Table of Contents

Covering Spaces

August 2022

Covering spaces are a cool thing in topology. Finding covering spaces is like unwrapping a topological space. There are intimate connections between the fundamental group and covering spaces. Read more

Sylow Theorems

December 2021

The Sylow Theorems are fundamental to the study of finite groups. We build up to their proof by (1) studying group actions, (2) focusing on existence, and finally (3) studying conjugation of Sylow subgroups. Read more

Products and Coproducts

December 2021

We get our feet wet in category theory by going through the universal properties of products and coproducts. We'll see some examples and prove uniqueness of products. Then, we prove uniqueness of coproducts by duality. Read more


October 2021

The FTFGMPID is one heck of an over powered theorem. It pretty quickly gives you the classification of finitely generated abelian groups, the Jordan normal form, etc. Read more

Relations, Well-Foundedness, and Noetherian Induction

August 2020

What exactly does induction require? We generalize the natural numbers with the notion of a well-founded relation, and correspondingly generalize induction. Read more