An Introduction to the Theory of Numbers | 
 enlarge | Authors: G. H. Hardy, Edward M. Wright, Andrew Wiles
Creators: Roger Heath-brown, Joseph Silverman
Publisher: Oxford University Press, USA
Category: Book
List Price: $60.00
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Rating:  9 reviews
Sales Rank: 398332
Media: Paperback
Edition: 6
Pages: 500
Number Of Items: 1
Shipping Weight (lbs): 2.2
Dimensions (in): 9.1 x 6.1 x 1.5
ISBN: 0199219869
Dewey Decimal Number: 512
EAN: 9780199219865
Publication Date: September 15, 2008 (In 7 Days)
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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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| Customer Reviews: Read 4 more reviews...
A classic introduction to a wide range of topics. September 2, 2001
Stuart-Little
59 out of 59 found this review helpful
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.
One of the greatest January 10, 2005
Alexandru Mitroi (Fullerton, CA United States)
30 out of 39 found this review helpful
First of all, let me say this about the one star review. Do not let yourself be infuenced by lesser mathematicians. Idiots in my opinion. To give this book one star, you must posses some special kind of mediocracy. Keep your stupidity to yourself Lucas.
No one writes like this anymore. Mathematicians like Hardy have passed. The subject has ballooned, and now you have to specialize within Number Theory. There are fewer and fewer that can posses knowledge of the entire subject of Number Theory. Remember what Harold M. Edwards said. You have to read the classics, and beware of secondary sources. Authors give their own spin on ideas. And who is to say they have a greater or lesser understanding of the subject. Furthermore, who can determine how well can they express themselves. How many mathematicians our days bother to study grammar and literature? The best example is Gauss' Disquisitiones Arithmeticae. Would you rather read a book written by Gauss himself, the man that established the subject? Or by some one who learned what some one learned what some one learned over a period of 200 years? Also know what Axler, author of Linear Algebra Done Right, said about reading mathematics books. For a mathematics book, if you spend less than half an hour per page you are going too fast. The last thing i will say is again attributed to Edwards. In his book on Advanced Calculus he encourages the reader to jump chapters. A book does not have to, and sometimes it should not, be read in order. It may take some practice to see how you need to jump around, but you will find that you can maximize your reading by doing so.
There are several point in which this book excels. First, in the writing style. Second, in how many ideas it introduces. Or how good an understanding the reader obtains of Number Theory. It is invaluable to have the big picture. Third, the author has in mind the future material the reader will encounter. He knows you will go beyond this book, and prepares you for what is to come. You do not enter higher courses blind.
The writting style is representative of that of Wiles and Loiville. It will show you how your mathematical writting should be. It takes a lot of practice to learn mathematical formalism and how to write proofs. This is the book to learn from. The author is not afraid to connect the ideas you are learning to other advanced ideas and to mathematical history, unlike present day authors. If you plan to be a mathematician, you must know its history. The writting is in a mathematical sense superfluos. It does not assume you are a genius, but strikes balance between what you should know and what you should be told.
The book is successful in providing you with the big picture, and how ideas you are learning reflect one ideas you will learn or have already learned. Having a big picture of the subject, which he describes in the second chapter, lets you know what you are learning now and puts the entire material in context. Gives you great perspective of the subject. Because a great deal of branches of number theory are discussed, you are not only better equiped to choose which branch might interest you, but it eases the transition to more advanced courses, such as Analytical Number Theory.
The author from the start discusses unanswered questions in Number Theory. I know alot of professors which think that the student should not be exposed to questions that surpass his mathematical knowledge. They are the weak mathematicians. Mathematics is about exploring and breaking limits. You should know what is beyond your reach, and the reach of every one else. The questions that still stand might be answered by some one that was intrigued by the challenge of answering them when they are helpless to do so. Fermat's Last Thorem is such an example. The guy learned it at the age of 10.
The last thing i will say about the book is this. Number theory has one scope. Namely, prime numbers. This book make it clear that the purpose of number theory is to determine the properties of numbers. It discusses the limitations of mathematics in attaining answers to Riemann Hypothesis, Fundamental theorem, trancedental and irrational and algebraic numbers, and so on. The book is, in my opinion, an expansion of the section on unanswered questions. And in doing so many more questions are asked and analyzed. There are prime numbers, and nothing else.
Nice intro to number theory March 13, 2007
G. Cantor (Mill Valley, CA USA)
3 out of 3 found this review helpful
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. My only mild complaints are: no subject index and some ambiguous and unusual notation here and there.
I agree that this book should be in the library of anyone serious about the topic, however, if you are beginning your study of number theory from scratch there are other books that may provide a better start. I would recommend Joe Roberts "Elementary Number Theory: A Problem Oriented Approach" and/or "An Introduction to the Theory of Numbers" by Niven, Zuckerman, and Montgomery.
Roberts offers a wide spectrum of problems, with detailed solutions, written along the lines of Polya & Szego's "Problems and Theorems in Analysis I & II". Nivens book is a solid traditional introduction.
It is fun to read Hardy and Wright though, it exhibits a style that is sadly missing today.
I have to say in closing that it would be good to ignore some of the previous reviews, specifically ones making reference to "idiots". They're unproductive, miss the point of reviewing, and exhibit a level of ignorance which Mark Twain identified years ago: "It is better to keep your mouth shut and appear stupid than to open it and remove all doubt."
Difficult at first but perfect in the end July 21, 2000
26 out of 30 found this review helpful
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.
The Classic Text November 22, 1998
josh.mullet@oberlin.edu (Oberlin, OH, USA)
20 out of 30 found this review helpful
Chances are, you already know of this work. It seems indeed superfluous to review it. But this book is the most amazing and revealing text in elementary number theory. You must purchase it. It is used by experts, yet accessible to any bright calculus student. If you have any interst in mathmematics, buy this book!!! For god's sake, don't deny yourself the classics!! Would you deny yourself Hamlet!?? Anna Karenina!!?? Moby Dick!!??
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