These are some notes I've created to help undestand different subjects in mathematics. This page is continuously expanding, and will include notes on machine learning when I find time to type them up.
Derivation of Brownian Motion from the Random Walk
I derive Brownian Motion from first principles Random Walk. This interesting derivation shows how discrete random walks relate to diffusion processes.
Derivative of Brownian Motion is White Gaussian Noise
This derives White Gaussian Noise as the derivative of Brownian Motion. This is enormously important in Ito calculus and stochastic differential equations.
A Friendly Introduction to Fourier Analysis
This derives the Fourier transform from the Fourier series, with an emphasis on intuitive continuity between these tools. The last part of the article I show how within a Hilbert space formulation all of this is very simple.