23 of 23 people found the following review helpful
Students: BUY THIS BOOK!!!,
This review is from: Topology (Undergraduate Texts in Mathematics) (Hardcover)
It is not too often that a book about topology is written with the goal of actually explaining in detail what is going on behind the formalism. The author does a brilliant job of teaching the reader the essential concepts of point set topology, and the book is very fun to read. The reader will walk away with an appreciation of the idea that topology is just not abstract formalism, but has an underlying intuition that is rich in imagery. The author has a knack for allowing readers to "see into the future" of what kind of mathematics is waiting for them and how topology is indispensable in its study.
At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: "If is often said against intuitive, spatial argumentation that it is not really argumentation but just so much gesticulation - just 'handwaving'. Shall we then abandon all intuitive arguments? Certainly not. As long as it is backed by the gold standard of rigorous proofs, the paper money of gestures is an invaluable aid for quick communication and fast circulation of ideas. Long live handwaving!". This has to rank as one of the best paragraphs that has every appeared in a mathematics book, for it nicely summarizes the need for developing a feel for the concepts behind mathematics before moving on to the rigorous proofs. Physicists in particular, who must assimilate mathematics very quickly in order to apply it to real problems must have a pictorial, "playful" understanding of the mathematical constructions.
Thus the language that the author employs is informal, and a listing of the best discussions in the book would really entail a listing of every one in the book. There is not one part of the book that is not helpful or interesting, and the author delves into many different areas that involve the use of topology.
If you are a beginning student in mathematics, BUY AND STUDY THIS BOOK...BUY AND STUDY THIS BOOK. You will take away so much for the price paid.
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Initial post: Sep 26, 2011 6:14:40 AM PDT
Bobby Bambino says:
Thanks Dr Carlson. I've mentioned this before, but your reviews are always so helpful!
Posted on Nov 16, 2011 4:07:17 AM PST
A. Cox says:
I have to agree with Bobby Bambino, I always read your (math book) reviews, and can pretty much say that they are always well written, well balanced and well informed.
But especially thanks to the quote about 'handwaving', I get sick hearing reviewers moaning about 'handwaving' in math books, on what appears to be the assumption that all you need to understand maths is just theorems and proofs.
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