A Course in Number Theory

Paperback | March 1, 1995

byH. E. Rose

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The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with acollection of problems, and hints and sketch solutions are provided at the end of the book, together with useful tables.

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From Our Editors

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 un...

From the Publisher

The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with acollection of problems, and hints and sketch soluti...

H. E. Rose is at University of Bristol.

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Format:PaperbackDimensions:416 pages, 9.21 × 6.14 × 0.91 inPublished:March 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198523769

ISBN - 13:9780198523765

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Table of Contents

1. Divisibility2. Multiplicative Functions3. Congruence Theory4. Quadratic Residues5. Algebraic Topics6. Sums of Squares and Gauss Sums7. Continued Fractions8. Transcendental Numbers9. Quadratic Forms10. Genera and the Class Group11. Partitions12. The Prime Numbers13. Two Major Theorems on the Primes14. Diophantine Equations15. Elliptic Curves: Basic Theory16. Elliptic Curves: Further Results and ApplicationsAnswers and Hints to ProblemsTablesBibliographyIndex to NotationGeneral Index

From Our Editors

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.

Editorial Reviews

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