filippo Mazzoli
These notes are inspired by our (incredibly brief) introduction to categories from Dr. Samuelson's MATH 205B class.
These notes are from a Fall 2025 - Winter 2026 reading course I'm doing with Dr. Samuelson. (Last updated: 16 February 2026)
It's mostly just filling in gaps from Fulton and Harris's book along with solutions to some exercises, but I've also spliced extra material about basic properties Lie groups and Lie algebras from Lee's Introduction Smooth Manifolds when relevant.
Warning! These are very much still in the works, some exercises haven't even been fully completed yet, and even worse: there could be some (many) errors!