The Structures of Mathematical Physics: An Introduction

This textbook provides an introduction to fundamental mathematical structures used in modern theoretical physics, including groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds, and Lie groups. It is designed for undergraduate students in physics and mathematics with no prior background in these topics. Applications to physics are included, and the book features worked examples, end-of-chapter problems, and guides to further reading.

Format: Paperback / softback
Length: 258 pages
Publication date: 23 July 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook serves as an essential introduction to a wide range of mathematical structures that form the foundation of modern theoretical physics. Designed primarily for undergraduate students in physics and mathematics with no prior background in these fields, it provides a thorough exploration of groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds, and Lie groups.

The text is organized in a logical and accessible manner, making it suitable for self-study. It begins with an overview of basic concepts and gradually builds upon them, presenting complex ideas in a step-by-step manner. Throughout the book, applications to physics are seamlessly integrated, showcasing the practical relevance of these mathematical structures. Examples such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations, and the Generalized Stokes's Theorem are presented at appropriate points, illustrating their importance in understanding physical phenomena.

To enhance the learning experience, the textbook includes numerous worked examples, end-of-chapter problems, and guides to further reading. These resources provide students with hands-on practice and help them deepen their understanding of the topics covered. Additionally, the book's clear and concise writing style makes it accessible to students with varying levels of mathematical proficiency.

Upon completing this textbook, readers will possess a solid foundation in the mathematical structures necessary for advanced study in theoretical physics or mathematics. They will be well-equipped to delve into more specialized texts and monographs, expanding their knowledge and expertise in this field. Whether students are aspiring physicists or mathematicians, this textbook serves as a valuable resource for anyone seeking to explore the frontiers of theoretical physics and mathematics.

Weight: 433g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030734510
Edition number: 1st ed. 2021