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The Structures of Mathematical Physics - Steven P. Starkovich

The Structures of Mathematical Physics

An Introduction
Buch | Hardcover
XXII, 258 Seiten
2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-73448-0 (ISBN)
CHF 104,80 inkl. MwSt

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.


Steven P. Starkovich is Associate Professor Emeritus of Physics at Pacific Lutheran University, where he served for seven years as Provost and Senior Vice President for Academic Affairs. His 20 years of classroom teaching spanned the entire undergraduate physics curriculum. He received his PhD in Physics from the University of Victoria in British Columbia, specializing in general relativity and cosmology.

Preface and Acknowledgements.- Sets and Relations.- Mappings and Functions.- Rings and Fields.- Linear Vector Spaces.- Algebras.- Basic Topology and Topological Groups.- Topological Vector Spaces.- Measure, Integration and Hilbert Space.- Operators and Spectra.- Annotated Bibliography and a Guide to Further Reading.- Index.

"This text approaches the reader with shocking breadth and niggardly depth. ... Around each definition, there is short---and pleasant---narrative and then a number of examples are described. Chapters end with a list of straightforward exercises ... . As a stand-alone mathematical dictionary, the text under review may serve a purpose ... ." (Ryan Grady, MAA Reviews, January 30, 2022)

“This text approaches the reader with shocking breadth and niggardly depth. … Around each definition, there is short---and pleasant---narrative and then a number of examples are described. Chapters end with a list of straightforward exercises … . As a stand-alone mathematical dictionary, the text under review may serve a purpose … .” (Ryan Grady, MAA Reviews, January 30, 2022)

Erscheinungsdatum
Zusatzinfo XXII, 258 p. 86 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Algebra Physics • Geometry Topology Physics • Group Theory Physics • Mathematical Methods • Mathematical Physics • Mathematical Structures in physics • Physics Math History
ISBN-10 3-030-73448-X / 303073448X
ISBN-13 978-3-030-73448-0 / 9783030734480
Zustand Neuware
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