Free book · PDF and EPUB
A Mathematics Refresher
From counting to calculus and beyond — a visual journey back through everything you once knew.
Written for people who use mathematics at one remove: you talk about cosine similarity and gradient descent every day, and somewhere along the way the machinery underneath went quiet. It starts at arithmetic and ends at the mathematics behind machine learning, and it does not skip the steps in between.
The EPUB uses MathML, which reads well in Apple Books and Thorium; a few older readers render equations poorly, so take the PDF if yours is one of them.
Four parts, in the order you lost them
- PART I Foundations Number systems, algebra, and how a proof actually works.
- PART II School level Functions through trigonometry, series, vectors, matrices, calculus.
- PART III BSc core Real analysis, linear algebra, multivariable, ODEs, groups, statistics.
- PART IV Mathematics for AI Embeddings and PCA, gradient descent, entropy and cross-entropy.
- 77pages
- 42figures drawn for this book
- 310exercises in three tiers
- 23chapters
There is an interactive version too
Twenty-five chapters taught as a flow: the idea, a method worked line by line, something to play with, then practice that never runs out and shows you the full working when you get one wrong. Drag a tangent along a curve, or make gradient descent diverge by nudging the learning rate.
Open the companion app →Written by Abdul Qabiz and co-authored with AI: Anthropic's Claude Fable and Claude Opus drafted, illustrated and checked much of the material under direction, and every numerical answer was verified in code before printing.
It went through several review passes, and errors will still have survived, as they do in every first edition. If you find one — a wrong answer, a muddled explanation, a figure that misleads — please report it on the blog so it can be corrected in the next edition.
2026 Edition · free to read and share