The Thing No One Ever Told Me at School

Imaging for a minute, you had never written a line of code before, and someone came along and showed you this:

let y = 0;
let x = [1, 2, 3];
let w = [4, 5, 6];

for (const i = 0; i < x.length; i++) {
  y = y + weights[i];
}

y = y + b;

As a coder, in pretty much any language, you will probably immediately recognise some variable declarations, a for loop plus a bit of Maths. You might be a little baffled at why someone would write code like this (more soon), but you’d probably know roughly what was going on.

I could have written this a lot more functionally, but this is a maths book, so I’m keeping the code super vanilla for now.

Think back though, to when you first saw code like this. It’s isn’t obvious to the untrained eye what is happening here. It’s obvious now because you learned the syntax, but back then, this was deep magic.

Now say I showed you this:

You might, if you knew a bit of Maths, recognise that this formula is the same thing. You might also, if you’re not new to this, recognise the formula for a simple linear perceptron, or you might not. Don’t worry, soon you will.

In the code, everything is relevant, the square and curly braces, the semicolons, the ordering of the lines.

In this equation too, everything is relevant, the sigma, the italics, capitals, subscripts, superscipts. Sometimes we write a dot or a bar or a star or a hat. All of these things have significance. Both the code and the equation express an idea in a way that is understandable.

This book is your coder’s guide to maths. It is a rosetta stone that will let you mentally translate equations into algorithms.

Our goal in this book will be to get to a point where we can understand all the mathematics needed to read modern machine learning papers, papers like “Attention is All You Need”, the paper that laid the groundwork for ChatGPT.

This book is actually 2 books

This book very specifically focusses on Maths so you can read and understand papers. The companion to this book, Python for Machine Learning will teach you how to put these ideas into practice. You may wish to switch between these two as you go, or remain focussed on one or the other.

Exercises

Like learning code, learning maths is interactive. You’ll find exercises sprinkled through this course. Doing these exercise will cement the ideas in your head.

The Thing No One Ever Told Me at School is

…that maths is code, and conversely code is maths. Maths has loops and variables. It has functions and arrays. It’s just written differently. If someone had explained this to me at the time I probably would have played closer attention and wouldn’t now be jogging to catch up!

Armed with this awareness, you, as a coder, can conceptualise learning maths as simply learning another syntax for something you already know. That’s easy, right?

Let’s go!