Mathematics for Machine Learning

Descriptions

Source: Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong (Imperial College London)
Prerequisites: High school math
Difficulty: 🌟🌟🌟
Class Hour: 80+

Mathematics for Machine Learning is a math textbook written specifically for machine learning. It covers all the mathematical foundations needed for ML: linear algebra, calculus, probability, and optimization theory.

The book's greatest strength: all mathematical content is framed around ML applications. You won't learn "useless" math — every concept has a corresponding application in ML.

Resources

Content Structure

Part 1: Mathematical Foundations

Linear algebra (vectors, matrices, linear transformations, eigenvalues)
Analytic geometry (distance, projection, hyperplanes)
Matrix decompositions (SVD, eigendecomposition, Cholesky)

Part 2: Mathematics for Machine Learning

Vector calculus (gradients, directional derivatives, Hessian)
Probability and distributions (Bayesian inference, MLE)
Optimization theory (gradient descent, convex optimization, constrained optimization)

Part 3: Applications

Principal Component Analysis (PCA)
Gaussian Mixture Models
Linear Regression
Support Vector Machines (SVM)

Self-Study Tips

Learn linear algebra and calculus basics first, then read this book. The book assumes familiarity with basic linear algebra and calculus concepts.

Focus on Parts 1 and 2. These are the core mathematical foundations for machine learning.

Do the exercises. Each chapter has problems to test your understanding.

Use alongside other courses. This book works well as a supplement to MIT 18.06 (Linear Algebra) and MIT 18.01 (Calculus).

Notes

The book is completely free, with PDF available on the official website. It is the companion textbook for Imperial College London's machine learning course.

If you only want to read one math book to prepare for machine learning, this is the best choice. It's more focused than traditional math textbooks and more mathematically rigorous than pure ML tutorials.