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Introduction to Smooth Manifolds
 
 
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Introduction to Smooth Manifolds [Paperback]

John M. Lee (Author)
4.8 out of 5 stars  See all reviews (4 customer reviews)

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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)

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Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
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This book is about smooth manifolds. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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4 Reviews
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4.8 out of 5 stars (4 customer reviews)
 
 
 
 
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5.0 out of 5 stars Extremely well written, Mar 24 2006
This review is from: Introduction to Smooth Manifolds (Paperback)
If you want to learn smooth manifold theory then this book is your best choice. Lee's style of writing is exceptionally ... smooth. The style is intended to iluminate the subject without comprimising rigor. It's a "real" math book so there is very little handwaving.

I particularly like the organization of the book. The short length of the chapters motivates the learning process and builds motivation (...that's one more chapter under my belt...). There are 20 chapters in total with average length of 20-30 pages. Long chapters in a book can lead one to forget what is being studied. By making the chapters short, Lee helps the reader focus on learning the particular topic. The sequence of the chapters then allows one to envision the whole picture.

The appendix contains some basic background from topology, linear algebra, and calculus. If you are not sure about a certain term you will probably find it there.

My hats off to Lee. I plan to buy his other books.

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5.0 out of 5 stars Extremely well written, Mar 24 2006
This review is from: Introduction to Smooth Manifolds (Paperback)
If you want to learn smooth manifold theory then this book is your best choice. Lee's style of writing is exceptionally ... smooth. The style is intended to iluminate the subject without comprimising rigor. It's a "real" math book so there is very little handwaving.

I particularly like the organization of the book. The short length of the chapters motivates the learning process and builds motivation (...that's one more chapter under my belt...). There are 20 chapters in total with average length of 20-30 pages. Long chapters in a book can lead one to forget what is being studied. By making the chapters short, Lee helps the reader focus on learning the particular topic. The sequence of the chapters then allows one to envision the whole picture.

The appendix contains some basic background from topology, linear algebra, and calculus. If you are not sure about a certain term you will probably find it there.

My hats off to Lee. I plan to buy his other books.

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5.0 out of 5 stars Excellent, lucid book on manifolds, Jan 28 2004
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Paul "kras" - See all my reviews
(REAL NAME)   
This review is from: Introduction to Smooth Manifolds (Paperback)
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.

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