# Informal notes

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.
## Stochastic processes

__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.

## Signal processing

__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.