A Physicist's Introduction to Algebraic Structures

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.