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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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

Ideals, Quotient Rings, and Fields

Let's take a formal approach to finite fields using ideals and quotient rings.

Jan 3

Ideals, Quotient Rings, and Fields

Jan 3

The Cayley-Hamilton Theorem, Pt. 1

Every square matrix satisfies its characteristic equation.

Sep 1, 2024

The Cayley-Hamilton Theorem, Pt. 1

Sep 1, 2024

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, 2024

Linear Algebra Over a Finite Field

Jul 2, 2024

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, 2024

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

Feb 24, 2024

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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

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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