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

##### By: Pal, Palash B.

Material type: BookPublisher: 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=HBItem type | Current location | Item location | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|

Books | Vikram Sarabhai Library General Stacks | 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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