---
title: "Essential Maths"
url: "/learn/essential-maths"
---

There is a version of this material that is a maths degree, and a version that
is a cheat sheet. Neither is useful. What is useful is the subset that changes
how you read a model: enough linear algebra to see what a layer does to a
vector, enough probability to know what a loss function is asserting.

Everything here is derived rather than quoted, and every result is followed by
the place it shows up in practice.

## Subcategories

- [Linear Algebra](/learn/essential-maths/linear-algebra.md): Five posts that build linear algebra from a vector as a point in space to the two decompositions — eigen and singular value — that later categories lean on constantly, and finish at the matrix calculus a backward pass actually performs.
- [Calculus & Optimization](/learn/essential-maths/calculus-and-optimization.md): Four posts on the calculus underneath every training loop: what a gradient is and why it points the way it does, why the chain rule is the one fact that makes deep networks trainable, what a loss landscape's shape actually implies, and how constraints get folded into an objective.
- [Probability & Statistics](/learn/essential-maths/probability-and-statistics.md): Four posts from sample spaces to the mathematical roots of the bias-variance tradeoff, with maximum likelihood estimation as the hinge: the idea that most loss functions in machine learning are not designed so much as derived from an assumption about noise.
- [Information Theory](/learn/essential-maths/information-theory.md): Two posts that give probability's likelihood-maximising view of loss a second, equivalent reading: entropy as a measure of uncertainty, cross-entropy as the cost of using the wrong model to describe it, and KL divergence as the gap between the two.