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This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.

Machine learning. --- Lie groups.

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Lie groups. --- Geometric group theory. --- Représentations de groupes de Lie. --- Groupes, Théorie géométrique des. --- Representations of Lie groups. --- Linear algebraic groups. --- Representations of Lie groups --- Lie groups

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This book is a sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie theory with applications. This volume is devoted mostly to Lie groups. Lie algebras and generating functions, both for standard special functions and for solution of certain types of physical problems. It is an informal treatment of these topics intended for physics graduate students or others with a physics background wanting a brief and informal introduction to the subjects addressed in a style and vocabulary not completely unfamiliar.

Lie groups. --- Lie algebras. --- Mathematical physics. --- SCIENCE / Physics / Mathematical & Computational.

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Finite simple groups. --- Group theory. --- Groupes simples finis. --- Groupes, Théorie des. --- Lie groups.

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This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.

Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Topology. --- Topological Groups. --- Functional Analysis. --- Topological Groups, Lie Groups. --- Groups, Topological --- Continuous groups --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Topological groups. --- Lie groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups