Discrete Math and Linear Algebra

Discrete Math and Linear Algebra starts with counting the ways something can happen and ends with a matrix that predicts where a system settles. Four units: Intro to Probability, (Not So Simple) Probability, Matrix Theory, and Markov Chains.

It is built to be worked, not just read. Each section opens with a concrete situation and works the idea all the way through, then hands you practice backed by 565 hints you can open one at a time when you are stuck, and 340 fully worked solutions for when you want to check the whole thing. Behind the course sit two appendices: algebra refreshers for the skills the course assumes you already have, and a study-tools set with the notation, glossary, methods, formulas, and properties gathered in one place.

Accessibility is built in, not bolted on. All 9,486 mathematical expressions are real MathML carrying a spoken-English label, so VoiceOver reads a formula as a sentence instead of spelling it out symbol by symbol. Of the 66 figures, 54 carry a full written description of what the diagram shows, reachable from the figure itself. Text is selectable and resizable, navigation is structural, and color contrast meets WCAG AA in both the light and dark palettes.

The twelve interactive widgets appear here as still images with descriptive captions. The live versions run in the free web edition at probability.megan-warren.com.

Written for grades 10 to 12, and for anyone who wants the math behind machine learning without the handwaving. 2026-2027 edition.