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Introduction to Topology: Pure and Applied Hardcover – June 28, 2007

ISBN-13: 978-0131848696 ISBN-10: 0131848690 Edition: 1st

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Product Details

  • Hardcover: 512 pages
  • Publisher: Pearson; 1st edition (June 28, 2007)
  • Language: English
  • ISBN-10: 0131848690
  • ISBN-13: 978-0131848696
  • Product Dimensions: 7.2 x 1.3 x 9.2 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #392,566 in Books (See Top 100 in Books)

Editorial Reviews

From the Back Cover

 Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics.  Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness.A useful reference for readers wanting an intuitive introduction to topology.

About the Author

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College. He received his PhD from the University of Wisconsin–Madison in 1983. He is particularly interested in the mathematical theory of knots, their applications, and their connections with hyperbolic geometry. He is the author of The Knot Book, an elementary introduction to the mathematical theory of knots and co-author with Joel Hass and Abigail Thompson of How to Ace Calculus: The Streetwise Guide, and How to Ace the Rest of Calculus: the Streetwise Guide, humorous supplements to calculus. He has authored a variety of research articles on knot theory and hyperbolic 3-manifolds. A recipient of the Deborah and Franklin Tepper Haimo Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, he was a Polya Lecturer for the MAA for 1998-2000, and is a Sigma Xi Distinguished Lecturer for 2000-2002. He is also the author of mathematical humor column called "Mathematically Bent" which appears in the Mathematical Intelligencer.

Robert Franzosa is a professor of mathematics at the University of Maine. He received his Ph.D from the University of Wisconsin–Madison in 1984. He has published research articles on dynamical systems and applications of topology to geographic information systems. He has been actively involved in curriculum development and in education outreach activities throughout Maine. He is currently co-authoring a text, Algebraic Models in Our World, which is targeted for college-level general-education mathematics audiences. He was the recipient of the 2003 Presidential Outstanding Teaching Award at the University of Maine.

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Customer Reviews

4.6 out of 5 stars
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Most Helpful Customer Reviews

25 of 25 people found the following review helpful By Amazon Customer on November 12, 2008
Format: Hardcover Verified Purchase
I purchased this book upon recommendation from an internet buddy. I'm currently taking my first topology course (at an undergraduate level) and using Topology (2nd Edition) as the assigned text. I understand that Munkres is the "standard", and I don't have any real complaints about it, but I wanted something else to help broaden my understanding, and Adams and Franzosa did a great job in providing a book that does exactly that.

While Munkres presents everything from a very mathematically rigorous point of view, it took me several chapters before I really understood what we were talking about in a sense other than developing a branch of mathematics. It's great to follow theorems and definitions, but Munkres left me sort of mystified as to why we were doing this for quite some time. On the other hand, this book is all about the why and the how.

Applications of topology are presented from the get-go, usually as sections appended to the chapter that introduces the concept, so that the applications are more of an optional exploration than a focus. This really helps to motivate the reader and highlight the important concepts; it also makes it much easier to explain to a curious friend what exactly it is that you're doing.

Rigorous definitions and theorems are almost always accompanied by a plainer explanation of what exactly we're working with and why, and some of the diagrams, especially in the sections on quotient maps, are invaluable in visualizing what's going on and keeping track of what's a subset of what being mapped to where.
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10 of 10 people found the following review helpful By Daniel O. Cajueiro on January 18, 2008
Format: Hardcover
Although this book is a great introduction to pure and applied topology with several examples, figures and exercises making it is a good option for self-learning, I believe that the main differential of this book is the applied part of the book where one may find applications in economics, dynamical systems, graph theory etc. Furthermore, in the preface of the book, the author shows the minimal path that you have to follow in order to have the minimal necessary knowledge to understand the applied part of the book.

On the other hand, if you are interested only in pure topology, due to the difference of price I suggest you the Theodore W. Gamelin and Robert Everist Greene's Introduction to Topology, which is also a very nice book and very much cheaper.
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5 of 6 people found the following review helpful A Kid's Review on April 26, 2008
Format: Hardcover
I was a student of Dr. Franzosa when this book was nothing more than a word document. I've been priveledged to watch it grow, draft by draft, into the complete text that it is now. As a student of topology I find this text refreshing, as the applications bring the theorems and lemmas and corollaries to life. Its written clearly, well illustrated and just plain fun. Another useful tool is a supporting website [...]
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11 of 16 people found the following review helpful By Alexander Green on April 13, 2009
Format: Hardcover
This book would be good for someone who has not had prior experience with proof-based mathematical courses before. It is full of examples, pictures and logically sound proofs.

Having said that, this book is NOT a sufficient introduction to topology for even a moderately advanced undergraduate in mathematics such as myself. It's proofs are wordy and convoluted which make them difficult to read and it inexplicably lacks many important proofs and theorems that are proved in other standard introductory textbooks (like for, example, the proof of the Urysohyn Metrization Theorem, proved in Munkres). At times the logic is so pedantic and wordy that I find it makes simple proofs difficult to read. Do yourself a favor and learn from one of the classics.
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