Structures of mathematical physics : an introduction
- Cham : Springer, 2021
- xxii, 258 p. ; ill., 24 cm
Includes bibliographical references and index.
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.
9783030734510
Algebraic structure Category theory Cauchy integral theorem Divergence theorem Generalized Stokes's theorem Hamilton's equation Hodge star operation Moore-Smith convergence theory Poisson algebra Rodigues formulas Schrodinger's equation Tietze extension theorem Trichotomy law Urysohn's theorem Weight function