PinnedJoseph MellorinCantor’s ParadiseAn Intro to TopologyTopology is the study of how you can squish and stretch things without gluing or cutting, but it can be intimidating. We’ll make it simple.·22 min read·Nov 16, 2022--7--7

PinnedJoseph MellorinCantor’s ParadiseThe Road to Quantum Mechanics, Part 1: Intro, Coordinates, and KinematicsIt’s a long road to understanding Quantum Mechanics, and there are no shortcuts. In this series, I’ll show you Quantum Mechanics from the…·20 min read·Dec 30, 2021--13--13

PinnedJoseph MellorinCantor’s ParadiseHow to Discover Finite Fields While Bored in Class, Pt. 1: Cellular AutomataI thought I was just drawing pretty lines, but my high school doodles turned out to be Linear Algebra over a finite field.·11 min read·Mar 14, 2022--4--4

Joseph MellorUpdate: I’m Still Active, the Math is Just TrickyI’m just writing this article to let you know I’m still writing and to explain my future plans.·5 min read·Feb 24, 2024--1--1

Joseph MellorinTechnological SingularityThe Rigid Body Lagrangian and the Inertia TensorThere’s more to the world than point particles.·22 min read·Dec 30, 2023----

Joseph MellorinTechnological SingularityRepresentations of Finite FieldsThere’s little to no easy-to-use, freely available software for working with general finite fields. Let’s fix that.·19 min read·Nov 25, 2023--3--3

Joseph MellorEigenvalues and EigenvectorsEigenvalues and eigenvectors are the most powerful tools in Linear Algebra.·16 min read·Sep 4, 2023--1--1

Joseph MellorUpdate: I’m Still Alive and Making ContentI haven’t published an article in a few months because I’ve been incredibly busy, but I’m starting to get more time to make content.·3 min read·Sep 3, 2023--3--3

Joseph MellorDifferential Forms and TensorsThe Levi-Civita symbol allows us to take determinants and rewrite Differential Forms in terms of tensors.·15 min read·Jun 26, 2023--1--1

Joseph MellorA Mathematical Approach to TensorsA matrix is a linear map of a vector to another vector. A tensor is a multilinear map of a tensor to another tensor.·17 min read·Jun 4, 2023--2--2