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Topology and Geometry for Physicists Paperback – February 11, 1988


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Product Details

  • Paperback: 311 pages
  • Publisher: Academic Press (February 11, 1988)
  • Language: English
  • ISBN-10: 0125140819
  • ISBN-13: 978-0125140812
  • Product Dimensions: 9 x 6 x 0.7 inches
  • Shipping Weight: 13.6 ounces
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #3,764,341 in Books (See Top 100 in Books)

Editorial Reviews

Review

"One of the most remarkable developments of the last decade in the penetration of topological concepts into theoretical physics. Homotopy groups and fibre bundles have become everyday working tools. Most of the textbooks on these subjects were written with pure mathematicians in mind, however, and are unnecessarily opaque to people with a less rigorous background. This concise introduction will make the subject much more accessible. With plenty of simple examples, it strikes just the right balance between unnecessary mathematical pedantry and arm-waving woolliness...it can be thoroughly recommended.
--T.W.B. Kibble, PHYSICS BULLETIN

From the Back Cover

This volume provides an easily comprehensible introduction to topological and geometrical methods in theoretical physics and applied mathematics. No detailed knowledge of topology or geometry is required in the reader, and advanced undergraduate or graduate physicists should have no difficulty in understanding the material.
The style and approach of the book reflect the fact that the authors are themselves physicists, and have taken trouble to clarify difficult mathematical concepts and to emphasize their physical motivation. The applications range from condensed matter physics and statistical mechanics to elementary particle theory, while the main mathematical topics are differential forms, homotopy, homology, cohomology, fibre bundles, connection and covariant derivatives and Morse theory.

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Customer Reviews

I haven't actually read this book, but from just skimming it, I see that it contains no exercises at all.
Technogeek
There are many fine diff. geometry books out there, some for physicists, some not, which you should check out - Nakahara's text is so much better.
Assaf Tal
In this book, proofs are sometimes only for special cases of theorems stated more generally and often contain logical errors.
Alberto Dominguez

Most Helpful Customer Reviews

51 of 59 people found the following review helpful By Assaf Tal on January 12, 2002
Format: Paperback
Nash's book commits the sin many mathematical physics textbooks out there commit: "oh, we're writing for dimwit physicists, lets just give them a few scrawny examples and assure them everything else works alright." I'm sorry but writing for physicists is NOT an excuse for writing a sloppy textbook. Would you feel alright not knowing how an integral is defined? Would you use a numerical evaluation software to calculate integrals in serious research without understanding the algorithm it uses? If you do then you're a pretty shoddy physicist. I'm not saying this out of some "macho" sentiment many purist physicists have - I'm simply saying this because I feel the way this book teaches you diff. geometry is wrong - it teaches you to draw pictures and go by the pictures. When the pictures run out, so does your understanding.

This book is supposed to teach differential geometry. However, very little can be learned from it unless one already knows differential geometry: definitions are sometimes not general and sometimes not present at all, theorems are often stated only for special cases and even more often than that not proved at all. Sure, the book offers nice geometrical intuition, but this is not enough. An example: the book "proves" Stoke's theorem around page 40. Now, even a rigorous and condensed book would have problems doing that, considering the amount of "machinery" one needs to build up for it (tensors, differential forms, manifolds and so forth). This means the book makes a mess of it - big time.
There are many fine diff. geometry books out there, some for physicists, some not, which you should check out - Nakahara's text is so much better. For geometrical intuition I suggest picking up Schutz's book.
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24 of 28 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on July 9, 2002
Format: Paperback
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.
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9 of 12 people found the following review helpful By Alberto Dominguez on May 11, 2002
Format: Paperback
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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13 of 19 people found the following review helpful By A Customer on April 9, 2000
Format: Paperback
This book is written by physicists. Like a book by M. Nakahara it describes basics of diff geometry and topology. Though it stresses physical intuition more than formal definitions. I especially liked discussion of fiber bundles and characteristic classes. Highly recommended.
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6 of 9 people found the following review helpful By A Customer on January 15, 2004
Format: Paperback
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.
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