Mathematical Foundations of Artificial Intelligence: Two Volume Set

Mathematical Foundations of Artificial Intelligence: Two Volume Set addresses the mathematical foundations essential for modern artificial intelligence, establishing a unified framework based on smooth manifold theory and Riemannian geometry.It explores how differential geometry provides a coherent language for representing, analyzing, and integrating AI systems across deep learning, generative modeling, physical AI, biological systems, and autonomous reasoning. The books define AI as a geometry-driven discipline and investigate the role of manifolds as natural domains for data representation and intelligent computation.Volume One develops core concepts-topological and smooth manifolds, Riemannian metrics, differential forms, Lie derivatives, and statistical geometry-while providing step-by-step applications to data science, genomics, drug discovery, and AI-driven systems.Volume Two reconstructs AI around four foundational pillars: geometry, physics, causality, and autonomy.It introduc