# Notes

You can read these free of charge, under the condition that all typos or errors be sent to me.

## University of Illinois, Chicago

(Fall '22) Math 520 Prime Avoidance, Nakayama's Lemma, Dimension Theory, Regular Rings, Depth and Length of Modules, Complexes, Catenary Rings, Hensel's Lemma, Injective Modules, Gorenstien Rings. This is a good companion set of notes to the last time I took commutative algebra at the University of Michigan; this class is far more algebraic and results driven, whereas the former course was more geometric and computation driven. The notes for this course can be found here.

(Fall '22) Math 554 Riemann Surfaces, holomorphic maps, monodromy, Riemann-Hurwitz/Riemann-Roch formulas, divisors, Serre Duality, sheaves, DeRham Cohomology, algebraic curves, canonical maps, Castelnuovo's bound, and some other related topics. While these notes are only for a bit more than half the course, they are organized and (relatively) consistent. The link to them can be found here.

## University of Michigan

(Fall '19) Math 614 Ring Spectra, Integral Extensions, Krull Dimension, Nakayama's Lemma, Associated primes/Primary Decomposition, Cohen-Macaulay Rings, Artin-Rees Lemma, and some more Homological Algebra. More detailed course information can be found here. The (mostly complete) solutions to the in class IBLs can be found here.

(Winter '19) Math 594 Groups, Fields, Representations, Galois Theory, and some Algebraic Number Theory. More detailed course information can be found here. (Mostly finished) TeXed notes can be found here.

(Fall '18) Math 593 Rings, Modules, Tensors, and some Homological Algebra. These notes have solutions to possible future homework problems, and therefore will not be made public. If you are interested in seeing these, please reach out.