The Higher Arithmetic: An Introduction to the Theory of Numbers

by H. Davenport

Overview

The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers and number theory, and primality testing. Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.

Product Details

ISBN-13:	9781139636551
Publisher:	Cambridge University Press
Publication date:	10/23/2008
Sold by:	Barnes & Noble
Format:	eBook
File size:	6 MB

About the Author

Harold Davenport F.R.S. was the late Rouse Ball Professor of Mathematics at the University of Cambridge and Fellow of Trinity College.

Table of Contents

Introduction; 1. Factorization and the primes; 2. Congruences; 3. Quadratic residues; 4. Continued fractions; 5. Sums of squares; 6. Quadratic forms; 7. Some Diophantine equations; 8. Computers and number theory; Exercises; Hints; Answers; Bibliography; Index; Additional notes.

Editorial Reviews

This iteration updates the 1992 edition with a chapter on computers and number theory, generally considered to be the "purest" branch of pure mathematics. As with previous editions since 1962, this text introduces concepts and theorems to undergraduate students and general readers not necessarily immersed in higher arithmetic. Includes exercises with answer guides, and references in English and French. The late Davenport was a professor of mathematics at the U. of Cambridge. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

'Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer's opinion, is far superior for this purpose to any other book in English.' From a review of the first edition in Bulletin of the American Mathematical Society

'… the well-known and charming introduction to number theory … can be recommended both for independent study and as a reference text for a general mathematical audience.' European Maths Society Journal

'Its popularity is based on a very readable style of exposition.' EMS Newsletter

From the Publisher