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Title: An Introduction to Manifolds (Universitext)
ISBN: 0387480986
Author:
Loring W. Tu
Publicate Date: 2007-10-29
Publish: 2007-10-29
List Price: $49.95
Average Customer Rating: 5.0
Format: Paperback
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Amazon Lowest New Price: $40.42
Amazon Lowest Used Price: $43.00
Amazon Merchant Price: $40.42
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| Customer Review: |
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1: Clear and Solid Exposition
This is my favorite book on Differentiable Manifolds. After reading this book the reader will obtain a solid background on the following essential notions: Charts and atlas of a manifold; tangent vectors (as derivations); differential of a smooth function between manifolds; submanifolds and embeddings; quotient spaces; partitions of unity; vector fields; vector bundles; differential forms and de Rham cohomology. And on the road, the reader gets a gentle exposure to Lie groups, Lie algebras; and some basic notion of Category and Functors.
I found the following aspects of the book especially attractive:
> Clear style of writing: The author is the coauthor of the acclaimed "Differential Forms in Algebraic Topology". See the comments for that book. The clarity has not decreased at all.
> Bite-sized sections: The materials contained in each section is approximately equal to that of a 50-minute lecture. This helps readers who plan self-study.
> Right amount of topics: This is not an encyclopedia on manifolds. However, it does contain the ``absolute must'' one should know about manifolds. And it does such a good job in presenting it, the reader will be left with a solid understanding on those essential topics.
I first read this book as a Physics student and had no trouble reading it. I later switched discipline to Mathematics, and I know that this book has helped me appreciate the beauty of Mathematics. I thank the author for writing such an wonderful book.
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2: An introduction it Manifolds
This is an excellent book. I wish that more books on advanced mathematics were written in this style. In contrast to most books on manifolds that tend to be very difficult for beginners to follow, Prof. Tu has made every effort to make this subject understandable to the nonexpert.
Greg Chirikjian
Professor, Mechanical Engineering
Johns Hopkins University
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3: fills a gaping hole
i think there is a jump from ugrad analysis/alg/top etc to early grad school concepts. i didnt know category theory, i only had the flimsiest notion of a manifold, etc etc. and this book fills in that jump wonderfully. it does the right mix of analysis-differential topology-topology so that you can go read a book like bott and tu later (that's what it was designed for).
so im having a good time with it.
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