Fractional Calculus is easier than you think — When we think of a derivative, what exactly is the thing we think of? Note: this article is a flyover bird’s eye view of some elementary fractional calculus. Most of the material is stuff I covered in my undergraduate thesis, which you can DM me for if you are interested. …

The best series have unexpected results. — In mathematics, there are few things as nice as an infinite sum. If we can, we like to turn them into geometric sums, and if we can’t, well, we try to figure out why. One famous summation problem is the Basel problem. The Basel problem is a natural question to…

A brief introduction to manifold theory, with some topology and analysis for good measure — When you read about physics and mathematics in the news, or see a Wikipedia article, you will likely come across the word “manifold”. It usually doesn’t come with any explanation, and it seems relatively important. Manifold theory is the theory which underlies General and Special relativity, as well as a…

Measurable Functions and Random Variables —

What exactly is a symmetry? — When we talk about mathematics in terms of its beauty, its symmetry, and its power, we often leave off exactly what these things are. Have you ever stopped to ask yourself what exactly a symmetry is? In this article, I will describe the mathematical study known as Group Theory, which…

The definitive 3! — Ok, so the title may be a little click-bait-ey, but hear me out. There are 3 (three) physics books you need to read to really get physics (up through classical mechanics) intuitively. I’ll also include some runners-up. I recommend these to everyone I know who wants to learn physics, but…

An intuitive guide to some of the main features of Complex Analysis — Complex Analysis is one of the most beautiful topics in mathematics. Famously, the equation

For most mathematicians and statisticians, some physicists, and some other various scientists, one of the hardest subjects they encounter is measure theory. Measure theory is the theory which underlies most of modern statistics and analysis, and in general is a very subtle and deep subject. What makes it so difficult…