An Introduction to the Theory of Numbers

by Edward Reynolds Wright, Edward M. Wright, E.M. Wright, et al.

Book Overview

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...

• Format: Paperback
• Language: English
• ISBN: 0199219869
• ISBN13: 9780199219865
• Release Date: August 2009
• Publisher: Oxford University Press
• Length: 656 Pages
• Weight: 2.15 lbs.
• Dimensions: 1.4" x 6.1" x 9.1"

Customer Reviews

Superb Introduction for the Mathematical Sophisticate

This classic deserves its reputation but be warned that it is not an introduction for mathematical neophytes. The authors take detours (which sometimes are looks ahead) from the main path of development that the sophisticate will enjoy but the novice may not be able to recognize as detours. Examples are the geometry of numbers (introduced in chapter 3), the Farey dissection of the continuum, and trigonometric sums. The authors also present deeper material than is usually considered an introduction. Their presentations are excellent but require sophistication for the following topics among others: quadratic fields, generating functions of arithmetical functions, Selberg's proof of the Prime Number Theorem, and Kronecker's theorem. This is a book to buy and keep provided you have the necessary mathematical sophistication. Final note: this book nicely complements Apostol's Introduction to Analytic Number Theory.

THE BOOK on number theory---BUY IT!!!!

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.

A classic introduction to a wide range of topics.

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 s

Difficult at first but perfect in the end

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.

Definitely the place to start number theory.

This is the perfect book for learning number theory. Don't let the title fool you, though: this book will last you a long time in your study. After completing this book, you'll have a firm grasp on number theory from the basics to some of the finer details.