An Introduction to Number Theory / Edition 1

An Introduction to Number Theory / Edition 1

by G. Everest, Thomas Ward
     
 

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ISBN-10: 1849969590

ISBN-13: 9781849969598

Pub. Date: 11/19/2010

Publisher: Springer London

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.

In particular, the book shows how

Overview

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.

In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory.

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.

Product Details

ISBN-13:
9781849969598
Publisher:
Springer London
Publication date:
11/19/2010
Series:
Graduate Texts in Mathematics Series , #232
Edition description:
Softcover reprint of hardcover 1st ed. 2005
Pages:
297
Product dimensions:
9.21(w) x 6.14(h) x 0.65(d)

Related Subjects

Table of Contents

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.- References.- Index.

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