Math for AI and Beyond

I've been interested in AI since undergrad.  Hofstatder's GED was one of my favorites.  In the 90s though, AI felt like it still purely academic.  Around 2015 I was lucky enough to work at a start up whose value proposition was focused on displacing an industry standard with AI.

I was impressed by how far things had come and decided to try to get back up to speed.  I took it upon myself to learn the math necessary for understanding modern Machine Learning and finished several math courses at a local school.  The canonical coursework calls for Calculus (through multivariable), Linear Algebra, and Statistics/Probability Theory.  I went a bit further and got into some math ended up being surprisingly helpful to everyday Software Engineering.

My goal here is to share some of them in case they help anyone else.

Information Theory There are so many immediately, practically useful ideas here for a computer scientist.  The fundamental concern is how to represent ideas as numbers.  It walks you through from Morse code to JPEG compression and beyond.

Topology Software is concerned primarily with discrete values.  Almost everything we touch can be expressed as tree.  Topology gets you thinking more deeply along these lines and guides you through some of the most common forms.

Linear Algebra At first this feels like just another high school/college math class.  Over the course of a couple years post completion, I started to see it everywhere in my work.  For me, the valuable takeaway was hardly, if at all about the mechanics of Linear Algebra and more about the abstractions.

Fundamentally, there is an optimal representation of a given problem space.  Achieving it involves eliminating redundancy.  Using it vastly reduces the complexity of any function within its domain.  This teaches really useful abstractions for general problem solving and maybe even how to think like a computer.

Numerical Analysis / Computational Linear Algebra

Mostly informative for the frameworks.  Discrete vs Continuous.  Analytical vs Numerical Approximation.  Concerns therein like limits of representation on a computer and rounding.  Helps add perspective on the types of problems we're concerned with as software engineers. Informative regarding various tools for solving different classifications of problems.

Signal Processing

Not immediately useful but instructive in learning about translating between continuous and discrete representations.  Waves are everywhere in nature so stimulating from a curiosity point of view.