## Articles

If you like my work, the easiest way to support me is to read and share my articles. Doing so helps out a lot and allows me to dedicate more of my time to writing these articles. If you really like my work, you can support me by donating to my kofi account. If you have trouble accessing any of the articles, let me know and I'll fix it.

### Newest Articles

These are some of my most recent articles. I'm putting them up top so you can see what I'm currently working on. Also, the more views an article gets in the earliest part of its life, the more the algorithm promotes it.

- The Road to Quantum Mechanics, Pt. 11: The Principle of Least Action
- How to Discover Finite Fields While Bored in Class, Part. 5: The Theory and Applications of Finite Fields
- How to Discover Finite Fields While Bored in Class, Pt. 4: Fields in Abstract Algebra
- The Road to Quantum Mechanics, Pt. 10: Lagrangian Mechanics
- How to Discover Finite Fields While Bored in Class, Pt. 3: Rings and Polynomials
- The Road to Quantum Mechanics, Pt. 9: An Intro to Differential Geometry

### How to Discover Finite Fields While Bored in Class

In this series, I want to talk about my journey from messing around with cellular automata led me to a deep understanding of Abstract Algebra. I moved this part up because The Road to Quantum Mechanics takes up a lot of room.

- Cellular Automata
- Algebra and Group Theory
- Rings and Polynomials
- Fields in Abstract Algebra
- Finite Fields
- Linear Algebra (Not Started)
- The Conclusion (Not Started)

### Road to Quantum Mechanics

It's a long road to understanding Quantum Mechanics, and there are no shortcuts. In this series, I'll show you everything you'll need to understand Quantum Mechanics. This series will also serve as a good discussion of many major topics in Classical Mechanics. I'm also putting the honorable mention Approaches to Solving Problems in Physics in this section because it's a great precursor to the rest of the series.

- Intro, Coordinates, and Kinematics
- Kepler's Laws and Newtonan Mechanics
- How to Use PDEs to Model Reality
- Eigenvalue Equations and PDEs
- The Spherical Harmonics
- Bra-Ket Notation and Orthogonality
- The Dirac Delta Function
- The Wave Equation
- An Intro to Differential Geometry
- Lagrangian Mechanics
- The Principle of Least Action
- The Double-Slit Experiment (Half Finished)
- Laplace and Fourier Transforms (Half Finished)
- Maxwell's Equations (Half Finished)
- The Lorentz Force Law (Started)
- The Electromagnetic Wave Equation (Not Started)
- Special Relativity (Not Started)
- The Full Electromagnetic Lagrangian (Not Started)
- Noether's Theorem (Not Started)
- Hamiltonian Mechanics (Started)
- Liouville's Theorem and Poincaré Sections (Not Started)
- Canonical Transforms (Started)
- Hamilton-Jacobi Equation (Not Started)
- Action-Angle Variables (Not Started)
- Canonical Perturbation Theory (Not Started)
- A Brief Intro to Probability and Statistics (Not Started)
- A Brief Intro to Statistical Mechanics (Not Started)

This list is bound to change multiple times as I'm going to rearrange the order of the topics and move topics around within the articles. For example, I might combine two articles, I might split an article, I might shave sections off certain articles and combine them into one article, etc.

#### Do You Really Need to Cover Classical Mechanics?

I am not taking the expressway to Quantum Mechanics. I want to create a story that people can follow. With that being said, most topics I intend to cover will be directly relevant to Quantum Mechanics. In my discussion of eigenvalues and eigenfunctions, I'll introduce the spherical harmonics and Hermitian operators. The discussion of electromagnetism and Hamiltonian Mechanics will lead naturally into the form of the canonical momentum needed to set up the Dirac Equation for a particle in an electromagnetic field. The discussion of Optics will lead naturally into the double slit experiment and the Born rule.

To be clear, just because these articles are "within" Classical Mechanics does not mean that they don't cover Quantum Mechanics. In fact, a lot of these articles will have derivations that would fit into a Quantum Mechanics textbook with some minor changes. When I get to the Quantum Mechanics part of the series, I'm going to be able to link back to one of the articles that explains the concept in Classical Mechanics. In doing so, I hope to spread out the complex parts of Physics so that I don't overload you with one million new ideas at the same time.

The few topics I intend to cover that aren't directly relevant to Quantum Mechanics will work as scaffolding for other topics, either by setting up relevant topics or serving as explicit examples of Classical Mechanics topics that show up in Quantum Mechanics. For example, the second article in the series covers Newtonian Mechanics, which doesn't apply to Quantum Mechanics. You don't have forces in Quantum Mechanics, position and momentum aren't well-defined, etc. It does, however, set the stage for later articles in the series, most notably the article on Lagrangian Mechanics. I don't have any plans on explicit examples of Classical Mechanics topics, but I'm willing to write an article of that sort if anyone wants me to write one.

#### That's a Lot!

To be clear, you could get by with only some of these articles depending on your specific interests. I'm trying to cover everyone from people working in Quantum Computing to Solid State Mechanics to Computational Physics to Theoretical Physics within one coherent framework, so I can't skip any of them.

Also, learning the bare minimum to do one specific thing is a bad way to approach a subject. For some reason, people seem to think the best way to learn something is to learn a few bare-bones ideas utterly unconnected to each other with no explanation. Everything you learn becomes a tool that you can use. To throw away tools because you see no immediate use for them is short-sighted.

The tool analogy breaks down when you consider that you don't know what you don't know. If I see a screw with a weird head, I know I need a screwdriver that can handle it. On the other hand, if you don't know Linear Algebra, you won't even know that you need to learn it to solve the problem.

I'm also leaning towards including extra information because people leave out a lot of information in their discussions without giving you the resources to figure out the information itself or even giving you something to look up. I'll have derivations that you won't find elsewhere on the internet or even in some major textbooks. By the end of this series, you should understand most of the major ideas in modern Physics AND have all the information you need to look into these concepts on your own.

### Big Bois

These are articles that I put a lot of effort into, but are unfortunately too long, meaning they get rejected by the algorithm. To help them survive, I've decided to give them their own section.

### Real Analysis and Calculus

I originally wrote an article on how to derive the Power Rule in Calculus from scratch, but the title was inaccurate because I relied on the Moore-Osgood Theorem, which is from Real Analysis, the field that underpins modern Calculus. Someone pointed this fact out, so I decided to write an article proving the Moore-Osgood Theorem. That article became three articles. If I decide to write more, I'll put them here.

- Let's Derive the Power Rule from Scratch!
- What is a Limit, Really?
- Uniform and Pointwise Convergence
- When Can You Switch Limits in Calculus?

### Entropy

Someone once decided to call entropy disorder, and the scientific discourse has never recovered. I have taken the crusade to rid the world of this nonsense.

- Stop Saying Entropy is Disorder
- Creationism and Entropy
- Let's Derive the Ideal Gas Law from Scratch!

I'm also putting this video in this section because it's relevant.

### Math

I have a few articles about math in general that don't fit anywhere else, but these are some of my biggest articles so I want to bring attention to them.

### Misc

When I eventually write more computer science articles, I'll probably give them their own section. Until then, I'm leaving them here.

- How to Talk About Math and Science
- This Week Had Some Truly Awful Science Takes
- Switch Statements Won't Fix Yandere Simulator
- The Memory Hierarchy

### TUACM

## YouTube

I have a YouTube channel where I upload videos on topics related to physics, math, and coding. Right now, I'm focusing on the series with some occasional streaming, so it's a little bare-bones at the moment.

## Request an Article

If you would like me to write an article for you, email me and we'll discuss rates. $30 per 500 words baseline, and the price will go up if I have to make my own pictures (including pictures of mathematical equations), write code, or do a significant amount of research.

Do not offer to pay me in exposure.