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This title in other editions

Elements of Number Theory (Undergraduate Texts in Mathematics)

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Elements of Number Theory (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

 This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals. The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer-Verlag, including Mathematics and Its History (Second Edition 2001), Numbers and Geometry (1997) and Elements of Algebra (1994).

Synopsis:

Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Synopsis:

Includes bibliographical references (p. 239-244) and index.

Table of Contents

* Preface * Natural numbers and integers * The Euclidean algorithm * Congruence arithmetic * The RSA cryptosystem * The Pell equation * The Gaussian Integers * Quadratic integers * The four square theorem * Quadratic reciprocity * Rings * Ideals * Prime ideals * Bibliography * Index

Product Details

ISBN:
9780387955872
Author:
Stillwell, J.
Publisher:
Springer
Author:
Stillwell, John
Location:
New York
Subject:
Number Theory
Subject:
Mathematics-Number Theory
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Undergraduate texts in mathematics
Series Volume:
no. 36
Publication Date:
December 2002
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
266
Dimensions:
235 x 155 mm 1240 gr

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Related Subjects


Science and Mathematics » Materials Science » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory
Science and Mathematics » Mathematics » Topology

Elements of Number Theory (Undergraduate Texts in Mathematics) New Hardcover
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$67.25 In Stock
Product details 266 pages Springer - English 9780387955872 Reviews:
"Synopsis" by , Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
"Synopsis" by , Includes bibliographical references (p. 239-244) and index.
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