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An Introduction to the Theory of Numbers [Paperback]

G. H. Hardy (Author), Edward M. Wright (Author), Andrew Wiles (Author), Roger Heath-Brown (Editor), Joseph Silverman (Editor)
4.5 out of 5 stars  See all reviews (17 customer reviews) |
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Book Description

Publication Date: September 15, 2008 | ISBN-10: 0199219869 | ISBN-13: 978-0199219865 | Edition: 6
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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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

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.

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 1.4 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #27,061 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
86 of 87 people found the following review helpful
Format: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.
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27 of 29 people found the following review helpful
By A Customer
Format: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.
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32 of 39 people found the following review helpful
By A Customer
Format: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.

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Most Recent Customer Reviews
AMAZING
This book is so amazing. It was written by a world class pure mathematician who also wrote "A Course in Pure Mathematics". Read more
Published 2 months ago by PersonReviewing
New improved edition of a classic
I have owned the 4th edition for years. You might think that Hardy and Wright is dated and can't possibly be relevant, but check the data. Read more
Published 18 months ago by hot4hypatia
There is no such thing as 'number theory'!
I'm not as impressed as the other reviewers here with this book, despite it's being in some sense a 'classic'. Read more
Published 21 months ago by Rerevisionist
Easy read
This book provides a gentle presentation to many subfields of number theory: including analytic, algebraic, and elementary. It discusses generating functions in everyday language. Read more
Published 24 months ago by physics jock
awesome book on number theory
I am an undergrad student in computer engineering. I bought this book after I looked at the table of contents and found some topics which I interested in. Read more
Published on April 18, 2010 by Sida Wang
Number Theory
The book was an excellent accumulation
of Number Theoretic ideas. However, it
failed to produce applications or clearcut
examples of the theorems.
Published on March 24, 2009 by Norman Morton
A Mathematical Classic Reviewed
Even though I have only read a small portion of this book, I can already tell that it deserves its "classic" label. Read more
Published on February 2, 2009 by Martin R. Christensen
Syntax and lack of background
I have yet to write a review on any of the textbooks that I have purchased from amazon, but I felt the need to give my insight into this book. Read more
Published on December 15, 2008 by Dylan D'silva
a milestone and a shining star in elementary number theory
it is surprising to find that so few people have anything to say about this book; Hardy was a giant among mathematicians and at last this book is translated in french... Read more
Published on March 7, 2008 by Gilles Benson
Nice intro to number theory
This is an unusual number theory book in that it covers topics of interest to the authors which are not often found in the "standard" introductory treatment. Read more
Published on March 12, 2007 by G. Cantor
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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integral quaternions, highest common divisor, divisible byp, odd convergents, having rational coefficients, rational cubes, arithmetical functions, consecutive convergents, special integers, fundamental parallelogram, congruent number, quadratic fields, complete quotient, rational integers, unique factorization property, simple continued fraction, fundamental lattice, rational primes, integral polynomial, integral coordinates, different prime factors, squared factor, elliptic curves
Key Phrases - Capitalized Phrases (CAPs): (learn more)
London Math, Acta Math, Number Theory, American Math, New York, Niedere Zahlentheorie, Reine Angew, Quarterly Journal of Math, Prime Number Theorem, Bulletin Amer, Dirichlet's Theorem, Göttinger Nachrichten, Acta Arith, The Möbius, Dickson's History, Gesammelte Abhandlungen, Ramanujan's Collected, Cambridge Phil, Indian Math, The L-series, Edinburgh Math, North Holland
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