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

ISBN-13: 9781108492201 / Angielski / Twarda / 2019 / 712 str.

Palash B. Pal

Opis

Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

Spis treści

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.