Palash B PalA Physicist's Introduction to Algebraic Structures
Vector Spaces, Groups, Topological Spaces and More
Palash B. Pal is Senior Professor in the Theory Division at the Saha Institute of Nuclear Physics, Kolkata. His current research includes elementary particle physics, with specializations in neutrinos, grand unified theories, and particles in electromagnetic fields. He has published more than 100 papers in journals of international repute. He has taught courses on mathematical methods, particle physics, quantum field theory, theoretical physics and classical field theory at graduate level. He carried out postdoctoral research at the University of Maryland, University of Massachusetts, University of Oregon and University of Texas.
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.
