Full Description
This book provides a systematic introduction to the mathematical structures underlying modern machine learning and artificial intelligence. It develops the functional, metric, algebraic, and optimization tools needed to formulate learning problems, analyze algorithms, and interpret model behavior beyond purely computational implementations.
The exposition begins with metric spaces, normed spaces, Hilbert spaces, reproducing kernel Hilbert spaces, operators, and fixed-point methods, emphasizing their role in data representation and learning. It then reviews the essential elements of linear algebra, including eigenanalysis, singular value decomposition, pseudoinverses, and matrix conditioning. A substantial part of the volume is devoted to learning dynamics and optimization, covering gradient methods, Newton-type methods, stochastic gradient descent, constrained optimization, duality, proximal methods, derivative-free optimization, and support vector machines. The final chapters connect these tools to linear inverse problems, regularized least squares, sparse recovery, dictionary learning, and total least squares.
The book is intended for graduate students, researchers, and practitioners seeking a rigorous but accessible mathematical foundation for modern AI.
