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An introduction to number theory

Author: Graham Everest; Thomas Ward
Publisher: New York ; London : Springer, 2005.
Series: Graduate texts in mathematics, 232.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Everest, Graham, 1957-
Introduction to number theory.
New York ; London : Springer, 2005
(OCoLC)60666920
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Graham Everest; Thomas Ward
ISBN: 9781846280443 1846280443
OCLC Number: 262680590
Description: 1 online resource (224 pages) : illustrations.
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.
Series Title: Graduate texts in mathematics, 232.
Responsibility: Graham Everest, Thomas Ward.

Abstract:

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 be introduced to some of the main themes in number theory.

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