- Paperback: 628 pages
- Publisher: Springer (2 October 2002)
- Language: English
- ISBN-10: 0387954481
- ISBN-13: 978-0387954486
- Product Dimensions: 15.5 x 3.7 x 23.5 cm
- Average Customer Review: Be the first to review this item
- Amazon Bestsellers Rank: #12,74,657 in Books (See Top 100 in Books)
Introduction to Smooth Manifolds (Graduate Texts in Mathematics) Paperback – 2 Oct 2002
Customers who bought this item also bought
From the reviews: "This book offers a concise, clear, and detailed introduction to analysis on manifolds and elementary differential geometry. … Some of the prerequisites are reviewed in an appendix. For the ambitious reader, lots of exercises and problems are provided." (A. Cap, Monatshefte für Mathematik, Vol. 145 (4), 2005) "The title of this 600 pages book is self-explaining. And in fact the book could have been entitled ‘A smooth introduction to manifolds’. … Also the notations are light and as smooth as possible, which is nice. … The comprehensive theoretical matter is illustrated with many figures, examples, exercises and problems. Some of these exercises are quite deep … ." (Pascal Lambrechts, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2004) "It introduces and uses all of the standard tools of smooth manifold theory and offers the proofs of all its fundamental theorems. … This is a clearly and carefully written book in the author’s usual elegant style. The exposition is crisp and contains a lot of pictures and intuitive explanations of how one should think geometrically about some abstract concepts. It could profitably be used by beginning graduate students who want to undertake a deeper study of specialized applications of smooth manifold theory." (Mircea Craioveanu, Zentralblatt MATH, Vol. 1030, 2004) "This text provides an elementary introduction to smooth manifolds which can be understood by junior undergraduates. … There are 157 illustrations, which bring much visualisation, and the volume contains many examples and easy exercises, as well as almost 300 ‘problems’ that are more demanding. The subject index contains more than 2700 items! … The pedagogic mastery, the long-life experience with teaching, and the deep attention to students’ demands make this book a real masterpiece that everyone should have in their library." (EMS Newsletter, June, 2003) "Prof. Lee has written the definitive modern introduction to manifolds. … The material is very well motivated. He writes in a rigorous yet discursive style, full of examples, digressions, important results, and some applications. … The exercises appearing in the text and at the end of the chapters are an excellent mix … . it would make an ideal text for a comprehensive graduate-level course in modern differential geometry, as well as an excellent reference book for the working (applied) mathematician." (Peter J. Oliver, SIAM Review, Vol. 46 (1), 2004)
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter mobile phone number.
|5 star (0%)|
|4 star (0%)|
|3 star (0%)|
|2 star (0%)|
|1 star (0%)|
Most helpful customer reviews on Amazon.com
someone who will do what it takes to learn Differential Geometry.
The title of this book is not 'Differential Geometry,' but 'Introduction to Smooth Manifolds;' a title I think is very appropriate. In this book, you will learn all the essential tools of smooth manifolds but it stops short of embarking in a bona fide study of Differential Geometry; which is the study of manifolds plus some extra structure (be it Riemannian metric, Group or Symplectic structure, etc). I should note, however, that it does cover elementary notions of Riemannian metrics and a fair amount of Lie Groups. At first I found it annoying that I had to work through over 500 pages of dense mathematics before I could study what I really had my heart set on: Riemannian Geometry. But, having read Lee's book cover to cover, I am glad that I waited and developed all the necessary tools.
Lee assumes the reader is well prepared, i.e. has had rigorous courses in Multivariable Analysis especially up to Inverse Function Theorem at the level of, say `baby Rudin' (but, Lee does prove this is complete detail), Group theory, Linear Algebra, and Topology. In my opinion, all of these are necessary for a deep understanding of the subject.
I would advice anyone who will work through Lee's tome to pick up a slimmer, more concise book to stay relatively grounded. My personal favorites are: Janich's `Vector Analysis' (I can't recommend this enough!), Barden's `Intro to Differentiable Manifolds,' Janich and Brocker's `Differential Topology' (hands down, the best pictures!), Milnor's `Topology from a Differentiable Viewpoint.'
** Merits **
-Pedagogical, motivational, student friendly (Excellent Index!), lots of details
-Moves slow, takes its time developing basics with lots of pictures and heuristic arguments
-Lots of worked out examples!
-Very good selection of problems
-Very useful appendix on Topology, Analysis, and Linear Algebra (A must read as the highlights of the subjects are conveyed with only the useful proofs thrown in)
-Prepares one for advanced books in Differential Geometry, i.e. Riemannian Geometry, Differential Topology, etc.
-The entire book can be covered in a semester and a half, leaving time to cover most of Lee's Riemannian geometry book.
** Simultaneous Merits, Stumbling blocks, and/or Distractions **
-Too much information for a first reading
-Too wordy (overly detailed in proofs)
-Subjects are introduced at the moment tools are available, not in their own separate chapters
-Not clear how chapters are interdependent (however, research mathematics is not artificially divided so it's refreshing to read a book that embraces this)
** Faults/Disadvantages **
-Lots of typos, so be sure to download the list of errata from the authors webpage
-Style not for everyone; some readers will prefer more reserved, concise treatments. To this end, I can recommend Warner's `Foundations of Differentiable Manifolds and Lie Groups'
-Need to look elsewhere for Riemannian geometry, i.e. there is no mention of a connection or curvature
-Not useful as a reference (unless, of course, you worked through it cover to cover and a have a feel for when things were introduced. However, the index is excellent)
Please have a look at the reviews by Mr. Raleigh and "math reader." I agree whole-heartedly with their assessment of Lee. They also talk about some aspects that I do not repeat =)
** Conclusion **
This book is incredibly addicting and FUN to read, work from, and learn!
Thanks professor Lee
Only one small detail: the tangent space consturction of SS chern (lectures on differential geometry) is perhaps a bit better but it`s rather difficult to appreciate it at first time.
In any case, this book is long and contains a lot of problems for you to do. Unfortunately I do not do them, but that is a different story. I'm nowhere near finishing all the stuff this book has to tell me, but whenever I need to find something I don't know this book tends to have it. The index is great. It might be the best of any book I've used. The greatness of this book is a little surprising juxtaposed with Lee's book on Riemannian geometry which is not exceptional.
Since this book is so large, and it says it's a graduate math book right on the cover, I like to take it out with me when I go out on the town. I find it's a great ice breaker with the ladies. I only wish it was the nice burnt orange of the newer springer books.
All in all, this is a great book, and really puts Spivak to shame.