Topology of Surfaces, Knots, and Manifolds

Rating:
Summary: Very Misleading Title, Quite Thin, No Rigor, and Overpriced
Review: This book is subtitled "A First Undergraduate Course" but is certainly below undergraduate level. A high school student could easily follow this--which might be a good thing in certain cases--but the rigor is lacking. In fact, there is barely a hint of any rigor whatsoever. It is mostly intuitive arguments and the author often says things like "but we won't bother worrying about mathematical technicalities". It does get you to be able to visualize certain things well, but the visualization techniques can be found in other books also. The book is very thin and a quick read--hardly worth the money they are trying to get for it. If you're really at the undergraduate level and want to learn some topology, try something like Mendelson's "Introduction to Topology" by Dover or one of the excellent topology books in the series "Undergraduate Texts in Mathematics" by Springer. Munkres is also a classic. If you're not an undergraduate in a math related field and just want to know about the ideas behind topology or perhaps see some visualization techniques, try something like "The Shape of Space" by Weeks. Overall I was very disappointed with this text. If you could purchase this book for under $20 it might be worth it, but even then I think the other books I quoted are better in both price and substance.

Rating:
Summary: Very Misleading Title, Quite Thin, No Rigor, and Overpriced
Review: This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and there are superfluous examples. The exercises in the text are well thought out and are not extremely difficult. The exercises complement the text very well. The text makes clear a lot of difficult concepts such as isotopic surfaces as opposed to homeomorphic surfaces. I particularly enjoyed the manner in which the topology of knots was explained. After reading this text, the reader should be able to better visualize the projective plain and even the Klein bottle as it exists in 4-dimensional space. I have not read a text on topology that I enjoyed reading as much since Munkres. This text is a must have for any topologist.

Rating:
Summary: No math library is complete without this book
Review: This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and there are superfluous examples. The exercises in the text are well thought out and are not extremely difficult. The exercises complement the text very well. The text makes clear a lot of difficult concepts such as isotopic surfaces as opposed to homeomorphic surfaces. I particularly enjoyed the manner in which the topology of knots was explained. After reading this text, the reader should be able to better visualize the projective plain and even the Klein bottle as it exists in 4-dimensional space. I have not read a text on topology that I enjoyed reading as much since Munkres. This text is a must have for any topologist.

Rating:
Summary: Fun, but not very substantive.
Review: This is a relatively fun romp through some very interesting concepts, but it lacks rigor. The book could have been much stronger if the author had simply developed some of the basic concepts (compactness, connectedness, homeomorphisms, homotopy, etc) rather than do a little hand-waving around a nice illustration. As it stands, this book is only 140 pages long, and does not develop any of its topics (manifolds, surfaces, graphs, knots) adequately. This book is far too weak to serve as a good text. Kinsey's TOPOLOGY OF SURFACES is much stronger, and costs less. Or look as something like Gamelin's INTRO TO TOPOLOGY. Or even Schaum's outline GENERAL TOPOLOGY, which deals with the basics, but is highly readable and rigorous.

Rating:
Summary: Fun, but not very substantive.
Review: This is a relatively fun romp through some very interesting concepts, but it lacks rigor. The book could have been much stronger if the author had simply developed some of the basic concepts (compactness, connectedness, homeomorphisms, homotopy, etc) rather than do a little hand-waving around a nice illustration. As it stands, this book is only 140 pages long, and does not develop any of its topics (manifolds, surfaces, graphs, knots) adequately. This book is far too weak to serve as a good text. Kinsey's TOPOLOGY OF SURFACES is much stronger, and costs less. Or look as something like Gamelin's INTRO TO TOPOLOGY. Or even Schaum's outline GENERAL TOPOLOGY, which deals with the basics, but is highly readable and rigorous.