- Paperback: 200 pages
- Publisher: Springer; Corrected edition (July 31, 1998)
- Language: English
- ISBN-10: 3540761977
- ISBN-13: 978-3540761976
- Product Dimensions: 7 x 0.7 x 9.2 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 25 customer reviews
- Amazon Best Sellers Rank: #297,207 in Books (See Top 100 in Books)
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Elementary Number Theory (Springer Undergraduate Mathematics Series) Corrected Edition
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From the reviews:
BULLETIN OF MATHEMATICS BOOKS
"?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."
G.A. Jones and J.M. Jones
Elementary Number Theory
"A welcome addition . . . a carefully and well-written book."―THE MATHEMATICAL GAZETTE
"This book would make an excellent text for an undergraduate course on number theory."
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Another Amazonian reviewer commented that "Number theory is like the cement on your driveway. Real and Complex analysis are the Porsche and Ferrari you drive home every night." I disagree. In any case, in my opinion the book's weak spots are those sections where the discussion forays into the realm of real and complex analysis, namely 9.4-6 ("Random Integers", "Evaluating Zeta(2)", "Evaluating Zeta(2k)"), 9.9 ("Complex variables"), 10.2 ("The Gaussian Integers"), a part of 10.6 ("Minkowsky's Theorem") and 11.9 ("Lame and Kummer"). "Sums of two squares" (Section 10.1) could also use improvement, but this is compensated by the excellent, independent treatment this topic receives in the "Minkowsky's Theorem" chapter.
On several occasions, from the very beginning, the book assumes familiarity with single-variable polynomials (particularly the division algorithm and the x^n-y^n expansion). Be prepared.
If it weren't for the forays mentioned above, the book would have been a straight fiver. But even as it stands, it's a tour-de-force of pedagogy and expository mathematical writing.
One last quibble. The book doesn't have a homepage, nor is there any indication of a way to contact the authors. Textbook publishers should learn from their colleagues in the applied computer science publishing industry (such as O'Reilly, Wrox, Apress, etc.) and always make a homepage available for every book, with, at the minimum, a link to an errata page, and a forum where readers of the book can discuss it, (preferably with the involvement of the author(s)).
For the small size it has there is a lot inside it, and the writing style is pleasant, although, sometimes, important details are, in an undesirable way, left out.
The fact the book has answers is indeed a very good thing, and good teachers should make their own set of exercises, so I don't think the fact that the exercises are answered at the end of the book is a drawback. Quite the contrary, it is a perfect suitable book for being self-taught and independent.
All the exercises have answers, or give you directions. They are spread around the text, appearing every time a new concept is been given, or a theorem is been shown. All theorems have proofs easy to follow.
Someone might find that the book should have addressed this or that, instead of the topics chosen, but this is how far any criticism of this textbook can go.
In few words: buy it!
I'm a real fan of the SUMS books (I've bought 4 of the titles in the series), because all of the books I've bought are well written, they're jammed full of useful information and they're relatively cheap!
The book strikes a good balance between keeping focused on number theory (there are chapters requirng a knowledge of rings and groups, but these structures only support the numbers, not abstract them away) and not being trivial (I've read too many number theory books that are 'bitty', in the sense that there is too much breadth and not enough depth).
In view of my current experiences with this textbook, I would recommend it to a mathematical hobbyist like myself, or to a professional student of mathematics -- or anyone wishing to tackle number theory.