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Title: Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
ISBN: 0750306068
Author:
Mikio Nakahara
Publicate Date: 2003-06-04
Publish: 2003-06-04
List Price: $69.95
Average Customer Rating: 4.0
Format: Paperback
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Amazon Lowest New Price: $59.52
Amazon Lowest Used Price: $67.08
Amazon Merchant Price: $62.95
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| Customer Review: |
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1: Too many errors to be useful for study
Reading all the glowing reviews of this book, I wonder whether the reviewers actually tried to use the book to understand the material, or just checked the table of contents. There are so many misprints, throughout, that one wonders if the book was proofread at all. Some of the mistakes will be obvious to every physicist - for example, one of the Maxwell equations on page 56 is wrong - others are subtle, and will confuse the reader. The careful reader, who wants to really understand the material and tries to fill in the details of some of the derivations, will waste a lot of time trying to derive results that have misprints from intermediate steps which have different misprints! Some chapters are worse than others, but the average density of misprints seems to be more than one per page.
The book might be useful as a list of topics and a "road map" to the literature prior to 2003, but that hardly justifies the cost (or the paper) of a whole book.
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2: Geometry Topology and Physics: A condesed view
This book provide a complete and useful review of geometrical instuments of mathematical physics from the beginnig to the most advanced topics of interest. It can be used by students at the beginnig of thei studies in this topics, and it's found to be a useful gallery for higher level students (or scholar).
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3: An excellent book
This is the best book of its type, that is, a book that contains almost all if not all the advance mathematics a theoretical physicist should know. I have studied chapters 2-9 and it has the perfect balance between rigorous presentation of topics and practical uses with examples. The level is for advance graduate students. The range of topics covered is wide including Topology topics like Homotopy, Homology, Cohomology theory and others like Manifolds, Riemannian Geometry, Complex Manifolds, Fibre Bundles and Characteristics Classes. I believe this book gives you a solid base in the modern mathematics that are being used among the physicists and mathematicians that you certainly may need to know and from where you will be in a position to further extent (if you wish) into more technical advanced mathematical books on specific topics, also it is self contained and brings lots of exercises that help learn the concepts presented, my advice, get it is a superb book!
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4: A great reference book.
No doubt, the interplay of topology and physics has stimulated phenomenal research and breakthroughs in mathematics and physics alike.
Unfortunately, there is so much mathematics to master that the average graduate physics student is left bewildered.....until now.
The text is an excellent reference book. I emphasize reference. The book presupposes an acquaintance with basic undergraduate mathematics including linear algebra and vector analysis.
The author covers a wide range of topics from tensor analysis on manifolds to topology, fundamental groups, complex manifolds, differential geometry, fibre bundles etc.
The exposition in necessarily brief but the main theorems and IDEAS of each topic are presented with specific applications to physics. For example the use of differential geometry in general relativity and the use of principal bundles in gauge theories, etc.
Unfortunately, there are very few exercises necessitating the use of supplementary texts. However, to the author's credit appropriate supplementary texts are provided. The author goes to great lengths to show which texts inspired the chapters and follows the same line of presentation.
Perhaps the greatest attribute of the text is to take disparate branches of mathematics and coallate them under one text with applications to physics. In doing so one gains a better grasp of how the fields of mathematics interact in the domain of physics.
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5: Great book.
This is a very useful book for understanding modern physics. You absolutely need such a book to really understand general relativity, string theory etc. For instance, Wald's book on general relativity will make much more sense once you go through Nakahara's book. It is very complete, clearly written, comprehensive and easy to read. I would also recommend Morita's "Geometry of differential forms' and Dubrovin,Novikov and Fomeko's 3 volume monograph, if you can find it. All in all, Nakahara's book is one of the best buys, precious book.
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