Mathematics for AI and Machine Learning: A Comprehensive Mathematical Reference for Artificial Intelligence and Machine Learning - Hardcover

by Fuheng Wu (Author), Yu Guo (Foreword by)

Mathematics for AI and Machine Learning is a comprehensive, graduate-level textbook that provides the rigorous mathematical foundations essential for understanding modern artificial intelligence and machine learning systems.

Companion Website: https: //math4ai.org

The book spans 21 chapters organized into four parts. Part I (Chapters 1-10) covers linear algebra fundamentals: vector spaces, inner products, matrix operations, subspaces, orthogonality, QR decomposition, LU factorization, eigendecomposition, symmetric matrices, and the Singular Value Decomposition (SVD)-establishing the mathematical foundation for representation in AI.

Part II (Chapters 11-12) addresses differentiation and optimization: matrix calculus with gradients and Hessians, and optimization methods including gradient descent and its variants-formalizing learning as structured search in parameter space.

Part III (Chapters 13-16) introduces probability and information theory: probability and random variables, entropy and KL divergence, the Evidence Lower Bound (ELBO), variational inference and latent variable models, and Bellman equations for reinforcement learning-shifting the perspective from fitting functions to modeling distributions.

Part IV (Chapters 17-21) ventures into score functions, dynamics, and diffusion: score functions and energy-based models, Langevin dynamics and sampling methods, stochastic differential equations with Itô calculus, ODE/SDE continuous limits of algorithms, and Fokker-Planck equations governing distribution dynamics-framing generative modeling as the study of distributional dynamics.

What distinguishes this textbook is its seamless integration of mathematical rigor with practical AI/ML applications. Each concept is motivated by real-world problems in machine learning, deep learning, large language models, graph neural networks, reinforcement learning, and modern generative frameworks. The full-color figures illuminate complex ideas, while extensive exercises reinforce understanding.

Designed for graduate students, researchers, and experienced practitioners, this book serves as both a learning resource and a comprehensive reference. Whether you're building foundation models, researching novel architectures, or seeking deeper understanding of the mathematics powering AI systems, this textbook provides the essential theoretical toolkit.