A Physicist's Introduction to Algebraic Structures: Vector Spaces, Groups, Topological spaces and more

Book Description 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.
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Content

A GENERAL INTRODUCTION
1. Rules of Logic
2. Sets and Functions
3. Algebraic Structures

B VECTOR SPACES
4. Basics
5. Operators on Vector Spaces
6. Infinite Dimensional Vector Spaces

C 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

D TOPOLOGY
20. Continuity of Functions
21. Topological Spaces
22. Homotopy Theory
23. Homology