Why the maths is the shortcut
There is a version of machine learning that avoids equations entirely, and you have just read it – that was the Primer. This course takes the other road, on the claim that the maths is not the hard way round but the short way: six ideas, each introduced at the moment a mechanism needs it.
Every explanation of machine learning eventually hits the same wall. You can say a model “adjusts itself to be less wrong” and be perfectly honest, and the reader still cannot picture what adjusting is. Not because the idea is hard, but because the plain-English version has no handles on it.
The maths is the handles. Six ideas carry every model on this site, and none of them arrives here as homework: each one shows up at the exact moment something needs it, and the thing it explains is running on the same page.
0.1The six pieces
Here is the whole course in one look, each chapter named for what it buys rather than what it covers.
- Vectors and similarity – how a machine answers “how alike are these two things?” with arithmetic.
- Matrices as maps – what a layer of a network actually does to the numbers passing through it.
- Slopes and the chain rule – how a machine with millions of knobs works out which nudge helps.
- Gradients and descent – the downhill walk from the primer, now with the fog lifted.
- Probability and expectation – why a model’s answer is a spread of options rather than a verdict.
- Entropy and cross-entropy – the exact number every language model is trained to shrink.
Each one ends where a mechanism begins. If you ever wonder why a chapter is asking you to care about an idea, the answer is always in its last section.
0.2What you need before starting
Honestly: nothing beyond school maths. If you can read a graph and are willing to let a letter stand for a number, you have the prerequisites. No calculus is assumed – chapter 3 builds the one derivative this course needs from scratch, slowly, and it is the only piece of calculus in the whole ladder.
And the escape hatch is built into the page you are reading. Every passage here exists at two depths, and the control at the top switches between them. Stuck in the Student lane? Drop to Curious for a section – it is the same argument, told without symbols – and climb back when the ground feels firm. That is what the two lenses are for; using them is not cheating, it is the intended way to read.