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 moreCovering 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 moreSylow 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 moreProducts 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 moreRelations, 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