Elementary Number Theory (Springer Undergraduate Mathematics Series) - Softcover

Jones, Gareth A.; Jones, Josephine M.

Softcover

ISBN 10: 3540761977 ISBN 13: 9783540761976

Publisher: Springer, 1998

Synopsis

An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

About this title

Review:

From the reviews:

BULLETIN OF MATHEMATICS BOOKS

"?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."

 

G.A. Jones and J.M. Jones

Elementary Number Theory

"A welcome addition . . . a carefully and well-written book."―THE MATHEMATICAL GAZETTE

"This book would make an excellent text for an undergraduate course on number theory."

―MATHEMATICAL REVIEWS

Synopsis:

This book gives an undergraduate-level introduction to Number Theory, with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares; in particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

About this edition

• Publisher: Springer
• Publication date: 1998
• ISBN 10: 3540761977
• ISBN 13: 9783540761976
• Binding: Paperback
• Edition number: 1
• Number of pages: 316