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Library | Materyal Türü | Barkod | Yer Numarası | Durum |
|---|---|---|---|---|
Searching... Pamukkale Merkez Kütüphanesi | Kitap | 0060349 | QC20S9982 2006 | Searching... Unknown |
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This book, first published in 2004, 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.
Reviews (1)
Choice Review
One often hears David Hilbert cited as a candidate for the last mathematician who grasped all the mathematics of his day. In 1900 he famously articulated, as few could presume to do, 23 problems that defined the challenges to 20th-century mathematicians; his sixth problem in particular asks for an axiomatization of physics. Many historians and others have actually tried to make light of Hilbert's own involvement with physics, describing him as "simply looking for another possible application of his mathematical theories." Corry (Tel Aviv Univ., Israel) reassesses both the depth of Hilbert's engagement with physics and the importance of physics within Hilbert's oeuvre, especially where this concerns his development of an axiomatic approach. Corry reconstructs the thread of Hilbert's intellectual development by reading carefully, alongside all the publications, the many informal lecture notes Hilbert generated as he taught. Corry distills mathematical complexities as deftly as he evokes complex personal interactions between important thinkers. Many readers will find particular interest in Corry's clarifications of Hilbert's interactions with Einstein concerning the general theory of relativity. Some of Hilbert's unpublished lecture notes ultimately became the basis of the influential Methods of Mathematical Physics, by R. Courant and D. Hilbert (2v., 1953-62), a book that has spawned a long line of descendants, including this work by Szekeres. Unlike Courant and Hilbert, Szekeres (formerly, Univ. of Adelaide) says he emphasizes the development of mathematical structures over the mere solution of differential equations, thus following along the lines of, say, Analysis, Manifolds and Physics, by Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick (CH, May'78), albeit targeting a less sophisticated audience. Essentially that means we have a primer on differential geometry, that key prerequisite to both relativity and particle physics, packaged with all its prerequisites (namely, linear and multilinear algebra, multivariable calculus, and topology). Some one-stop-shop books on mathematical physics all but omit the physics, but Szekeres strikes a nice balance (but do not ever expect any pedagogical consensus surrounding what such a book should include or omit!). Rich detail, good design, and apt illustration should make the book easy for students to use. ^BSumming Up: Corry: Highly recommended. Szekeres: Recommended. For both: Upper-division undergraduates through faculty. D. V. Feldman University of New Hampshire