Alan Baker

Comprehensive Course in Number Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy-Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 23. August 2012
• Englisch
• ISBN-13: 9781139558372
• Artikelnr.: 38278890

Autorenporträt

Alan K. Baker was born in Birmingham, UK in 1964. After graduating from the University of Reading in 1991, he endured a series of increasingly unpleasant jobs, culminating in a nine-month stint as a meat-packer in a Sheffield sausage factory, which served to increase his fascination with the macabre and outlandish. Since 1997, he has published a number of books on the paranormal and popular history, which have been translated into seven languages.

Inhaltsangabe

Preface
Introduction
1. Divisibility
2. Arithmetical functions
3. Congruences
4. Quadratic residues
5. Quadratic forms
6. Diophantine approximation
7. Quadratic fields
8. Diophantine equations
9. Factorization and primality testing
10. Number fields
11. Ideals
12. Units and ideal classes
13. Analytic number theory
14. On the zeros of the zeta-function
15. On the distribution of the primes
16. The sieve and circle methods
17. Elliptic curves
Bibliography
Index.

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Preface; Introduction; 1. Divisibility; 2. Arithmetical functions; 3. Congruences; 4. Quadratic residues; 5. Quadratic forms; 6. Diophantine approximation; 7. Quadratic fields; 8. Diophantine equations; 9. Factorization and primality testing; 10. Number fields; 11. Ideals; 12. Units and ideal classes; 13. Analytic number theory; 14. On the zeros of the zeta-function; 15. On the distribution of the primes; 16. The sieve and circle methods; 17. Elliptic curves; Bibliography; Index.

Rezensionen

'[Baker] ... possesses ... powerful gifts for precision and concision ... [the book] never seems rushed or artificially compressed. Highly recommended.' D. V. Feldman, Choice