A Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological spaces and more
 Author: Palash B. Pal, Saha Institute of Nuclear Physics, India
 Publication planned for: June 2019
 availability: Not yet published  available from June 2019
 format: Paperback
 isbn: 9781108729116
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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.
Read more · Includes detailed proofs of important theorems · More than 400 problems to test the understanding of concepts, including answers to many of them · Indepth 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
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×Product details
 Publication planned for: June 2019
 format: Paperback
 isbn: 9781108729116
 dimensions: 244 x 170 mm
 availability: Not yet published  available from June 2019
Table of Contents
Preface
Part A General Introduction
Chapter 1. Rules of Logic
Chapter 2. Sets and Functions
Chapter 3. Algebraic Structures
Part B Vector Spaces
Chapter 4. Basics
Chapter 5. Operators on vector spaces
Chapter 6. Infinite dimensional vector spaces
Part C Group Theory
Chapter 7. General properties of groups
Chapter 8. Finite groups
Chapter 9. Representation of finite groups
Chapter 10. Symmetries of regular geometrical objects
Chapter 11. Countably infinite groups
Chapter 12. General properties of Lie groups
Chapter 13. Rotations and translations
Chapter 14. Unitary groups and their representations
Chapter 15. Orthogonal groups and their representations
Chapter 16. Parameter space of Lie groups
Chapter 17. Representations of the Lorentz group
Chapter 18. Roots and weights
Chapter 19. Some other groups and algebras
Part D Topology
Chapter 20. Continuity of functions
Chapter 21. Topological spaces
Chapter 22. Homotopy theory
Chapter 23. Homology
Appendices
References
Index.
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