Sorry, this item is not available in
Image not available for
Color:
Image not available

To view this video download Flash Player

 


or
Sign in to turn on 1-Click ordering
Sell Us Your Item
For a $20.18 Gift Card
Trade in
More Buying Choices
Have one to sell? Sell yours here
Tell the Publisher!
I'd like to read this book on Kindle

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

An Introduction to Manifolds (Universitext) [Paperback]

Loring W. Tu
4.6 out of 5 stars  See all reviews (10 customer reviews)

Buy New
$47.96 & FREE Shipping. Details
Rent
$33.09
In Stock.
Ships from and sold by Amazon.com. Gift-wrap available.
In Stock.
Rented by RentU and Fulfilled by Amazon.
Want it Tuesday, July 15? Choose One-Day Shipping at checkout. Details
Free Two-Day Shipping for College Students with Amazon Student

Formats

Amazon Price New from Used from
Hardcover --  
Paperback $47.96  
Up to 50% Off Select Psychology Titles
For a limited time, enjoy special savings on select psychology books from Springer. Learn more

Book Description

October 8, 2010 1441973990 978-1441973993 2nd ed. 2011
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Frequently Bought Together

An Introduction to Manifolds (Universitext) + Differential Forms in Algebraic Topology (Graduate Texts in Mathematics)
Price for both: $96.31

Buy the selected items together


Editorial Reviews

Review

From the reviews of the second edition:

“This book could be called a prequel to the book ‘Differential forms in algebraic topology’ by R. Bott and the author. Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. … The text also contains many exercises … for the ambitious reader.” (A. Cap, Monatshefte für Mathematik, Vol. 161 (3), October, 2010)

From the Back Cover

Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology."

Product Details

  • Series: Universitext
  • Paperback: 410 pages
  • Publisher: Springer; 2nd ed. 2011 edition (October 8, 2010)
  • Language: English
  • ISBN-10: 1441973990
  • ISBN-13: 978-1441973993
  • Product Dimensions: 1 x 6 x 8.9 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #169,492 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews
39 of 39 people found the following review helpful
5.0 out of 5 stars Clear and Solid Exposition July 21, 2008
By pnmti
Format:Paperback
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.
Comment | 
Was this review helpful to you?
24 of 24 people found the following review helpful
5.0 out of 5 stars fills a gaping hole April 14, 2008
Format:Paperback|Verified Purchase
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.
Comment | 
Was this review helpful to you?
28 of 30 people found the following review helpful
5.0 out of 5 stars An introduction it Manifolds May 1, 2008
Format:Paperback
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
Comment | 
Was this review helpful to you?
7 of 7 people found the following review helpful
4.0 out of 5 stars A smooth introduction to manifolds March 14, 2011
Format:Paperback|Verified Purchase
Manifolds are natural generalizations of smooth surfaces. Differential forms nicely summarize what kind of integrations are possible over a manifold. Stokes theorem is a beautiful generalization of classical theorems of vector analysis.

In vector analysis, one meets the fact that whether a curl-free vector field has a potential or not in a specific domain depends on the topological properties of the domain (on simple-connectedness). This problem nicely generalizes to De Rham theory.

Tu's book is a friendly and smooth introduction to these topics and more. I can recommend it to any student of mathematics who likes beautiful general mathematical concepts and has the patience and enthusiasm to understand a large number of definitions that this theory requires.
Was this review helpful to you?
6 of 6 people found the following review helpful
5.0 out of 5 stars Great Text and Clear Exposition February 3, 2013
Format:Paperback|Verified Purchase
When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn't encountered formally before.

Loring Tu has done an excellent job of making sure even the uninitiated student can make his/her way through this text, having sprinkled a few easy exercises through the text itself to emphasize the learning and familiarity with definitions, with more difficult exercises at the end (including computations as well as topics that force a student to understand and digest the section immediately preceding the problems). He labels every problem, so a student doesn't wade through pages of text needlessly trying to discover which part of the text will be most useful, but this method allows the student to hone in on the material which is exactly pertinent to that problem. I am by far not the best and brightest student, but I have been able to read the text and given a few hours for each section, complete all exercises throughout the reading and at the end of the section. With many hints and solutions at the end of the textbook, I can be sure I'm not only learning the material, I'm learning it correctly!

I would agree with some of the other reviewers that this should be a text every graduate student in mathematics should read. It is not out of the realm of possibilities for a student to read it on his/her own, and the enlightenment gained from the generalizations of multivariate calculus is really a gift to oneself, as well as to any future students the person may have, for they will be able to answer any up-and-coming student's questions with a clarity surpassing any instructor I've personally had, which would have been very helpful as a budding mathematician.
Comment | 
Was this review helpful to you?
Most Recent Customer Reviews
Search Customer Reviews
Search these reviews only


Sell a Digital Version of This Book in the Kindle Store

If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store. Learn more

Forums

There are no discussions about this product yet.
Be the first to discuss this product with the community.
Start a new discussion
Topic:
First post:
Prompts for sign-in
 



Look for Similar Items by Category