Joseph Mellor – Medium

Joseph Mellor

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Cantor’s Paradise

An Intro to Topology

Topology 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.

Nov 16, 2022

An Intro to Topology

Nov 16, 2022

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Cantor’s Paradise

The Road to Quantum Mechanics, Part 1: Intro, Coordinates, and Kinematics

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…

Dec 30, 2021

The Road to Quantum Mechanics, Part 1: Intro, Coordinates, and Kinematics

Dec 30, 2021

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Published in
Cantor’s Paradise

How to Discover Finite Fields While Bored in Class, Pt. 1: Cellular Automata

I thought I was just drawing pretty lines, but my high school doodles turned out to be Linear Algebra over a finite field.

Mar 14, 2022

How to Discover Finite Fields While Bored in Class, Pt. 1: Cellular Automata

Mar 14, 2022

The Cayley-Hamilton Theorem, Pt. 1

Every square matrix satisfies its characteristic equation.

Sep 1

The Cayley-Hamilton Theorem, Pt. 1

Sep 1

Linear Algebra Over a Finite Field

Let’s actually answer some questions about the cellular automata that I introduced to you a few years ago.

Jul 2

Linear Algebra Over a Finite Field

Jul 2

Update: I’m Still Active, the Math is Just Tricky

I’m just writing this article to let you know I’m still writing and to explain my future plans.

Feb 24

Update: I’m Still Active, the Math is Just Tricky

Feb 24

Published in
Technological Singularity

The Rigid Body Lagrangian and the Inertia Tensor

There’s more to the world than point particles.

Dec 30, 2023

The Rigid Body Lagrangian and the Inertia Tensor

Dec 30, 2023

Published in
Technological Singularity

Representations of Finite Fields

There’s little to no easy-to-use, freely available software for working with general finite fields. Let’s fix that.

Nov 25, 2023

An apple representing finite fields.

Nov 25, 2023

Eigenvalues and Eigenvectors

Eigenvalues and eigenvectors are the most powerful tools in Linear Algebra.

Sep 4, 2023

Eigenvalues and Eigenvectors

Sep 4, 2023

Update: I’m Still Alive and Making Content

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.

Sep 3, 2023

Update: I’m Still Alive and Making Content

Sep 3, 2023

Joseph Mellor

Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at https://josephmellor.xyz/articles/.

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