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…

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…

If there were one theorem to rule them all, it would be the Generalized Stokes’ Theorem. Over the past few articles, we’ve been setting up the fundamental concepts behind differential forms: the raising operator ♯, the lowering operator ♭, the wedge product ∧, the Hodge star ⋆, and the exterior…

Now that finals season is mostly over, I can get back to making art for my articles. There’s not much to say here. I’m going to try to make as much art for my upcoming articles as possible. I’m going to spend most of the stream making art for the…

You haven’t seen much from me for a few weeks, but I’ve been doing a lot behind the scenes. It’s been about three weeks since I’ve published my last article for two reasons: I want to finish writing most of the articles in the Mathematical Objects arc before I publish…

Euclidean space is the natural environment for Calculus, but manifolds allow us to extend Calculus to curved spaces. We’ve been working with manifolds since the first article in this series, but we didn’t say we were working with manifolds until An Intro to Differential Geometry. …