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Title: Tensor Geometry: The Geometric Viewpoint and Its Uses (Graduate Texts in Mathematics, Vol 130) by C.T.J. Dodson, T. Poston ISBN: 3-540-52018-X Publisher: Springer Verlag Pub. Date: October, 1991 Format: Hardcover List Price(USD): $69.95 |
Average Customer Rating: 4.8 (5 reviews)
Rating: 5
Summary: A must for mathematicians interested in cosmology
Comment: Besides providing in clear-cut fashion the mathematics essential to research in cosmology, the authors simplify many concepts the physicists make opaque.
Rating: 4
Summary: Excellent, But Has Flawed Editing
Comment: I found this book much more comprehensible than the Bishop & Goldberg text (perhaps because the specifics of my particular graduate program made this approach more accessible). The only problem is that in some important areas of the text there are typographical errors; this text needs a new corrected edition--otherwise I have no complaints. The only recommendation I would make to a prospective reader is to obtain a copy of the excellent, old, out-of-print (but still readily avilable used, on the web) Vector and Tensor Analysis by Louis Brand and master the tensor chapter in it. This will prepare the reader to gain an idea of where the authors are heading with their modern, abstract functional analysis approach.
The reader will be greatly assisted by a solid understanding of linear algebra and a preparatory course in functional analysis wouldn't hurt, either. This material is challenging even for a math graduate student; any high school student who could master this book would have to be gifted, indeed.
Rating: 5
Summary: Good introduction
Comment: I agree with previous reviewers, and only wish to add a few comments: 1. This book assumes very little on the part of the reader, which makes it ideal for beginners, as long as they're mature readers. 2. Like many books out there, everything in this book is real and finite dimensional, which is a bit disappointing. 3. It's not as advanced as the writers or reviewers would like to think. For instance, no differential forms, no killing vectors, and although there's a chapter on lie groups it treats only their geometrical aspects and not the algebraic ones. 4. However, it contains two (extensive) chapters on SR and GR which are pure gold, I say! Everything is done from the geometrical point of view, and only AFTER all of the math has been introduced, so the discussion is mature and elegant. In short, this is a good book to read for the geometrical intuition but don't count on it to explain everything about differential geometry. Enjoy!
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Title: Symmetry in Mechanics by Stephanie Frank Singer ISBN: 0817641459 Publisher: Birkhauser Boston Pub. Date: 15 February, 2001 List Price(USD): $33.95 |
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Title: Lie Groups for Pedestrians by Harry J. Lipkin ISBN: 0486421856 Publisher: Dover Pubns Pub. Date: 15 July, 2002 List Price(USD): $12.95 |
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Title: Introduction to Topological Manifolds by John M. Lee ISBN: 0387950265 Publisher: Springer Verlag Pub. Date: 25 May, 2000 List Price(USD): $42.95 |
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Title: Introduction to Smooth Manifolds by John M. Lee ISBN: 0387954481 Publisher: Springer Verlag Pub. Date: 23 September, 2002 List Price(USD): $49.95 |
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Title: Differential Forms and Connections by R. W. R. Darling ISBN: 0521468000 Publisher: Cambridge University Press Pub. Date: 22 September, 1994 List Price(USD): $32.00 |
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