Catalogue


Number theory with applications /
James A. Anderson, James M. Bell.
imprint
Upper Saddle River, N.J. : Prentice Hall, c1997.
description
ix, 566 p.
ISBN
0131901907 (alk. paper)
format(s)
Book
Holdings
Subjects
subject
More Details
imprint
Upper Saddle River, N.J. : Prentice Hall, c1997.
isbn
0131901907 (alk. paper)
catalogue key
764042
 
Includes bibliographical references.
A Look Inside
Full Text Reviews
Appeared in Choice on 1998-02:
This is not a traditional number theory text (such as those by Niven and Zuckermann or Rosen). Anderson and Bell suggest that it contains material appropriate for science majors, education majors, and mathematics majors. This is true, but instructors need to plan their courses carefully. There is a core of material presented and then several chapters on different topics that require only that core material. Besides the many applications, there are also exercises following each section, few in number but well chosen to illustrate the topics in the sections. The text itself is well written with many historical notes. As in most books designed for a diverse audience, there is always the question of how the book will compare with the specialized works designed for a more narrow audience (e.g., a number theory text aimed specifically at mathematics majors). A worthy book. Undergraduates. J. R. Burke; Gonzaga University
Reviews
This item was reviewed in:
Choice, February 1998
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Summaries
Unpaid Annotation
This book presents a self-contained logical development of basic number theory, supplemented with numerous applications and advanced topics. Focuses on the axiomatic development of number theory--showing how to prove theorems and understand the nature of number theory. Drawing applications from many areas--e.g., physics, statistics, computer science, mathematics, astronomy, cryptography, and mechanics, this book features extensive, detailed worked examples that illustrate many number theoretic patterns. Treats applications in depth with substantive discussion of the context of each application.
Main Description
This book presents a self-contained logical development of basic number theory, supplemented with numerous applications and advanced topics.Focuses on the axiomatic development of number theoryshowing how to prove theorems and understand the nature of number theory. Drawing applications from many arease.g., physics, statistics, computer science, mathematics, astronomy, cryptography, and mechanics, this book features extensive, detailed worked examples that illustrate many number theoretic patterns. Treats applications in depth with substantive discussion of the context of each application.
Table of Contents
SETS
Sets and Relations
Functions
Generalized Set Operations
Elementary Properties of Integers
Introduction
Axioms for the Integers
Principle of Induction
Division
Representation
Congruence
Application: Random Keys
Application: Random Number Generation I
Application: Two's Complement
Primes
Introduction
Prime Factorization
Distribution of the Primes
Elementary Algebraic Structures in Number Theory
Application: Pattern Matching
Application: Factoring by Pollard's r
Congruences And The Function
Introduction
Chinese Remainder Theorem
Matrices and Simultaneous Equations
Polynomials and Solutions of Polynomial Congruences
Properties of the Function f
The Order of an Integer
Primitive Roots
Indices
Quadratic Residues and the Law of Reciprocity
Jacobi Symbol
Application: Unit Orthogonal Matrices
Application: Random Number Generation II
Application: Hashing Functions
Application: Indices
Application: Cryptography
Application: Primality Testing
Arithmetic Functions
Introduction
Multiplicative Functions
The M"bius Function
Generalized M"bius Function
Application: Inversions in Physics
Continued Fractions
Introduction
Convergents
Simple Continued Fractions
Infinite Simple Continued Fractions
Pell's Equation
Application: Relative Rates
Application: Factoring
Bertrand's Postulate
Introduction
Preliminaries
Bertrand's Postulate
Diophantine Equations
Linear Diophantine Equations
Pythagorean triples
Integers as Sums of Two Squares
Quadratic Forms
Integers as Sums of Three Squares
Integers as Sums of Four Squares
The Equation ax2 + by2 + cz = 0
The Equation x4 + y4 = z
Logic And Proofs
Axiomatic Systems
Propositional Calculus
Arguments
Predicate Calculus
Mathematical Proofs
Peano's Postulates And Construction Of The Integers
Appendix C
Table of Contents provided by Publisher. All Rights Reserved.

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