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Elementary Number Theory (Springer Undergraduate Mathematics Series), by Gareth A. Jones, Josephine M. Jones
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An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
- Sales Rank: #215217 in Books
- Brand: Brand: Springer
- Published on: 1998-07-31
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .72" w x 7.01" l, .95 pounds
- Binding: Paperback
- 200 pages
- Used Book in Good Condition
Review
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."
―MATHEMATICAL REVIEWS
Most helpful customer reviews
2 of 2 people found the following review helpful.
Phenomenal book for Self-study
By Madhusa Karunanayake
The pacing in this book is phenomenal. Every topic is explained with more than enough detail and without tangents.
The one thing this book does better than any other Number Theory book are the in-chapter questions. The questions are done so well that WANT to do them. You feel as if you are missing vital information by not doing them. This is one of the few books I can study for hours on end because you are constantly being engaged as you are working through the chapter, instead of mindlessly reading and hoping you remember everything you've just read. They questions aren't very difficult (full worked solutions for every problem if needed), but they are just hard enough to make you have to think.
That is also it's only downside. You cannot jump between sections sometimes. The book assumes you follow it from the beginning of a section to the end as it sometimes teaches you vital information via the in-chapter questions.
If you are looking to self-study then you will not find a better book. I've tried every Number Theory book with decent ratings on Amazon, and this is by far the best.
7 of 7 people found the following review helpful.
An almost perfect square
By Itai
That the book's almost square is easily gathered from the photo. That it's almost perfect must be verified by reading it. And what an enjoyable verification indeed awaits those who take on the challenge! Not that reading it is a challenge - on the contrary, the Joneses take every effort to ensure your learning experience be as painless as possible. Every proof is complete, all exercises are solved. The proofs are always selected for their instructional merit, rather than for their mathematical "elegance" (read: brevity and algebraic gimmickry). As one Amazonian reviewer put it: you could read it through, lying in a bubble bath.
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)).
4 of 5 people found the following review helpful.
A Satisfactory Text for Elementary Number Theory
By Joseph A. Schrock
I've recently received my copy of Elementary Number Theory by Jones and Jones, and I'm (thus far) satisfied with the textbook. Although I'm not a professional mathematician, I have worked toward a degree in math and still love to study it. For me, the current textbook for number theory is a challenge to master, but with all the solutions to problems provided, I find it quite palatable to work toward an understanding of number theory, using this text.
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.
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