- Series: Oxford Science Publications
- Paperback: 456 pages
- Publisher: Oxford University Press; 5 edition (April 17, 1980)
- Language: English
- ISBN-10: 0198531710
- ISBN-13: 978-0198531715
- Product Dimensions: 9.2 x 1 x 6.1 inches
- Shipping Weight: 1.4 pounds
- Average Customer Review: 4.7 out of 5 stars See all reviews (15 customer reviews)
- Amazon Best Sellers Rank: #1,482,638 in Books (See Top 100 in Books)
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An Introduction to the Theory of Numbers (Oxford Science Publications) 5th Edition
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Top customer reviews
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."
Gauss once said "Number theory is the queen of mathematics", and this book helps to show why. First published in 1938, it has been kept up over the years. If you are interested in number theory, this book is a MUST.
If you are very gifted and love prime numbers, I also recommend Prime Numbers by Carl Pomerance and Richard Crandall. Pomerance is one of the country's most talented prime number theorists. It is incredibly dense, but very deep.
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.
Most recent customer reviews
Learn from the master and true genius of number theory: G. H. Hardy.
of Number Theoretic ideas. However, it
failed to produce applications or clearcut
examples of the theorems.