Abstract Algebra: Tensor Products
N.B. Singh
This audiobook is narrated by a digital voice.
"Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics.
Duration - 3h 21m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. "Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics. Duration - 3h 21m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:00:37
Introduction to Tensor Products
Duration:00:00:53
Historical Development
Duration:00:04:12
Motivation and Intuition
Duration:00:04:36
Basic Definitions
Duration:00:04:15
Examples and Counterexamples
Duration:00:05:14
Importance in Algebraic Structures
Duration:00:05:01
Relation to Direct Sum and Homomorphisms
Duration:00:05:19
Summary and Overview
Duration:00:04:45
Tensor Product Spaces
Duration:00:00:49
Construction and Existence
Duration:00:04:48
Properties of Tensor Products
Duration:00:03:31
Basis and Dimension
Duration:00:06:58
Tensor Contraction and Extension
Duration:00:03:25
Symmetric and Exterior Powers
Duration:00:03:21
Applications in Geometry and Physics
Duration:00:02:31
Tensor Algebra
Duration:00:00:59
Algebraic Structures of Tensors
Duration:00:03:06
Tensor Products of Vector Spaces
Duration:00:02:45
Universal Property of Tensor Algebra
Duration:00:02:57
Tensor Rank and Tensor Rank Decomposition
Duration:00:02:58
Non-commutative Algebras and Tensor Products
Duration:00:03:07
Representations and Modules
Duration:00:03:24
Applications in Coding Theory
Duration:00:02:56
Multilinear Maps and Tensors
Duration:00:01:03
Multilinear Forms and Multilinear Maps
Duration:00:03:20
Tensor Product of Multilinear Maps
Duration:00:03:25
Symmetry and Antisymmetry of Tensors
Duration:00:03:37
Algebraic Manipulations with Multilinear Maps
Duration:00:03:50
Tensor Derivatives and Applications
Duration:00:03:05
Decompositions and Canonical Forms
Duration:00:03:34
Computational Techniques and Algorithms
Duration:00:03:37
Tensor Products of Modules
Duration:00:01:03
Module Structures and Tensor Products
Duration:00:03:30
Tensor Product of Module Homomorphisms
Duration:00:02:59
Dual Modules and Tensor Products
Duration:00:04:26
Exact Sequences and Tensor Products
Duration:00:04:24
Injective and Projective Modules
Duration:00:04:38
Tensor Products in Representation Theory
Duration:00:05:12
Applications in Algebraic Geometry
Duration:00:05:14
Universal Property of Tensor Products
Duration:00:01:14
Universal Mapping Property
Duration:00:05:03
Categorical Approach to Tensor Products
Duration:00:05:34
Functorial Properties and Adjunctions
Duration:00:05:34
Tensor Products in Category Theory
Duration:00:05:52
Natural Transformations and Functors
Duration:00:04:25
Coherence Theorems and Equivalences
Duration:00:04:17
Applications in Mathematical Logic
Duration:00:03:41
Applications of Tensor Products
Duration:00:01:15
Tensor Products in Quantum Mechanics
Duration:00:04:12
Tensor Networks and Machine Learning
Duration:00:03:35
Algebraic Structures in Topology
Duration:00:03:25
Applications in Group Cohomology
Duration:00:03:19
Homological Algebra and Tensor Products
Duration:00:03:32
Differential Forms and Tensor Products
Duration:00:03:49
Future Directions and Open Problems
Duration:00:03:34