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 kwledge of group theory, abstract vector spaces or topology is required.
Peter Szekeres received his PhD from King's College London in 1964, in the area of general relativity. He subsequently held research and teaching positions at Cornell University, King's College and the University of Adelaide, where he stayed from 1971 till his recent retirement. Currently he is a Visiting Research Fellow at that institution. He is well known internationally for his research in general relativity and cosmology, and has a good reputation for his teaching and lecturing.