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: Expectancy of Fixed Point Permutations Using Generating Functions

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

Directed Reading Programs

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

An Introduction

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