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Introduction to Smooth Manifolds

4.37  ·  Rating details ·  73 ratings  ·  5 reviews
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, ve ...more
Hardcover, 708 pages
Published August 26th 2012 by Springer (first published January 1st 2002)
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Vincent
Dec 15, 2019 is currently reading it  ·  review of another edition
Shelves: mathematics
It's hard to judge differential geometry books at this point because I'm familiar with the material, but overall I think it's one of the best self-study books I've found. Very good at motivating the definitions.
William Bies
Mar 01, 2020 rated it really liked it  ·  review of another edition
As philosophers of mathematics are wont to comment on, geometry differs from arithmetic in that it involves spatial intuition, while, in contrast, the number theorist may proceed from a pure concept of number, entirely abstracted from the world in which we happen to live. For this reason, the reputation of geometry has suffered in certain quarters, and this reviewer does not think that Bertrand Russell’s logical atomism does, in fact, succeed in removing all intuitive content from the continuum— ...more
Noud
Jul 22, 2012 rated it it was amazing  ·  review of another edition
Introduction to Smooth Manifolds from John Lee is one of the best introduction books I ever read. I read most of this book, except for the appendices at the end and proofs of some corollaries. This book covers a couple of subjects:
(*) First the theory of smooth manifolds in general (ch1, 2, 3, 4, 5 and 6), smooth maps, (co)tangent spaces, (co)vector fields and vector bundles. These first few chapters contain a lot of examples. These six chapters can be used as a first introduction course to smo
...more
Andrew
Mar 12, 2017 rated it really liked it  ·  review of another edition
The advantage of a long-winded approach emphasizing a geometric way of thinking is to place intuition first and formalism second. Give the reader an intuitive view of the subject--get them to "see" the right picture in as many words necessary (and I do expect that it helps to have a strong ability to visualize when learning the subject, at least using this approach). Within this approach (and especially when grounding everything in well-selected examples), the book is quite successful, chapters ...more
Leonhard Euler
May 08, 2011 rated it liked it  ·  review of another edition
Shelves: math
Should be pithier.
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