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Joseph Mellor

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Joseph Mellor

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Nov 16, 2022

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.

An Intro to Topology

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Joseph Mellor

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Dec 30, 2021

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…

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

Pinned

In

Cantor’s Paradise

by

Joseph Mellor

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Mar 14, 2022

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.

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

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Science Spectrum

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Joseph Mellor

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May 21

Creationists Don’t Understand Radiometric Dating

Creationists say the Earth is 6,000 years old. Fundamental Laws of Physics say otherwise.

Creationists Don’t Understand Radiometric Dating

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Science Spectrum

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Joseph Mellor

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May 2

Creationists Don’t Understand Transitional Species

A transitional species has some characteristics of its ancestors and some of its descendants. You now know more about them than a…

Creationists Don’t Understand Transitional Species

In

Science Spectrum

by

Joseph Mellor

·

Apr 27

The Electromagnetic Lagrangian

This Lagrangian must give all four of Maxwell’s Equations. Our derivation will imply a strange connection between space, time, and a…

The Electromagnetic Lagrangian

In

Science Spectrum

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Joseph Mellor

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Oct 10, 2025

Classical Lagrangian Field Theory

We’ve described particle motion using a Lagrangian, so what about a field? We’ll also derive the Laplacian in spherical coordinates.

Classical Lagrangian Field Theory

In

Science Spectrum

by

Joseph Mellor

·

Jul 16, 2025

Maxwell’s Equations and Differential Forms

We’ve introduced a lot of concepts in the past arc. Let’s put them into practice.

Maxwell’s Equations and Differential Forms

Joseph Mellor

·

Jan 3, 2025

Ideals, Quotient Rings, and Fields

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

Ideals, Quotient Rings, and Fields

Joseph Mellor

·

Sep 1, 2024

The Cayley-Hamilton Theorem, Pt. 1

Every square matrix satisfies its characteristic equation.

The Cayley-Hamilton Theorem, Pt. 1

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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