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A physicist's introduction to algebraic structures: vector spaces, groups, topological spaces and more

By: Pal, Palash B.
Material type: materialTypeLabelBookPublisher: New York Cambridge University Press 2019Description: xxii, 693 p. Includes index.ISBN: 9781108729116.Subject(s): Algebraic structure | Mathematics | Vector space | Boolean algebraDDC classification: 530.15255 Summary: An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts. Includes detailed proofs of important theorems Offers more than 400 problems to test the understanding of concepts, including answers to many of them In-depth coverage of topics includes vector space, group, and topological space Topology is introduced after group theory, helping students understand the topological properties of group parameter spaces https://www.cambridge.org/gb/academic/subjects/physics/theoretical-physics-and-mathematical-physics/physicists-introduction-algebraic-structures-vector-spaces-groups-topological-spaces-and-more?format=HB
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Slot 1697 (2 Floor, East Wing) Non-fiction 530.15255 P2P4 (Browse shelf) Available 200154

Table of Contents
Preface
Part I. General Introduction:
1. Rules of logic
2. Sets and functions
3. Algebraic structures
Part II. Vector Spaces:
4. Basics
5. Operators on vector spaces
6. Infinite dimensional vector spaces
Part III. Group Theory:
7. General properties of groups
8. Finite groups
9. Representation of finite groups
10. Symmetries of regular geometrical objects
11. Countably infinite groups
12. General properties of Lie groups
13. Rotations and translations
14. Unitary groups and their representations
15. Orthogonal groups and their representations
16. Parameter space of Lie groups
17. Representations of the Lorentz group
18. Roots and weights
19. Some other groups and algebras
Part IV. Topology:
20. Continuity of functions
21. Topological spaces
22. Homotopy theory
23. Homology
Appendices
References
Index.

An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.

Includes detailed proofs of important theorems
Offers more than 400 problems to test the understanding of concepts, including answers to many of them
In-depth coverage of topics includes vector space, group, and topological space
Topology is introduced after group theory, helping students understand the topological properties of group parameter spaces

https://www.cambridge.org/gb/academic/subjects/physics/theoretical-physics-and-mathematical-physics/physicists-introduction-algebraic-structures-vector-spaces-groups-topological-spaces-and-more?format=HB

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