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Title: Lectures on Classical Differential Geometry by Dirk J. Struik ISBN: 0-486-65609-8 Publisher: Dover Pubns Pub. Date: 01 April, 1988 Format: Paperback Volumes: 1 List Price(USD): $10.95 |
Average Customer Rating: 4.5 (2 reviews)
Rating: 4
Summary: Good treatment of classical differential geometry
Comment: Struik's book provides solid coverage of curve and surface theory from the classical point of view, i.e. the kind of stuff Monge, Serret, Frenet and Gauss did. I agree that the book should be on the shelves of mathematicians. A number of classical topics are simply not in vogue these days, and one can find them discussed at length in Struik, or in the exercises. In this sense the book certainly has a more geometric flavor than a number of contemporary texts.
However, Struik can't be used to understand what is happening today. For these purposes,books by O'Neill and do Carmo would be more appropriate. The discussion of manifolds and coordinate charts, the discussion of connection forms, differential forms, covariant derivatives, exterior derivatives, pullbacks and pushforwards can be found in these texts. This is the language of modern geometry.It leads on naturally to tensors, fibre bundles, de Rham cohomology and so on and so forth.The emphasis in modern geometry is on global phenomena, the interaction between local and global (e.g. Morse theory or De Rham cohomology), and the attempt to do everything in an algebraic setting (projective modules, spectral sequences, categories etc.) For this purpose, Struik is useless, though he does have some coverage of forms (he calls them by their earlier name of 'pfaffians').
The price of the book makes it an attractive purchase.
Rating: 5
Summary: Struik's book - a classic on classical differential geometry
Comment: I simply cannot believe I am the first reviewer of this book!This book should be on the shelf of every mathematician interested in geometry, every computer graphics specialist, everyone interested in solid modelling. For ten bucks, you get a great summary of a wide range of topics in "classical differential geometry" -- the stuff geometers were interested in one hundred years ago. Today it's gauge and string theory -- but the topics discussed in this book are timeless, and many have seen remarkable renaissances in recent years. It is a wonderful little book ... I am using it to teach a basic differential geometry course next year.
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Title: Differential Geometry by Erwin Kreyszig ISBN: 0486667219 Publisher: Dover Pubns Pub. Date: 01 June, 1991 List Price(USD): $14.95 |
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Title: Schaum's Outline of Differential Geometry (Schaum's) by Lipschutz, Martin Lipsxhultz, Martin Lipschultz ISBN: 0070379858 Publisher: McGraw-Hill Trade Pub. Date: 01 June, 1969 List Price(USD): $15.95 |
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Title: Tensors, Differential Forms, and Variational Principles by David Lovelock, Hanno Rund ISBN: 0486658406 Publisher: Dover Pubns Pub. Date: 01 April, 1989 List Price(USD): $14.95 |
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Title: Elementary Differential Geometry by Andrew Pressley ISBN: 1852331526 Publisher: Springer Verlag Pub. Date: 15 January, 2001 List Price(USD): $44.95 |
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Title: Functional Analysis by Frigyes Riesz, Bela Sz.-Nagy ISBN: 0486662896 Publisher: Dover Pubns Pub. Date: 01 June, 1990 List Price(USD): $16.95 |
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