Mathematics

This section contains an overview of my mathematical development. This includes subjects I have studied, topics I plan to learn or explore, and self-written notes. The notes are evidence for my learning, for my future reference, and may be helpful or useful to others if they see fit. Because these are my notes, as of now, they will have little kicks of my personality. I will also offer my best summary of each subject if I have studied it or if I am studying it.

My Goals

I have two long-term goals within mathematics. One of them is to teach math to others in a way that is clear and helps understanding. I think we've all been there when it comes to being taught something in a way that didn't quite connect. My other goal is to pursue research that is meaningful and engaging that contributes lasting value.

Current Coursework (Spring 2026)

• Measure-Theoretic Probability Theory
• Advanced Calculus II
• Rings, Fields, and Galois Theory

Subjects Studied

• Group Theory
• Introductory Partial Differential Equations
• Abstract Linear Algebra
• Advanced Calculus I
• Other Undergraduate Courses

Planned Coursework (Fall 2026)

• Partial Differential Equations
• Topology
• Functional Analysis

Planned Areas of Self-Study

• Commutative Algebra
• Homological Algebra
• Classical Fourier Analysis
• Formal Set Theory

Long-Term Notes Project

I am developing structured notes for the subjects I study or have studied. This is an ongoing project intended to strengthen my understanding and serve as a helpful resource for others.

Selected Subjects

Group Theory

Group Theory is usually the first exposure someone has to more abstract mathematical thinking beyond just learning how to write proofs. Up until this point, math has been fairly concrete or easily visualized. In other subjects, it can be "clear" as to why you'd want to study them. In Group Theory, and other algebraic subjects, you're working with objects that seem to have a completely "artificial" construction. In particular, Group Theory studies objects that have a predictable symmetry. A good geometric example would be the triangle and studying its behavior under rotations of 120 degree increments and flips down the middle.