A Course in Modern Mathematical Physics

by Peter Szekeres

• ISBN13: 9780521536455
• ISBN10: 0521536456
• Format: Nonspecific Binding
• Copyright: 2004-12-16
• Publisher: Cambridge University Press

Summary

This book 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.

Author Biography

Peter Szekeres 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.

Table of Contents

Preface

Sets and structures

Groups

Vector spaces

Linear operators and matrices

Inner product spaces

Algebras

Tensors

Exterior algebra

Special relativity

Topology

Measure theory and integration

Distributions

Hilbert space

Quantum theory

Differential geometry

Differentiable forms

Integration on manifolds

Connections and curvature

Lie groups and lie algebras

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