Description

Book Synopsis
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 and measure angle.

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.

A Physicists Introduction to Algebraic Structures

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    A Hardback by Palash B. Pal

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      Book details

      Publisher Cambridge University Press
      Published 23 May 2019
      ISBN-13 9781108492201
      978-1108492201
      ISBN-10 1108492207
      Also in:
      Statistical physics

      Description

      Book Synopsis
      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 and measure angle.

      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.

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