Synopses & Reviews
Ideal for undergraduate and graduate students in pure mathematics, this new text introduces the central, fundamental topics in number theory, including: divisibility and multiplicative functions; congruence and quadratic residues; continued fractions, diophantine approximation and transcendence; partitions; and diophantine equations and elliptic curves. In addition, some more advanced results are given, such as the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. Based on 20 years of teaching number theory, the approach is thoroughly classroom tested. Each chapter concludes with an extensive selection of sample problems, and an appendix contains hints, sketch solutions, and useful tables, making this the perfect self-contained tool for teaching and learning number theory.
Review
"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
Review
"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
Synopsis
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.
About the Author
Elizabeth Martin (MA) is Managing Editor of Market House Books Ltd.
Table of Contents
1. Divisibility
2. Multiplicative Functions
3. Congruence Theory
4. Quadratic Residues
5. Algebraic Topics
6. Sums of Squares and Gauss Sums
7. Continued Fractions
8. Transcendental Numbers
9. Quadratic Forms
10. Genera and the Class Group
11. Partitions
12. The Prime Numbers
13. Two Major Theorems on the Primes
14. Diophantine Equations
15. Elliptic Curves: Basic Theory
16. Elliptic Curves: Further Results and Applications