Chris’s Notes

Welcome to this part of my website. I occasionally store notes under this path of my website which are listed below.

Note: A lot the elements on my site are not designed for dark mode and I’m too lazy to fix that so you need to use light mode.

[proof=Advanced Modern Algebra: Part 1 (3rd ed.) by Rotman] Chapter B-2: Zorn’s Lemma

• Transcendence [/proof]

[proof=An Introduction to Homological Algebra by Weibel] Chapter 1: Chain Complexes

• 1.1 Complexes of $R$-Modules [/proof]

[proof=Complex Geometry: An Introduction by Huybrechts] Chapter 1: Local Theory

• 1.1 Holomorphic Functions of Several Variables

Chapter 2: Complex Manifolds

• 2.1 Complex Manifolds: Definitions and Examples [/proof]

[proof=Ideal, Varieties, and Algorithms by Cox, Little, and O’Shea] Chapter 2: Gröbner Bases

• 2.1 Introduction
• 2.2 Ordering on the Monomials in $k[x_1, \ldots, x_n]$
• 2.3 A Division Algorithm in $k[x_1, \ldots, x_n]$
• 2.4 Monomial Ideals and Dickson’s Lemma
• 2.5 The Hilbert Basis Theorem and Gröbner Bases [/proof]

[proof=Introduction to Lie Algebras and Representation Theory by Humphreys]

• Chapter 3
  • 10 Root systems [/proof]

[proof=PMC Analysis Reading Group] Meeting notes:

• 5/30/2026 [/proof]

[proof=POLYNOMIALS by Lascoux]

• Chapter 1 - Operators on polynomials
• Chapter 9 - Key polynomials for type $B,C,D$ [/proof]