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Title: Introduction to Smooth Manifolds by John M. Lee ISBN: 0-387-95448-1 Publisher: Springer Verlag Pub. Date: 23 September, 2002 Format: Paperback Volumes: 1 List Price(USD): $49.95 |
Average Customer Rating: 4.5 (2 reviews)
Rating: 5
Summary: Excellent, lucid book on manifolds
Comment: Topics are explained with exceptional clarity; portions of the book are well tied together; and the order of exposition flows very well. Lie groups are introduced quite early on, but their full power is not revealed until later in the book. I can't laud this book enough. I had a firm, well-developed basis of differential geometry after reading through this book for a course. The excersises are illuminating, as are the examples. Theorems and their proofs are clearly labeled. The motivational explanations prefacing theorems do an excellent job of conveying the intuition behind ideas.
I would recommend this book over Boothby any day. I haven't read Spivak, so I can't compare Lee to it, but Lee definitely seemed like an excellent choice for an intro grad class on differential geometry.
Rating: 4
Summary: get the hardcover!!
Comment: I just finished a 20-week course from this book. It is well-written, with a healthy number of examples and many exercises (interspersed throughout the text) and problems (at the end of each chapter). The style is rather informal: this is good for the novice to this subject, which groans under the weight of its own notation. The presentation is well-organized, clear, and accessible. Dr. Lee maintains current errata for the book (some did make it into the problems unfortunately) at his website.
One thing I might suggest is that if you plan to use this book heavily (e.g., for a course rather than for reference or bedtime reading) you should consider investing in the hardcover version is possible. The book is lengthy and the binding tends to split. Mine is still in one piece, but only just. You have to be very gentle with this book to keep it intact.
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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: Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics , Vol 176) by John M. Lee ISBN: 0387983228 Publisher: Springer Verlag Pub. Date: October, 1997 List Price(USD): $44.95 |
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Title: Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach ISBN: 048668735X Publisher: Dover Pubns Pub. Date: 22 September, 1995 List Price(USD): $11.95 |
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Title: Algebraic Topology by Allen Hatcher ISBN: 0521795400 Publisher: Cambridge University Press Pub. Date: 15 November, 2001 List Price(USD): $32.00 |
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Title: Functional Analysis by Walter Rudin ISBN: 0070542368 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1991 List Price(USD): $132.45 |
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