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Math for Data Science is a comprehensive treatment that is accessible to readers with working knowledge of calculus and linear geometry. It is in three parts which share a common vocabulary: linear geometry and principal components, then calculus, probability, and statistics, then machine learning. The reward for following the climb is a single geometric framework in which the same ideas - projection, convexity, information - recur at every level.
The first part (Chapters 1–3) develops linear geometry and principal components: eigenvectors as maximum variance directions, the pseudoinverse as the "closest twice" solution, the singular value decomposition as rotation, scaling, rotation.
The second part (Chapters 4–6) develops calculus, probability, and statistics from first principles: information and the cumulant-generating function as convex duals, the central limit theorem proved via moment-generating functions, and maximum likelihood estimator convergence derived using information and surprisal.
The third part (Chapter 7) develops neural network training: trainability — the question of whether gradient descent converges — is characterized precisely for logistic regression in terms of the geometry of convex hulls, the resulting dichotomy with the perceptron follows, and stochastic gradient descent is carefully derived for strongly convex losses.
Concepts are motivated by data and developed geometrically, theorems are proved from first principles, and the material is supported by Python code. Included are 471 exercises together with all solutions, and eight appendices supply the background the main text assumes.