An Introduction to the Theory of Numbers (Paperback)

~ (Author), Edward M. Wright (Author), Andrew Wiles (Author), Roger Heath-Brown (Editor), Joseph Silverman (Editor)
Key Phrases: integral quaternions, highest common divisor, divisible byp, London Math, Acta Math, Number Theory (more...)

Editorial Reviews

Review

`Review from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable.' Nature

`This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory.' Mathematical Gazette

`...an important reference work... which is certain to continue its long and successful life...' Mathematical Reviews

`...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own.' Matyc Journal

Product Description

An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.
Updates include a chapter by J. H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.
The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.

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Product Details

• Paperback: 500 pages
• Publisher: Oxford University Press, USA; 6 edition (September 15, 2008)
• Language: English
• ISBN-10: 0199219869
• ISBN-13: 978-0199219865
• Product Dimensions: 9.1 x 6.1 x 1.5 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (13 customer reviews)
• Amazon.com Sales Rank: #62,315 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

65 of 66 people found the following review helpful:

5.0 out of 5 stars A classic introduction to a wide range of topics., September 1, 2001

By	Stuart-Little - See all my reviews

This review is from: An Introduction to the Theory of Numbers (Oxford Science Publications) (Paperback)

Every serious student of number theory should have this classic book on their shelf. Even though only "elementary" calculus and abstract algebra are used, a certain mathematical maturity is required. I feel the book is strongest in the area of elementary --not necessarily easy though -- analytic number theory (Hardy was a world class expert in analytic number theory). An elementary, but difficult proof of the Prime number Theorem using Selberg's Theorem is thoroughly covered in chapter 22.

While modern results in the area of algorithmic number theory are not presented nor is a systematic presentation of number theory given (it is not a textbook), it contains a flavor, inspiration and feel that is completely unique. It covers more disparate topics in number theory than any other n.t. book I know of. The fundamental results in classical, algebraic, additive, geometric, and analytic number theory are all covered. A beautifully written book.

Other recommended books on number theory in increasing order of difficulty:

1) Elementary Number Theory, By David Burton, Third Edition. Covers classical number theory. Suitable for an upper level undergraduate course. Primarily intended as a textbook for a one semester number theory course. No abstract algebra required for this book. Not a gem of a book like Davenport's The Higher Arithmetic, but a great book to seriously start learning number theory.

2) The Queen of Mathematics, by Jay Goldman. A historically motivated guide to number theory. A very clearly written book that covers number theory at a graduate or advanced undergraduate level. Covers much of the material in Gauss's Disquisitiones, but without all the detail. The book covers elementary number theory, binary quadratic forms, cyclotomy, Gaussian integers, quadratic fields, ideals, algebraic curves, rational points on elliptic curves, geometry of numbers, and introduces p-adic numbers. Only a slight bit of analytic number theory is covered. The best book in my opinion to start learning algebraic number theory. Wonderfully fills the otherwise troublesome gap between undergraduate and graduate level number theory.

Full of historical information hard to find elsewhere, very well researched. To cover all the material in this book would likely take two semesters, though most of the important material could be covered in one semester. Requires a background in abstract algebra (undergraduate level), and a little advanced calculus. Some complex analysis for sections 19.7 and 19.8 would be helpful, but not at all a requirement. The author recommends Harold Davenport's The Higher Arithmetic, as a companion volume for the first 12 chapters; according to Goldman it is a gem of a book.

3) Additive Number Theory, by Melvyn Nathanson. Graduate level text in additive number theory, covers the classical bases. This book is the first comprehensive treatment of the subject in 40 years. Some highlights: 1) Chen's theorem that every sufficiently large even integer is the sum of a prime and a number that is either prime or the product of two primes. 2) Brun's sieve for upper bound on the number of twin primes. 3) Vinogradov's simplification of the Hardy, Littlewood, and Ramanujan's circle method.

17 of 18 people found the following review helpful:

5.0 out of 5 stars THE BOOK on number theory---BUY IT!!!!, July 2, 2004

By A Customer

This review is from: An Introduction to the Theory of Numbers (Oxford Science Publications) (Paperback)

It was always claimed that of all the mathematicians who ever lived, Hardy was one of the greatest writers. This book certainly confirms that view. From the very beginning, one thinks, "Wow, this guy REALLY knows what he's talking about." Hardy was, in fact, one of the greatest number theorists of the twentieth century. Hardy gives actual intuitive motivation for almost all of the theorems in the book (intuition is often overlooked by mathematical authors who use the confusing traditional "theorem-proof" approach), and his proofs are elegant and easy to follow. Once, I spoke to the chair of the math department at a major University (Wash U. in St. Louis) and he told me that he reads Hardy and Wright at least once a year to refresh himself on the basics. I would recommend this book to anyone who is learning about number theory for the first time, and wishes to pursue the subject through self-study.

27 of 33 people found the following review helpful:

5.0 out of 5 stars Difficult at first but perfect in the end, July 21, 2000

By A Customer

This review is from: An Introduction to the Theory of Numbers (Oxford Science Publications) (Paperback)

My initial reaction through the first chapters was one of embarrassment at my lack of understanding. I could not believe a book, hailed by so many as a standard and essential resource, could be so much out of my reach. Then, amid the last page or so of chapter 1 I had an epiphany. The book, from that point on, was completely clear and logical while retaining an extraordinary amount of breadth in coverage.

Add my staunch support and recommendation to the long list of kudos that this book has accrued. There are, to my knowledge, no better books for the beginning student of number theory. If you have any interest whatsoever in the theory of numbers, this book is essential.