Notes

Below are some notes I made using LaTeX on various areas of mathematics, and also some handwritten notes. I am in graduate school now and I am still learning new things, which means I will probably continue to make some notes, but definitely not in the near future.

Graduate

Mathematical Physics: I wrote a two volume notes on relevant topics of mathematical physics.

Volume I: Mostly on general relativity and quantum mechanics, with a more mathematical perspective.
Volume II: Mostly on supermanifolds, quantum field theory (QFT), and a supersymmetric proof of the Atiyah-Singer index theorem using functional integral and localization technique. A large part of this also formed my master thesis.
Master thesis
Complex Algebraic Geometry
Smooth Manifolds and Differential Topology

Undergraduate

LaTeX notes:

Commutative Algebra
Galois Theory
Topology
Solution to Problems from Reed and Simon's Functional Analysis

Handwritten notes (warning: incomplete, and significantly lower quality compared to the LaTeX notes):

Complex Analysis
Real Analysis
Homological Algebra
Fundamental Groups
Cohomology Groups
Quantum Mechanics
Basic Riemannian Geometry
Advanced Riemannian Geometry

High School

Analysis
Linear Algebra
Ordinary Differential Equations