A Course in Modern Mathematical Physics
Groups, Hilbert Space and Differential Geometry

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

Peter Szekeres (Author)

9780521829601, Cambridge University Press

Hardback, published 16 December 2004

618 pages, 48 b/w illus. 341 exercises
24.9 x 17.5 x 3.8 cm, 1.22 kg

' … the book may serve as an easily accessible introductory text on a wide range of the standard and more basic topics in mathematics and mathematical physics for the beginner, with an emphasis on differential geometry. a nice feature is that a considerable number of examples and exercises is provided, together with numerous suggestions for further reading: there is also an extensive index which will be particularly helpful for beginners in the subject.' General Relativity and Gravitation Journal

This book, first published in 2004, provides an introduction to the major mathematical structures used in physics today. It covers the concepts and techniques needed for topics such as group theory, Lie algebras, topology, Hilbert space and differential geometry. Important theories of physics such as classical and quantum mechanics, thermodynamics, and special and general relativity are also developed in detail, and presented in the appropriate mathematical language. The book is suitable for advanced undergraduate and beginning graduate students in mathematical and theoretical physics, as well as applied mathematics. It includes numerous exercises and worked examples, to test the reader's understanding of the various concepts, as well as extending the themes covered in the main text. The only prerequisites are elementary calculus and linear algebra. No prior knowledge of group theory, abstract vector spaces or topology is required.

Preface
1. Sets and structures
2. Groups
3. Vector spaces
4. Linear operators and matrices
5. Inner product spaces
6. Algebras
7. Tensors
8. Exterior algebra
9. Special relativity
10. Topology
11. Measure theory and integration
12. Distributions
13. Hilbert space
14. Quantum theory
15. Differential geometry
16. Differentiable forms
17. Integration on manifolds
18. Connections and curvature
19. Lie groups and lie algebras.

Subject Areas: Maths for engineers [TBJ], Statistical physics [PHS], Thermodynamics & heat [PHH], Maths for scientists [PDE]