A Course in Number Theory
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Product details:
- Edition number 2
- Publisher Clarendon Press
- Date of Publication 14 September 1995
- ISBN 9780198523765
- Binding Paperback
- No. of pages416 pages
- Size 234x156x23 mm
- Weight 625 g
- Language English
- Illustrations line figures, tables 0
Categories
Short description:
A new edition of this classic textbook, this book is the only publication which covers all the main areas of number theory, including up-to-date as well as established material. The increased use of computers in mathematics is reflected in the text, and each chapter ends with a collection of problems, with hints or sketch solutions provided at the end of the book together with useful tables.
MoreLong description:
This textbook covers with 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. Nine main areas of the subject are treated: (i) divisibility and multiplicative functions; (ii) congruences and quadratic residues; (iii) the basics of algebraic numbers and sums of squares; (iv) continued fractions, diophantine approximations and transcendence; (v) quadratic forms; (vi) partitions; (vii) the prime numbers; (viii) diophantine equations; and (ix) elliptic curves (this part has been considerably extended for this edition). 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 breifly 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.
It is of interest both to students and teachers working in this field.
Table of Contents:
Divisibility
Multiplicative Functions
Congruence Theory
Quadratic Residues
Algebraic Topics
Sums of Squares and Gauss Sums
Continued Fractions
Transcendental Numbers
Quadratic Forms
Genera and the Class Group
Partitions
The Prime Numbers
Two Major Theorems on the Primes
Diophantine Equations
Elliptic Curves: Basic Theory
Elliptic Curves: Further Results and Applications
Answers and Hints to Problems
Tables
Bibliography
Index to Notation
General Index
