Topology Now! (Classroom Resource Material) 1st Edition by Robert Messer (PDF)

Description

Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.

User’s Reviews

Editorial Reviews: Review A marvelous introduction to geometric topology for students with mathematical talent, but not much mathematical experience. — W. B. Raymond Likorish, University of Cambridge Book Description An undergraduate textbook on topology designed to have very few prerequisites. About the Author Robert Messer received his PhD. In 1975 from the University of Wisconsin. He has been at Albion College since 1981. Philip Straffin’s received his his Ph.D. from the University of California at Berkeley, with a thesis in algebraic topology under Emery Thomas. He has taught at Beloit College since 1970. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The authors have obvious intelligence and talent, but ultimately the big-picture pedagogical approach falls a bit short.I have to agree with some of the other reviews in the sentiment that the topics are not always well-motivated; and the lack of rigor is as often a deterant to as a facilitator of understanding.Still, I have to give this textbook 4 stars for the following reasons:1. It is truly accessible—it may not be the best choice for many students, but it is helpful for all of them2. Broad yet compact—this makes the book valuable for a course where the instructor can supplement with other material.

⭐If you want an example of how not to write a science and mathematics book, this book is as good as you will find. Somehow, the authors manage to make simple and relatively intuitive concepts ambiguous and complicated. While they attempt to motivate the material, they fail at it miserably and you feel that you have just had a kitchen sink dished at you. When attempting to do exercises, you will more likely than not need to refer to other sources or simply struggle to figure out what the assignment is asking.In short, there are books out there which you could skim and retain some material. Then, if you feel that you are missing some details, you could go back and work out all the details or read more carefully. This book is in the other category. No matter how much you reread a paragraph, you will struggle to get anything out of it (because of the poor writing style).

⭐This book is bad on many levels, possibly uncountably infinite levels. Nowhere in this book is there any motivation for the material, the author just throws various topics from topology at you and expects you to be interested, which I wasn’t. The assignment’s in the book are dull and boring and the entire book is entirely confusion. I find it slightly ironic that the book is called topology now, when every chapter I was waiting for the topology to begin. The only chapter in the book that is at least mediocre was the last chapter in the book. Other than that the author spends 25% of the book (right in the middle) discussing knot theory, a concept that he never relates to the rest of the book, or gives any motivation to learning he just throws it out there. Overall this book is too confusing for non-math majors and not rigorous enough for math-majors, so if you’re looking for a good introductory topology book try Introduction to Topology by Colin Adams.

⭐What more can I say … I ordered this for a friend who requested it, and who finds it invaluable. And it came very quickly. Can’t do better than that. Sorry I’m not qualified to comment on the book’s academic content.

⭐

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