Description
Book SynopsisThis 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.
Trade Review“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)
Table of ContentsPreface 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.
