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.
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||
 Sell Back Your Copy for $11.71
Whether you bought it on Amazon or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $11.71.
Used Price$19.84
Trade-in Price$11.71
Price after
Trade-in$8.13 |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $2 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Editorial Reviews
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
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
Most Helpful Customer Reviews
83 of 85 people found the following review helpful
Format:Paperback
I picked this up when I hit a small snag as I reviewed my undergraduate mathematics in order to return to graduate school for my master's in mathematics.
What started off as a small aside while reviewing another text (to recall some fundamentals, but in a rigorous way), turned into pure joy as I began a delightful excursion into "Elementary Number Theory," for its own sake, under the guidance of Jones & Jones.
Although many find Gallian and a host of others, Rudin included, to be the way to go, Jones & Jones [parallel to these authors] have a way of setting out proofs that appealed to me - for whatever that's worth.
ALL exercises have answers at the back, practically a sine qua non for all people who self-study and have to "grade" their own homework. The authors tie the relevance of the theories together without the sometimes heavy handed pop references to the Beatles, or to arcane things such as "yellow pigs." This is not to say the authors did not pay attention to the history and dates which they sprinkle in as they spin the development of the theories. Yet, they are always mindful of the mathematics which they teach and never get too cute.
It is the beauty of the number theory that is center stage, here, and like Zen, is achieved on the basis of its own elegant simplicity. But simplicity does not mean simple minded nor so brief that the authors lose the student. I felt in lock step with the authors page after page, proof after proof.
Perhaps I never understood Abstract Algebra quite well enough because I did not have as strong as grasp in elementary number theory as I should have had, but Jones & Jones certainly present the subject matter in a way that a somewhat rusty college grad could quickly sink her teeth into and enjoy. In short, this helped me close ground, but fast, while at the same time it opened my eyes to other proofs in other courses that I had committed to memory yet never full appreciated.
In any case this book was money VERY well spent and worth its modest price of admission.
51 of 53 people found the following review helpful
Format:Paperback
A few weeks ago I ordered three books about Number Theory, and this is the one I like most. I am not a beginner in maths, but I am a beginner in Number Theory. This book start with the basics, and it has exercises with answers! I think this is a good book for self-study, it is easier to read than the books from Leveque.
27 of 27 people found the following review helpful
Format:Paperback
Ever since my undergraduate days aeons ago, I have always had an aversion to any number theory, but Jones and Jones have changed my mind completely. In the last year, I came across a few articles that made me want to learn more about the topic, but wasn't sure where to start, as I wanted a book that had proofs that I could follow, and yet also gave me some motivation to dive into more complicated mathematics such as elliptic curves. Elementary Number Theory fit the bill perfectly and has served as a wonderful introduction to the subject that I could follow and enjoy.
This book is the perfect blend of text and formulae for me, and seems an excellent combination of rigour and looseness, always trying to keep a steady pace for the reader without bogging down in pedantic details that are irrelevant to any but the most fastidious of readers. At the same time, the authors also ensure that the reader gains an appreciation of actually proving theorems about numbers, instead of relying on mere intuition or hunches.
As mentioned by other reviews here, the authors have included complete solutions to all of the exercises, which are sprinkled throughout each chapter, as well as at the end of each chapter. This is a welcome change to so many math texts that have "exercises left to the reader," and has been a requirement for me when reading a text in an unfamiliar subject. The exercises are selected appropriately to the content of the chapters and I found them to be a welcome complement to the rest of the book.
In addition, the book discusses applications of number theory to cryptography in a very readable fashion, with any additional mathematics required for the book (in this case some simple group theory and analysis) in two appendices. A book on number theory would also be incomplete without at least a brief discussion of Andrew Wiles and Fermat's Last Theorem. Of course, Elementary Number Theory steps up to the plate appropriately and gives an overview of the history of the theorem and a (necessarily) thin overview of Wiles' proof.
I think, however, one of the best features of the book is that Jones and Jones have attempted to make the text very readable, in the sense that you could sit in a bath and enjoy part of a chapter without any trouble. I have always enjoyed reading mathematics without pen and paper handy, mainly because it improves my memory and visualization when working through problems, and this text helps greatly in that regard. They do not go for the obscure, and realize that the people who are reading this text are doing so for the first time (hence the title) and will not be overly impressed if the authors had chosen to blind us with their brilliance. The authors understand that we are mere mortals with busy lives, and appreciate a smoothly flowing textbook without having to stumble through unique and cryptic notation or a difficult proof without any explanation.
This book is the perfect blend of text and formulae for me, and seems an excellent combination of rigour and looseness, always trying to keep a steady pace for the reader without bogging down in pedantic details that are irrelevant to any but the most fastidious of readers. At the same time, the authors also ensure that the reader gains an appreciation of actually proving theorems about numbers, instead of relying on mere intuition or hunches.
As mentioned by other reviews here, the authors have included complete solutions to all of the exercises, which are sprinkled throughout each chapter, as well as at the end of each chapter. This is a welcome change to so many math texts that have "exercises left to the reader," and has been a requirement for me when reading a text in an unfamiliar subject. The exercises are selected appropriately to the content of the chapters and I found them to be a welcome complement to the rest of the book.
In addition, the book discusses applications of number theory to cryptography in a very readable fashion, with any additional mathematics required for the book (in this case some simple group theory and analysis) in two appendices. A book on number theory would also be incomplete without at least a brief discussion of Andrew Wiles and Fermat's Last Theorem. Of course, Elementary Number Theory steps up to the plate appropriately and gives an overview of the history of the theorem and a (necessarily) thin overview of Wiles' proof.
I think, however, one of the best features of the book is that Jones and Jones have attempted to make the text very readable, in the sense that you could sit in a bath and enjoy part of a chapter without any trouble. I have always enjoyed reading mathematics without pen and paper handy, mainly because it improves my memory and visualization when working through problems, and this text helps greatly in that regard. They do not go for the obscure, and realize that the people who are reading this text are doing so for the first time (hence the title) and will not be overly impressed if the authors had chosen to blind us with their brilliance. The authors understand that we are mere mortals with busy lives, and appreciate a smoothly flowing textbook without having to stumble through unique and cryptic notation or a difficult proof without any explanation.
Most Recent Customer Reviews
very good introduction to number theory
Some reviewers have said it assumes almost no previous knowledge, and that's not entirely true. If you are complete new to math in general that's not the book, it is better to use... Read more
Published 14 months ago by Al-Mahed
The knowledge I had expected, but too out of place, and does not help...
I originally bought this book to gain the knowledge and have an advantage in competing in Math Olympiads, but this book deters from that purpose. Read more
Published on March 12, 2010 by Litong Song
Probably the best maths book I've ever read
This is a great little book thats packed full of great number theory results. It is well written.
I'm a real fan of the SUMS books (I've bought 4 of the titles in the... Read more
I'm a real fan of the SUMS books (I've bought 4 of the titles in the... Read more
Published on November 16, 2009 by Pd Farleigh
Nice book with some flaws
"Elementary Number Theory" by Jones and Jones is a nice book, easily accessible to the average undergraduate math major. Read more
Published on April 21, 2009 by Robert Beeler
A Satisfactory Text for Elementary Number Theory
I've recently received my copy of Elementary Number Theory by Jones and Jones, and I'm (thus far) satisfied with the textbook. Read more
Published on April 19, 2009 by Joseph A. Schrock
An almost perfect square
That the book's almost square is easily gathered from the photo. That it's almost perfect must be verified by reading it. Read more
Published on February 6, 2009 by Itai
Very good beginning text
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. Read more
Published on October 5, 2008 by Luis Loureiro
Satisfied Customer
The book I ordered for a Christmas gift was received on time and was in perfect shape.
Published on January 17, 2008 by Karen Holt
I Hate Number Theory
I hate number theory. Number theory is like the cement on your driveway. Real and Complex analysis are the Porsche and Ferrari you drive home every night. Read more
Published on August 18, 2007 by Charles Saunders
If you are a beginner, this is the book
This book presumes so little of the reader that anyone can start learning number theory using this book. There are plenty of exercises and all of them have solutions. Read more
Published on January 9, 2007 by Seetharama Rao V. Durbha
Inside This Book
(learn more)
First Sentence:
We start with a number of fairly elementary results and techniques, mainly about greatest common divisors. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Elementary Number Theory, Euler's Theorem, Inversion Formula, Proof Let, Minkowski's Theorem, Fundamental Theorem of Arithmetic, Binomial Theorem, Fermat's Little Theorem, Gauss's Lemma, Lagrange's Theorem, Prime Number Theorem, Wilson's Theorem, Euclid's Elements, Fermat's Last Theorem, Inclusion-Exclusion Principle, Andrew Wiles, Proof Putting, Proof Suppose, Riemann Hypothesis, Taniyama-Shimura Conjecture New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We start with a number of fairly elementary results and techniques, mainly about greatest common divisors. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Elementary Number Theory, Euler's Theorem, Inversion Formula, Proof Let, Minkowski's Theorem, Fundamental Theorem of Arithmetic, Binomial Theorem, Fermat's Little Theorem, Gauss's Lemma, Lagrange's Theorem, Prime Number Theorem, Wilson's Theorem, Euclid's Elements, Fermat's Last Theorem, Inclusion-Exclusion Principle, Andrew Wiles, Proof Putting, Proof Suppose, Riemann Hypothesis, Taniyama-Shimura Conjecture New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 17
books:
See all 17 books this book cites
49
books
cite this book:
See all 49 books citing this book
- A Course in Arithmetic (Graduate Texts in Mathematics) by Jean Pierre Serre in Back Matter
- Primality and Cryptography (Wiley Teubner on Applicable Theory in Computer Science) by Evangelos Kranakis in Back Matter
- Vector Calculus by Paul C. Matthews in Front Matter
- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Back Matter
- Linear Algebra (Undergraduate Texts in Mathematics) by Larry Smith in Front Matter
See all 17 books this book cites
- Elementary Number Theory in Nine Chapters by James J. Tattersall in Back Matter (1), and Back Matter (2)
- Information and Coding Theory (Springer Undergraduate Mathematics Series) by Gareth A. Jones in Front Matter, and page 184
- A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) by Ian Anderson in Front Matter
- Real Analysis by John M. Howie in Front Matter
- Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series) by Marek Capinski in Front Matter
See all 49 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
