- Series: Springer Undergraduate Mathematics Series
- Paperback: 224 pages
- Publisher: Springer; 1st ed. 2005. Corr. print 2010. edition (July 1, 2005)
- Language: English
- ISBN-10: 1852337826
- ISBN-13: 978-1852337827
- Product Dimensions: 6.1 x 0.6 x 9.2 inches
- Shipping Weight: 15.5 ounces (View shipping rates and policies)
- Average Customer Review: 3.8 out of 5 stars See all reviews (10 customer reviews)
- Amazon Best Sellers Rank: #575,454 in Books (See Top 100 in Books)
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Essential Topology (Springer Undergraduate Mathematics Series) 1st ed. 2005. Corr. print 2010. Edition
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From the reviews:
"This book presents the most important aspects of modern topology, essential subjects of research in algebraic topology … . The book contains all the key results of basic topology and the focus throughout is on providing interesting examples that clarify the ideas and motivate the student. … this book contains enough material for two-semester courses and offers interesting material for undergraduate-level topology, motivating students for post-graduate study in the field and giving them a solid foundation." (Corina Mohorianu, Zentralblatt MATH, Vol. 1079, 2006)
"This text provides a concise and well-focused introduction to point set and algebraic topology. The main purpose is to quickly move to relevant notions from algebraic topology (homotopy and homology). Throughout the book the author has taken great care to explain topological concepts by well-chosen examples. It is written in a clear and pleasant style and can certainly be recommended as a basis for an introductory course on the subject." (M. Kunzinger, Monatshefte für Mathematik, Vol. 152 (1), 2007)
From the Back Cover
Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.
While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.
With chapters on:
* continuity and topological spaces
* deconstructionist topology
* the Euler number
* homotopy groups including the fundamental group
* simplicial and singular homology, and
* fibre bundles
Essential Topology contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well prepared for it.
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Top Customer Reviews
What was delivered was the copyright 2010 "corrected"? version, and the print quality is very bad: very light type which is not easy to read.
Another complaint: His English does not always seem grammatically correct to me. (Maybe I'm sheltered living in the eastern US?) For example, "Since the arrows rotate 720 degrees as we go around the circle, so deg(f) = 2." does not sound like a full sentence to me. If I had only seen it once or twice I might mistake it for another typo, but this sort of sentence structure is all over the book. It really disrupts the flow for me.
The first half of this book covers point-set topology, the second half algebraic. If you want to read this book in full, knowing basic algebra is an absolute must. If you have familiarity with, for example, quotient groups, free groups, and the rank/nullity theorem from linear algebra you should be fine. If you only care about the first half, knowing naïve set theory and basic operations on matrices should suffice.
To summarize, the exposition is actually pretty good, but there are too many errors for me to recommend it.
IMPORTANT: Apparently, a lot of mistakes have been corrected in the most recent printing. Please read the comments to this review for details.
The topics are well motivated. Crossley does a good job in explaining why we should care about these particular lemmas and theorems. The proofs are usually elegant. I find the estetic pleasures a good math book should provide.
Theorems are proved in a rigorous yet intuitive style that one feels like it was an explanation rather than a dry proof typically found in the advanced math books.
Important key ideas are also sufficiently illustrated through examples and exercises.
If one finds it verbose, I'd recommend croom--a bit more like the typical math books but accessible.