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Title: Introduction to Topological Manifolds (Graduate Texts in Mathematics) by John M. Lee ISBN: 0-387-95026-5 Publisher: Springer-Verlag Telos Pub. Date: 25 May, 2000 Format: Paperback Volumes: 1 List Price(USD): $42.95 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: Review of a non-mathematician
Comment: Being a physicist I've always been fascinated with the use of manifolds and differential geometry in mechanics, field theory, etc ... Most differential geometry books I've encountered only devote about 1 chapter to manifolds and smooth manifolds at that. However this text takes its time to teach the reader what the author states he thinks is the minimum amount of general knowledge about topological manifolds (no discussion of smooth/analytic manifolds is included). The author takes his time developing everything from scratch, not even assuming any experience with (point set) topology, so this book is particularly suited for those who shy away from the subject just because they're not mathematicians and don't know topology. The only prerequisites are advanced calculus and linear algebra, nothing too fancy. The writing itself is very clear and while rigorous this book does not get lost in the boring lemma-theorem-proof vicious cycle so many other math books fall flat at. Throughout the book are scattered exercises for the reader to do (about 10-20 each chapter) and there are problems at the end of each chapter (no solutions/hints included). All-in-all I feel this text has offered me a much greater understanding of manifolds and the general theory dealing with them. Highly recommended.
Rating: 5
Summary: A very readable text
Comment: An excellent text for a beginning graduate level class. This is NOT a comprehensive text covering the material in exhaustive detail, but it is an excellent overview of surfaces, simplicial complexes, homotopy, homology, and the briefest peek at cohomology. The sequence is efficient, and the author does a good job of motivating the discussions, rather than simply dumping an abstraction into your lap. As always, one should be familiar with point-set and groups before jumping in. If you are looking for a text at an undergraduate level, see Armstrong's Basic Topology or Kinsey's Topology of Surfaces.
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Title: Introduction to Smooth Manifolds by John M. Lee ISBN: 0387954481 Publisher: Springer-Verlag Pub. Date: 23 September, 2002 List Price(USD): $49.95 |
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Title: Topology from the Differentiable Viewpoint by John W. Milnor, John Milnor ISBN: 0691048339 Publisher: Princeton University Press Pub. Date: 24 November, 1997 List Price(USD): $17.95 |
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Title: Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics , Vol 176) by J.M. Lee, John M. Lee ISBN: 0387983228 Publisher: Springer-Verlag Telos Pub. Date: 01 October, 1997 List Price(USD): $44.95 |
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Title: Counterexamples in Analysis (Dover Books on Mathematics) by Bernard R. Gelbaum, John M. H. Olmsted ISBN: 0486428753 Publisher: Dover Publications Pub. Date: 01 June, 2003 List Price(USD): $14.95 |
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Title: Analysis on Manifolds by James R. Munkres ISBN: 0201315963 Publisher: Westview Press Pub. Date: June, 1997 List Price(USD): $76.00 |
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