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Elementary Number Theory (Springer Undergraduate Mathematics) (Springer Undergraduate Mathematics Series) (Paperback)

by Gareth A. Jones (Author), Josephine M. Jones (Author) "We start with a number of fairly elementary results and techniques, mainly about greatest common divisors ..." (more)

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Product details

Paperback: 200 pages
Publisher: Springer; 1st ed. 1998. Corr. 2nd printing edition (31 Jul 1998)
Language English
ISBN-10: 3540761977
ISBN-13: 978-3540761976
Product Dimensions: 23.4 x 15.6 x 2.4 cm

Average Customer Review: 5.0 out of 5 stars See all reviews (6 customer reviews)

Amazon.co.uk Sales Rank: 158,713 in Books (See Bestsellers in Books)
Popular in these categories:
#36 in Books > Science & Nature > Mathematics > Mathematical Theory > Number Theory
#87 in Books > Science & Nature > Mathematics > Algebra

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Product Description

This book gives an undergraduate-level introduction to Number Theory, with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) 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.

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We start with a number of fairly elementary results and techniques, mainly about greatest common divisors. Read the first page

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Customer Reviews

6 Reviews

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31 of 31 people found the following review helpful:

5.0 out of 5 stars A smooth introduction to number theory, 7 Sep 2001

By	Luis Loureiro "Locan" (Lund Sweden) - See all my reviews

This is a nice little book (290 pages), which can be used as course litterature for an introductory course in number theory or a by-side reading for somebody taking a first course. It's exposition is so pedagogical and clear that I could study the book from the beginning to the end on my own without help. This is pretty rare for a mathematical book. It covers not only the basic subjects likes divisibility, primes and congruences but more advanced subjects like Euler's functions, quadratic residues, Riemann zeta function as well. there is even a final chapter on Fermat's Last Theorem, which is quite accessible. I would not hesitate to recommend this book to anybody starting to study number theory. Finally it contains complete solutions to all exercises.

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26 of 26 people found the following review helpful:

5.0 out of 5 stars An excellent introduction to number theory, 19 Nov 2001

By	john_ellis50@hotmail.com (Derby, England) - See all my reviews

This is an excellent textbook. It is very clear and self-contained, making it possible to work through it without the need to refer elsewhere. I found that it was pitched at just the right level, challenging but not overwhelming, and a good mix of exercises, all with full solutions. The structure is very well thought out, so that it is always clear where arguments are heading. Probably the best maths textbook I've ever read; other authors please take note!

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14 of 14 people found the following review helpful:

5.0 out of 5 stars Superb introduction to number theory, 25 Jun 2003

By	S. Powell "Zteve" (Hursley, Hampshire UK) - See all my reviews (REAL NAME)

This book is one I would have liked to have read when I was an undergraduate. It is quite the best mix of 'old style' and 'new style' number theory that I have ever seen in a book. Compared to, say, Hardy and Wright's classic book it is much more accessible, and uses terminology and techniques that are now commonplace to modern (under)graduate readers to both simplify and demystify the subject. Then again, it covers less ground than H. and W., but as a starting point it succeeds admirably.

I came to this book just as I was myself trying to gather together everything I knew (or could redisover) about the Phi groups (the groups of units of the rings Z_n); this book did it all for me; and mostly in a way that delighted the mind. I was reluctant to read it (I prefer to try myself before 'cheating') but when I did I found all that I needed there: and authors sympathetic to my own viewpoint. What a delightful feeling of coming home.

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Most Recent Customer Reviews

5.0 out of 5 stars an investment in mathematical knowledge
Binding and printing quality

The paper on which its printed is of high quality and the binding is secure. Read more

Published 4 months ago by ab..c

5.0 out of 5 stars Number Theory from the roots up
Very helpfull book, I am having no lessons on number theory, yet the chapters I have been through I feel very confident with. Read more

Published 11 months ago by Mr. Daniel H. Johnson

5.0 out of 5 stars A smooth introduction to number theory
This is a nice little book (290 pages), which can be used as course litterature for an introductory course in number theory or a by-side reading for somebody taking a first... Read more

Published on 7 Sep 2001 by Luis Loureiro

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