A Course in Number Theory / Edition 2

by H. E. Rose

Overview

Perfect for students approaching the subject for the first time, this book offers a superb overview of number theory. Now in its second edition, it has been thoroughly updated to feature up-to-the-minute treatments of key research, such as the most recent work on Fermat's coast theorem. Topics include divisibility and multiplicative functions, congruences and quadratic resolves, the basics of algebraic numbers and sums of squares, continued fractions, diophantine approximations and transcendence, quadratic forms, partitions, the prime numbers, diophantine equations, and elliptic curves. More advanced subjects such as the Gelfond-Schneider, prime number, and Mordell-Weil theorems are included as well. Each chapter contains numerous problems and solutions.

Product Details

ISBN-13:	9780198523765
Publisher:	Oxford University Press
Publication date:	12/14/1995
Series:	Oxford Science Publications Series
Edition description:	REV
Pages:	416
Product dimensions:	9.21(w) x 6.17(h) x 0.94(d)

About the Author

University of Bristol

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 Applications

Editorial Reviews

"This excellent book on number theory is detailed and readable. If the appropriate chapters are selected, it is suitable for upper-undergraduate and graduate levels..... The book contains excellent problems, a bibliography, and many references to computer applications. Rose's second edition can serve as a good textbook or a fine reference book and can be used for independent study by anyone interested in learning number theory." —The Mathematics Teacher

"The book nicely presented central areas of numbers theory".—Dr. Jurgen Hurrelbrink, Louisiana State University—Baton Rouge

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

"The author shows an impeccable taste in his choice of topics and gives a lot of historical discussion, making this book a pleasant one to browse, and a great text on which to base a first undergraduate number theory course . . . . It should give students a tantalizing glimpse into a beautiful area of number theory, and inspire them to further explore the subject."—Mathematical Reviews

From the Publisher