It’s time to get our hands dirty with some topology! Instead of studying spaces directly, we’re going to study a way of studying a topological space (sort of meta, but that’s the fun of it). In particular, we’re going to view a space as a collection of analogous subspaces appropriately glued together satisfying a few restrictions. … Continue reading What Is a Delta Complex?
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
Here’s another written version of a presentation I gave in 2018 at UMN’s Undergraduate Mathematics Research Seminar (UMRS). 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: Expectancy of Fixed Point Permutations Using Generating Functions
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
Today I have something wonderful for budding mathematicians: directed readings. Recently at my university I became a member of the mathematics department’s directed reading program (DRP). The DRP is semester based and it pairs an undergraduate student (mentee) with a graduate student (mentor). The pair decides on a mathematical topic to pursue, specifically a reading … Continue reading Directed Reading Programs
Hi again! This is the start of a series where I will post written versions of my presentations. The material below is a presentation I gave at the start of February in 2019 about the abelianness of groups of order using representations. In late 2018 I became involved in my mathematics department’s directed reading program … Continue reading Presentation: Representation Theory and Group Theory
Hello, and thanks for stopping in! This is The Modular Perspective: a blog about mathematics. Roll Credits… Just kidding! That wouldn’t be much of an introduction now would it? I suppose, in the same light as presenting mathematics, I should give you motivation as to what this blog is about. In my early undergraduate career I … Continue reading An Introduction