A Course in Number Theory - Hardcover

Rose, H. E.

Hardcover

ISBN 10: 0198532628 ISBN 13: 9780198532620

Publisher: Clarendon Press, 1988

Synopsis

This textbook deals with the central topics in number theory as taught in universities throughout the world. Number theory is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent subtheories and a long list of unsolved problems. Excluding topics which rely heavily on more advanced complex analysis and algebraic number theory this book considers eight central areas: divisibility and multiplicative functions; congruences and quadratic residues; an introduction to algebraic numbers and sums of squares; continued fractions, diophantine approximation and transducence; quadratic forms; partitions; the prime numbers; diophantine equations and elliptic curves. Some more advanced results are also given including the Gelfond-Schneider theorem, the prime number theorem and the Mordell-Weil theorem. Each chapter ends with a collection of problems; hints or sketch solutions are given at the back of the book together with various tables.

About this title

Review:

It is of interest both to students and teachers working in this field. (EMS Newsletter, No. 21, 1996)

An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory. (American Mathematical Monthly)

From the Back Cover:

This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.

About this edition

• Publisher: Clarendon Press
• Publication date: 1988
• ISBN 10: 0198532628
• ISBN 13: 9780198532620
• Binding: Hardcover
• Edition number: 1
• Number of pages: 364