The Arithmetic of Polynomial Rings over Finite Fields

Today we're going to talk about something quite exciting and unexpected: the arithmetic of polynomial rings over finite fields and its similarity to the arithmetic of the integers. We'll first run though some preliminary observations about the arithmetic of the polynomial rings which will suggest that it behaves similar to the arithmetic of the integers.… Continue reading The Arithmetic of Polynomial Rings over Finite Fields

Presentation: UMRS Spring 2018

Here's another written version of a presentation I gave in 2018 at UMN's USMR (undergraduate mathematics research seminar). I spoke about using generating functions to compute the expectancy of fixed points in permutations. Some of the proofs in this talk are technical, so I've decided to cut them and only present the critical ones. After… Continue reading Presentation: UMRS Spring 2018

An Introduction to Topological Groups

Hey there, and welcome back! Today we're going to talk about an interesting merger of abstract algebra and topology, namely topological groups. Last week a colleague asked me if there were any mathematical topics which were used in class but that I was never previously taught. While I do self study a lot, I had… Continue reading An Introduction to Topological Groups