Mathematical foundations of machine learning, including linear algebra, vector calculus, probability, and optimization.
Authored by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (published by Cambridge University Press with a permanently free official PDF), Part I of this textbook bridges university math directly to machine learning—covering matrix decompositions, vector calculus (Jacobians and backpropagation gradients), probability distributions, and continuous optimization.
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Phase 1 Comprehensive Written Textbook Reference (Modules 1.1–1.4)
Complete official PDF textbook and companion Jupyter notebooks are freely downloadable from the authors' website.
Status: Verified (2026-11-09)
Review these foundations before starting so you get the most out of this material:
In Phase 1: Mathematics for AI
Use Chapters 2–7 as your primary written textbook reference across all four modules of Phase 1 (Linear Algebra, Vector Calculus, Probability, and Optimization).
Vector spaces, dot products, matrix multiplication, projections, norms, cosine similarity, eigendecomposition, and SVD.
Derivatives, the chain rule, partial derivatives, gradients, Jacobians, Hessians, and the mathematical mechanics of gradient descent.
Probability distributions, Bayes' theorem, expectation, variance, maximum likelihood estimation, entropy, cross-entropy, and KL divergence.
SGD, mini-batching, Momentum, RMSProp, Adam, learning-rate schedules, numerical stability, log-sum-exp, finite-difference gradient checking, and computational graphs.
Mathematical formulation and NumPy implementation of linear regression, logistic regression, MSE, binary cross-entropy, and decision boundaries.
A university-level linear algebra course covering vector spaces, matrices, linear systems, eigenvalues, and related topics.
University course on vectors, matrices, partial derivatives, gradient vectors, directional derivatives, and multivariable optimization.
Rigorous introduction to discrete and continuous probability distributions, conditional probability, Bayes' theorem, expectation, variance, and maximum likelihood estimation.