Mathematical Foundations of Deep Learning offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks and the theory and algorithms of optimal control and reinforcement learning integrated with deep learning techniques to contemporary generative models that drive today’s advances in artificial intelligence. Designed as both a textbook for graduate and advanced undergraduate students as well as a long-term reference, this volume aims to equip students with a solid mathematical understanding of deep learning while serving researchers, scientists, and engineers seeking a principled framework for developing and analyzing modern artificial intelligence systems. Features• Comprehensive and rigorous, featuring detailed theoretical developments, mathematical proofs, and algorithmic frameworks throughout. • Materials thoughtfully selected from this book support a full one-semester course for graduate students and advanced undergraduates. • Concise yet precise exposition of core deep learning concepts and techniques, presented using exact and rigorous mathematical language.