It’s a long road to understanding Quantum Mechanics, and there are no shortcuts. In this series, I’ll show you Quantum Mechanics from the ground up. The word “quantum” roughly means “amount.” In the modern world, it functions as a shorthand for “Quantum Mechanics,” especially when used as an adjective. When…

I thought I was just drawing pretty lines, but my high school doodles turned out to be Linear Algebra over a finite field. When I was in high school and college, I would always try to read ahead in my classes so I’d be prepared when the topics came up…

There’s little to no easy-to-use, freely available software for working with general finite fields. Let’s fix that. Over the past few years, I’ve spent a lot of effort trying to figure out the best way to explain concepts to a wide audience, which requires that I first figure out the…

Eigenvalues and eigenvectors are the most powerful tools in Linear Algebra. We’ve talked about matrices and linear transformations in the previous article in the context of solving systems of equations, but there are often many cases where we have a linear transformation of a space to itself. …

I 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. I apologize for the radio silence. It’s been about two months since I’ve published an article or video. …

The Levi-Civita symbol allows us to take determinants and rewrite Differential Forms in terms of tensors. We’ve spent roughly five articles (or six if you count Vectors and Covectors) talking about Differential Forms, but concepts in Physics are expressed mostly in terms of tensors. If we want our progress in…

A matrix is a linear map of a vector to another vector. A tensor is a multilinear map of a tensor to another tensor. There are a lot of bad explanations in science and math. “Spin is like a ball that’s spinning, except it’s not a ball and it’s not…

The article on tensors will come out soon, but I might also want to work on making stream lines. Blender is quickly becoming one of my favorite tools to use. It’s incredibly powerful, runs at breakneck speeds, and it has a great workflow once you get used to it. The…

I only need to make a featured image before I can publish my next article. Unfortunately, I can’t find any depictions of tensors. Before I get into my main topic, I want to announce that I’ve finally finished the Differential Forms arc (previously named the Mathematical Objects arc) by publishing…