You’ll only need a middle-school understanding of physics and chemistry to follow this article. I’ll cover everything but the math.

There are few transformations more radical in nature than the rusting of iron. Corrosion turns iron from a shiny, strong, malleable conductor into a dull, weak, brittle insulator. What I…

Buckle up. Real analysis pulls no punches.

In my previous article, *Let’s Derive the Power Rule from Scratch!*, I ended the proof by citing the Moore-Osgood theorem to justify switching limits to prove the power rule for irrational powers. While I think it’s fair game to cite basic theorems, I’m…

How can a sequence of continuous functions converge to a discontinuous function?

As with many fields, calculus started with a bunch of intuition and tricks. Over the next few centuries, mathematicians worked to justify their intuition and tricks by adding rigor to the field. …

You’ve seen limits in Calculus class and you know it has something to do with approaching, but how would you use it in a proof?

If you’re reading this article, you likely have a good, intuitive understanding of limits. The limit of *f(x)* as *x* approaches *a *is the value…

With nothing but a good model, a few definitions, and some math, we’ll derive a fundamental relationship of chemistry.

Anyone who has ever taken a chemistry class has seen the Ideal Gas Law:

We misunderstand entropy because we’re taught it’s a measure of disorder, but the real definition of entropy is far more useful and intuitive.

Look, I get it. You can’t throw a textbook at someone with no formal understanding of statistical mechanics when they ask a question. An answer that someone…

How pop-science can lead to science denial.

In appealing to the general public, pop-science must simplify science. While science communicators must often leave out the math in their simplifications, they can go too far and leave out other important information. Worse, some of these simplifications change the facts, giving false…

From nothing but the definitions of derivatives and limits, we’ll prove one of the first derivative rules you’ll learn in undergrad calculus.

Becoming a master at physics requires a lot of work, but learning the techniques and guidelines in this article is taking the first step.

People often talk about physics as if it were merely a set of facts and equations: ** F=ma**, energy can neither be created nor destroyed,

I am only going to talk about one commonly proposed solution to the excessive use of `if`

statements in the code of *Yandere Simulator* and nothing else about its development or any controversy surrounding it.

*Yandere Simulator *is filled to the brim with `if else`

chains (sections of code in…

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