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Title: Topology and Geometry for Physicists by Charles Nash, Siddhartha Sen ISBN: 0-12-514081-9 Publisher: Academic Press Pub. Date: 28 January, 1988 Format: Paperback Volumes: 1 List Price(USD): $86.95 |
Average Customer Rating: 3.4 (5 reviews)
Rating: 4
Summary: Excellent overview and graphical explanation
Comment: This book shows you the geometric view of some advanced mathematical topics. It can greatly assist your intuition of what is going on in a mathematical setting when reading a true mathematics book. Armed with this book the other advanced text in Topology, Algebraic Geometry and Differential Geometry make more sense from a Physics point of view.
Rating: 3
Summary: Good attempt
Comment: When reading this book one can both admire these authors and feel sympathy with them. They have made an honest effort to explain the concepts of differential geometry and topology in a way that is understandable and appreciated by the physicist reader. But the book falls short in many places, although there are some places where they do a fine job. They have taken on a very difficult project in this book, for it is quite straightforward to expound on the formalism of mathematics, but explaining it in a way that grants insight into its conceptual meaning is another matter altogether. Many physicists complain, with justification, that the way mathematics is presented in textbooks is not sufficient for giving them a deep appreciation of the underlying ideas involved. This, they argue, is what is needed for devising new physical theories and results based on these ideas. Physicists must assimilate very complex mathematical ideas very quickly in order to formulate these theories in a reasonable time frame. This is especially true in high energy physics, which in the last two decades has used mathematics like it has never been used before. Indeed, the mathematical complexity of high energy physics is dizzying, and if progress is going to be made in this field by the students of the 21st century, they are going to need mathematics books and documents that are more than just formal expositions. But, again, writing these kinds of books is very hard to do, and has yet to be done in a book to this date, although there are helpful discussions scattered throughout the mathematical literature.
Some of the concepts that need more in-depth explanation include: the theory of characteristic classes, sheaf theory, the theory of schemes in algebraic geometry, and spectral sequences in algebraic topology. There are of course many others, and some of the ones that the authors do a fairly good job of explaining in this book include: 1. the reason that the continuity of a function is defined in terms of inverses of open sets; 2. The orientability of a manifold; 3. The fundamental group and its relation with the first homology group. 4. The discussion on Morse theory.
Rating: 3
Summary: Covers a lot of ground . . . but not always well
Comment: Unlike many physics students, I grant a lot of leeway to books on mathematics for physicists. I think it's all right for an author to engage in hand-waving arguments if this enhances physical intuition or even to make the occasional statements without proof if this allows more ground to be covered. However, if a proof actually is presented, I expect this proof to be correct. In this book, proofs are sometimes only for special cases of theorems stated more generally and often contain logical errors.
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Title: Quantum Field Theory in a Nutshell by A. Zee ISBN: 0691010196 Publisher: Princeton Univ Pr Pub. Date: 10 March, 2003 List Price(USD): $49.50 |
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Title: Loops, Knots, Gauge Theories and Quantum Gravity by Rodolfo Gambini, Jorge Pullin ISBN: 0521654750 Publisher: Cambridge Univ Pr (Trd) Pub. Date: September, 2000 List Price(USD): $40.00 |
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Title: Differential Geometry, Gauge Theories, and Gravity by M. Göckeler, T. Schücker, P. V. Landshoff, D. R. Nelson, D. W. Sciama, S. Weinberg ISBN: 0521378214 Publisher: Cambridge University Press Pub. Date: 28 July, 1989 List Price(USD): $30.00 |
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Title: Modern Differential Geometry for Physicists (World Scientific Lecture Notes in Physics, Vol. 61) by C. J. Isham ISBN: 9810235623 Publisher: World Scientific Pub Co Pub. Date: June, 1999 List Price(USD): $28.00 |
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Title: Geometry, Topology and Physics by Mikio Nakahara ISBN: 0750306068 Publisher: Institute of Physics Publishing Pub. Date: October, 2003 List Price(USD): $55.00 |
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