Hello, I'm Joseph.

I'm a fourth-year CCS Mathematics student at UCSB. I'm a big fan of math, beach runs, programming, and guitar.

Partially Ordered is my math blog and programming portfolio. Get ready for Algebra, Topology, and much more.

Featured Posts

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

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

Featured Projects

Marching Cubes

Marching Cubes Algorithm, Implemented in Javascript with WebGL


Physically Simulated Particles, Rendered with WebGL


A Real Time Strategy Game, made with Python, Flask, Javascript, and Socket.io.