A Course in Number Theory

Rose (Autor)

Buch | Softcover

416 Seiten

1995 | 2nd Revised edition
Clarendon Press (Verlag)
978-0-19-852376-5 (ISBN)

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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.

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.

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

Erscheint lt. Verlag	14.9.1995
Zusatzinfo	line figures, tables
Verlagsort	Oxford
Sprache	englisch
Maße	156 x 234 mm
Gewicht	625 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	0-19-852376-9 / 0198523769
ISBN-13	978-0-19-852376-5 / 9780198523765
Zustand	Neuware