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.

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 (more advanced real analysis after basic measure theory and Lebesgue integral),  

Homological Algebra (very poor quality),

 Fundamental Groups, Cohomology Groups, 

Quantum Mechanics (huge shoutout to Prof. Gary Horowitz!!!), 

Basic Riemannian Geometry (LaTeXed notes. The first part is on vector bundles, differential forms, and integration, which has been incorporated in the "Smooth Manifolds and Differential Topology" notes above), and Advanced Riemannian Geometry .

High School

Analysis, Linear Algebra, Ordinary Differential Equations