Kaj Hansen
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 (recorded 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 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
- 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
Outside of math, I am interested in Christian theology, existentialism, and phenomenology. 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. Sharing knowledge and beauty is my utmost passion. Currently searching for fulfilling employment.
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) under the "BattleTag" MementoMori#11653.
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Athens, GA
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Member for 7 years
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