As an undergraduate, I studied mathematics at the University of Georgia. In early 2014, I put together a short series of expository videos on Ramsey theory that can be viewed here (produced and published by my good friend Eddie Beck).

I'm active primarily in the point-set topology and various abstract algebra tags. Here's a handful 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 in a given semigroup
• On the infinite dihedral group $D_{\infty}$
• 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, Example 3

Outside of math, I am interested in existentialism, Christianity, and exploring the nature of consciousness. I also hold music in the highest regard. I (at least try to) listen to a wide variety of genres, from minimalist / ambient to folk to psychedelic rock, with a particular soft spot for "extreme" metal⁠—especially death and black.

If you want to connect with me elsewhere, I play chess here under the username Kaj_Hansen and Starcraft II (main-racing as Terran) under the "BattleTag" MementoMori#11653. Feel free to add me.