An Introduction to the Theory of Numbers (Oxford Science Publications) [Paperback]

G. H. Hardy (Author), E. M. Wright (Author)

Book Description

ISBN-10: 0198531710 | ISBN-13: 978-0198531715 | Publication Date: April 17, 1980 | Edition: 5

This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford, Cambridge, Aberdeen, and other universities. It is neither a systematic treatise on the theory of numbers nor a 'popular' book for non-mathematical readers. It contains short accounts of the elements of many different sides of the theory, not usually combined in a single volume; and, although it is written for mathematicians, the range of mathematical knowledge presupposed is not greater than that of an intelligent first-year student. In this edition, the main changes are in the notes at the end of each chapter. Sir Edward Wright seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present, both in the notes and in the text, a reasonably accurate account of the present state of knowledge.

Editorial Reviews

Review

"A really good book!"--Fernando Gouvea, Colby College

About the Author

Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number
theory, and in particular on its applications to prime numbers and to
Diophantine equations.
--This text refers to the Hardcover edition.

Product Details

• Paperback: 456 pages
• Publisher: Oxford University Press, USA; 5 edition (April 17, 1980)
• Language: English
• ISBN-10: 0198531710
• ISBN-13: 978-0198531715
• Product Dimensions: 9.1 x 5.9 x 0.9 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (16 customer reviews)
• Amazon Best Sellers Rank: #1,133,358 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

85 of 86 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
(VINE VOICE)   

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.

26 of 27 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.

32 of 39 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.