An Introduction to Number Theory

2005
ISBN: 978-1-85233-917-3
Verlag: Springer

Buch, Englisch, Band 232, 297 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1370 g

Reihe: Graduate Texts in Mathematics

An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.

A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.

Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory.

Zielgruppe

Graduate

Autoren/Hrsg.

Ward, Thomas

Everest, G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

A Brief History of Prime.- Diophantine Equations.- Quadratic Diophantine Equations.- Recovering the Fundamental Theorem of Arithmetic.- Elliptic Curves.- Elliptic Functions.- Heights.- The Riemann Zeta Function.- The Functional Equation of the Riemann Zeta Function.- Primes in an Arithmetic Progression.- Converging Streams.- Computational Number Theory.