# Category Archives: Uncategorized

## Teaching Lessons from a Summer of Taking Mathematics Courses

Although I am a mathematics education graduate student and am not required to take mathematics courses as a part of my PhD, I had the opportunity to take several mathematics graduate courses this summer as part of a Mathematics Graduate … Continue reading

## Introduction to Ideal Class Groups

Algebraic number theory is a really interesting subject, but unlike some other subjects, it’s not 100% clear what objects people study. This post provides an introduction to the class group of a finite dimensional field extension of $\mathbb{Q}$, an object often … Continue reading

Posted in Math, Number Theory, Uncategorized | Tagged , | 1 Comment

## What is a Manifold? (6/6)

In posts 1-3 we were able to reduce all of the geometry of a curve in 3-space to an interval along with two or three real-valued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading