A Course in Number Theory (Oxford Science Publications) - Brossura

Rose, H. E.

Brossura

ISBN 10: 0198523769 ISBN 13: 9780198523765

Casa editrice: Oxford University Press, 1998

Riassunto

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.

Su questo libro

Recensione

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

Contenuti

• 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
• Answers and Hints to Problems
• Tables
• Bibliography
• Index to Notation
• General Index

Dettagli dell?edizione

• Editore: Oxford University Press
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0198523769
• ISBN 13: 9780198523765
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 416
• Contatto del produttore: non disponibile