As an undergraduate, I studied mathematics at the University of Georgia. I have a short series of expository videos on Ramsey theory that can be viewed here (recorded and published by my good friend Eddie Beck).

Active primarily in the point-set topology and various abstract algebra tags, here's a few of my less run-of-the-mill contributions to this site:

- Finding primitive elements for finite extensions of $\mathbb{Q}$: a Galois-theoretic technique
- Constructing connected spaces with arbitrarily many path components
- On symmetric polynomials
- Square-and-multiply: an algorithm for computationally efficient exponentiation
- What is topology anyway?
- Finding Galois groups $\cong S_n$ via generating sets: an example
- If $\text{Gal}(p) \cong G_1$ and $\text{Gal}(q) \cong G_2$, when is $\text{Gal}(pq) \cong G_1 \times G_2$?
- Visualizing ring homomorphisms
- The intersection of two compact sets need not be compact
- A continuous function $f:[a,b] \to \mathbb{R}$ is Riemann integrable
- Quotient spaces are ill-behaved with respect to separation axioms
- The box topology on infinite products: problems with continuity
- The Galois group of an irreducible, rational, cubic polynomial is determined by its discriminant
- A one-point
*connectification*of any topological space - A simple application of the Banach fixed-point theorem
- Proving that closed & open subsets of locally compact Hausdorff spaces are locally compact—without
*too*much machinery - Friendly logarithms: Example 1, Example 2

Outside of math, I am interested in Christian theology, existentialism, and phenomenology. I avidly read and edit Wikipedia, and I also hold music in the highest regard. I play trumpet and piano and try to expose myself to a wide variety of genres, from minimalist / ambient to folk to psychedelic rock, with a soft spot for "extreme" metal—especially death and black. Sharing knowledge and beauty is my utmost passion.

If you want to connect with me elsewhere, I play chess here, where I'm training to become a titled player, as well as Starcraft II (main-racing as Terran) with the "BattleTag" MementoMori#11653.