An Introduction to Algebraic Topology (Graduate Texts in Mathematics) | 
 enlarge | Author: Joseph J. Rotman
Publisher: Springer
Category: Book
List Price: $74.95
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Rating:  2 reviews
Sales Rank: 968157
Media: Hardcover
Pages: 433
Number Of Items: 1
Shipping Weight (lbs): 1.8
Dimensions (in): 9.2 x 6.4 x 1.3
ISBN: 0387966781
Dewey Decimal Number: 514.2
EAN: 9780387966786
Publication Date: July 22, 1998
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Product Description
This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, simplicial, and cellular), homotopy groups, and cohomology rings. It is suitable for a two- semester course at the beginning graduate level, requiring as a prerequisite a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced, making this book of great value to the student.
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| Customer Reviews:
 Good textbook December 9, 1999
13 out of 14 found this review helpful
Rotman's book presents all the material one would expect of an introductory text, in the language of Categories although still accessible to those who have never seen categories before. While Rotman's style and exposition is excellent, the book often gets bogged down in cumbersome notation. Also some other textbooks(e.g. Munkres Elements of Algebraic Topology) give more motivation to the material and explain what is actually going on geometrically(as opposed to algebraically). Also, the exercises are generally quite easy. Overall, I recommend Rotmans book to people who don't mind being patient, and waiting to see the whole picture.
 Rotman does it again. May 25, 2006
Jason Schorn (Spokane, WA)
7 out of 8 found this review helpful
Each text that I have read by Rotman is logically sound, well thought out, there are ample explanations, exercises as well as examples, and moreover, Rotman does an excellent job proving results. Sure he leaves the reader to prove certain results but, in general, all major concepts he will prove or, when it comes to familiar sticking points for students, Rotman will show that reader how to effectively prove these types of results. Now, Algebraic Topology is not an easy subject (actually it is a beautiful and far-reaching subject) and, depending upon the authors approach, the level of 'mathematical' maturity required can quickly escalate. Rotman's text is just above middle of the road with respect to this proverbial and undefined notion-'mathematical maturity'. Not as far-off as Spanier and not quite as gentle as Hatcher. For the reader who has this maturity or the necessary background, then Rotman's text is a must read provided you enjoy texts that follow the theorem-proof-theorem format. Furthermore, the logical consistecny with respect to how and when material is present to the reader places this text in a league of it's own. Without a doubt I could imagine any beginning graduate student or confident undergradute tackling this text on their own. For example, I am no math wizard but with only a background consisting of point-set topology with an introduction to the Fundamental Group, Abstract Algebra (Hungerford style) and Analysis (Rudin style) I was able to begin reading and, in particular, solving problems from Rotman's text while a senior undergraduate. For those of you who would like to learn the subject and learn it well but who are scared of this text (Springer can do that to people) I wouls strongly recommend pairing this text with Allen Hatchers or Part II of James Munkres' text depending on your level of enjoyment with respect to suffering your way through texts. In fact, I would suggest reading Munkres in its entirety since, this approach would properly prepare your for Rotman's text and the transition would be seamless. Finally, if, while reading this text you find yourself feeling lost during the initial chapters due to the use of Category Theory, I would suggest pushing forward and not becoming too hung up on acquirring a 'total' understanding. Things will make more sense as you progress through the later chapters. Enjoy and good luck!
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