Introduction to Topology: Pure and Applied | 
 enlarge | Authors: Colin Adams, Robert Franzosa
Publisher: Prentice Hall
Category: Book
List Price: $133.33
Buy New: $72.21
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Rating:  3 reviews
Sales Rank: 545710
Media: Hardcover
Pages: 512
Number Of Items: 1
Shipping Weight (lbs): 2.2
Dimensions (in): 9.4 x 7.1 x 1.3
ISBN: 0131848690
Dewey Decimal Number: 514
EAN: 9780131848696
Publication Date: June 28, 2007
Availability: Usually ships in 1-2 business days
Shipping: International shipping available
Condition: Brand New. Delivery is usually 5 - 8 working days from order, International is by Royal Mail Airmail
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Product Description
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.
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| Customer Reviews:
A great introduction to pure and applied topology January 18, 2008
Daniel O. Cajueiro (Brasilia, Brazil)
2 out of 2 found this review helpful
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.
An excellent text with supporting website April 26, 2008
1 out of 1 found this review helpful
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 http://germain.umemat.maine.edu/faculty/franzosa/ITPA.htm
Fabulous Introduction to Topology! November 12, 2008
L. Martin (Pittsburgh, PA, USA)
1 out of 1 found this review helpful
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. This book does a good professor's job--instead of merely regurgitating theory and leaving you to put the pieces together, it's an excellent guide to a deeper understanding of the subject.
The exercises are plentiful and well-chosen. The authors gently guide the reader along the right path when asking for a new proof, and there are enough examples given to help the reader broaden her thinking to new approaches. The last several chapters go into more detail about specific topics that take the general concepts in advanced directions; this structure avoids breaking the flow of information. Overall, the text is very well-organized, and the authors have painstakingly highlighted suggested paths through the material.
This is, however, an introductory text, and it sticks mostly to point-set topology. There are a few results that I was surprised to see missing, and a few concepts that were skipped entirely (for instance, the distinction between the product topology and the box topology--the box topology is not discussed). For my purposes, it everything I could hope for--a patient discussion that expanded and clarified the topics I've already encountered using Munkres. As an introductory text, I couldn't imagine anything better.
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