Mathematics, Reconnected

A dependency-driven path from arithmetic to the mathematics of computing

Chris Collins · Version 0.1 · October 2026 · Three volumes

33 chapters, from numbers and algebra through calculus, discrete math, linear algebra, probability, statistics and numerical methods to machine learning. Every topic covers why it works, a worked example with every step shown, where it's used, and a mastery check. The companion code has a Python walkthrough, exercises with tests, interactive labs and a quiz for every chapter.

Volume 1 Foundations to PrecalculusCh. 1–15 · PDF 34 MB Volume 2 Continuous MathematicsCh. 16–20, 26–28, 32 · PDF 25 MB Volume 3 Discrete and Probabilistic MathematicsCh. 21–25, 29–31, 33 · PDF 21 MB
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