Beginning Number Theory

ISBN-10: 0763737682

ISBN-13: 9780763737689

Edition: 2nd 2006 (Revised)

Authors: Neville Robbins

List price: $217.95
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The Essentials of Computer Organization and ArchitectureLinda Null, Pennsylvania State University, Julia Lobur, Pennsylvania State University The Essentials of Computer Organization and Architecture, Second Edition is not just for computer science majors. It would also be appropriate for anyone desiring an overview of computer organization and architecture, with an emphasis on the necessary foundation concepts. Another goal of this book is to serve as a resource for students and professionals interested in knowing how computers work and how they are designed, and ultimately in using these fundamental concepts to improve any computer-related project they might undertake. The Essentials of Computer Organization and Architecture, Second Edition is a textbook designed as the main text for a one-semester organization and architecture course for computer science majors typically taken in the their sophomore or junior year. Appropriate Courses --Computer Architecture-Computer Organization-Computer Organization & Architecture
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Book details

List price: $217.95
Edition: 2nd
Copyright year: 2006
Publisher: Jones & Bartlett Learning, LLC
Publication date: 12/29/2005
Binding: Hardcover
Pages: 338
Size: 7.25" wide x 9.25" long x 0.75" tall
Weight: 1.606
Language: English

Preface
About This Book
Features
Preliminaries
Introduction
Conjectures, Theorems, and Proofs
Well-Ordering and Induction
Well-Ordering Principle
Sigma Notation and Product Notation
Binomial Coefficients
Greatest Integer Function
Review Exercises
Divisibility
Introduction
Divisibility, Greatest Common Divisor, Euclid's Algorithm
Greatest Common Divisor via Euclid's Algorithm
Least Common Multiple
Representations of Integers
Decimal Representations of Integers
Binary Representations of Integers
Review Exercises
Primes
Introduction
Primes, Prime Counting Function, Prime Number Theorem
Test of Primality by Trial Division
Sieve of Eratosthenes, Canonical Factorization, Fundamental Theorem of Arithmetic
Sieve of Eratosthenes
Determining the Canonical Factorization of a Natural Number
Review Exercises
Congruences
Introduction
Congruences and Equivalence Relations
Equivalence Relations
Linear Congruences
Linear Diophantine Equations and the Chinese Remainder Theorem
Polynomial Congruences
Modular Arithmetic: Fermat's Theorem
Wilson's Theorem and Fermat Numbers
Pythagorean Equation
Review Exercises
Arithmetic Functions
Introduction
Sigma Function, Tau Function, Dirichlet Product
Dirichlet Inverse, Moebius Function, Euler's Function, Euler's Theorem
An Application to Algebra
Review Exercises
Primitive Roots and Indices
Introduction
Primitive Roots: Definition and Properties
Primitive Roots: Existence
Indices
Review Exercises
Quadratic Congruences
Introduction
Quadratic Residues and the Legendre Symbol
Gauss' Lemma and the Law of Quadratic Reciprocity
Solution of Quadratic Congruences
Algorithm for Solving Quadratic Congruences
Quadratic Congruences with Composite Moduli
Jacobi Symbol
Review Exercises
Sums of Squares
Introduction
Sums of Two Squares
Sums of Four Squares
Review Exercises
Continued Fractions
Introduction
Finite Continued Fractions
Infinite Continued Fractions
Approximation by Continued Fractions
Periodic Continued Fractions: I
Periodic Continued Fractions: II
Review Exercises
Nonlinear Diophantine Equations
Introduction
Fermat's Last Theorem
Pell's Equation: x[subscript 2] - Dy[subscript 2] = 1
Mordell's Equation: x[subscript 3] = y[subscript 2] + k
Review Exercises
Computational Number Theory
Introduction
Pseudoprimes and Carmichael Numbers
Miller's Test and Strong Pseudoprimes
Factoring: Fermat's Method and the Continued Fraction Method
Trial Division
Fermat's Method
Continued Fraction Method
Quadratic Sieve Method
Pollard p - 1 Method
Review Exercises
Cryptology
Introduction
Character Ciphers
Block Ciphers
One-Time Pads: Exponential Ciphers
Public-Key Cryptography
Signatures
Review Exercises
Some Open Questions in Elementary Number Theory
Tables
Answers to Selected Exercises
Bibliography
Index
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