As part of the "Master's Phase" of the Ph.D. program here at UCR, we are required to take 4 graduate "core" sequences. During this time I've taken notes by hand, however, I also TeX these as well. On this page, I'll upload these notes as I update them, as well as list the professors I had taken these courses with (or sat in on for differential equations). No doubt that these are riddled with errors. These are written nearly as presented in lecture, with my own thoughts (and some choice quotes from professors) added. The only exception is the Part A differential equations notes. I did not sit in on this class, but Emerald Win (another graduate student at UCR) generously shared her handwritten notes which I then TeX'd. The notes assume undergraduate knowledge in math, but (hopefully) not too much background prerequisite knowledge. I also have my notes from some electives I've taken here (Commutative and Homological Algebra) as well as a course on Category Theory from UCLA.
Graduate Compendium
Full Text - Last Updated 7/16/25
These are the collection of all the below notes, as well as every exercise, midterm, and final that has been given in the two years I took these courses. There are no solutions in this document, however I have most of the solutions; If you ever want to know how to solve a problem- feel free to reach out.
Algebra
Notes: Last updated 6/8/22
Instructors: Part A - Dr. Wee Liang Gan, Part B - Dr. Jacob Greenstein, Part C - Dr. Carl Mautner
Complex Analysis
Notes: Last Updated 6/1/22
Instructors: Part A - Dr. Bun Wong, Part B - Dr. James Kelliher, Part C - Dr. Brian Collier
Real Analysis
Notes: Last Updated 6/20/23
Instructors: Part A - Dr. Qi Zhang , Part B - Dr. Zhenghe Zhang, Part C - Dr. Feng Xu
Topology
Notes: Last Updated 6/20/23
Instructors: Part A - Dr. Stefano Vidussi, Part B - Dr. Peter Samuelson, Part C - Dr. Fred Wilhelm
Differential Equations
Notes: Last Updated 6/20/23
Instructors: Part A - Dr. Weitao Chen, Part B - Dr. Amir Moradifam, Part C - Dr. Po-Ning Chen
Commutative Algebra
Notes: Last Updated 4/10/23
Instructor: Dr. Jose Gonzalez
Homological Algebra
Notes: Last Updated 6/20/23
Instructor: Dr. Wee Liang Gan
Algebraic Topology
Notes: Last Updated 3/27/24
Instructor: Dr. Brian Collier
Deformation Theory
Notes: Last Updated 12/13/24
Instructor: Dr. Jacob Greenstein
Algebraic Groups
Notes: Last Updated 7/16/25
Instructor: Dr. Carl Mautner
Functional Analysis
Notes: Last Updated 7/16/25
Instructor: Dr. Zhenghe Zhang