Description: About this productProduct InformationThis text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester, undergraduate number theory course taken primarily by mathematics majors and students preparing to be secondary school teachers. Although the text was written with this readership in mind, very few formal prerequisites are required. Much of the text can be read by students with a sound background in high school mathematics.Product IdentifiersPublisherMcGraw-Hill Higher EducationISBN-100072325690ISBN-139780072325690eBay Product ID (ePID)1871075Product Key FeaturesFormatHardcoverPublication Year2001LanguageEnglishDimensionsWeight25.1 OzWidth6.6in.Height0.8in.Length9.5in.Additional Product FeaturesDewey Edition22Table of Content1 Some Preliminary Considerations 1.1 Mathematical Induction 1.2 The Binomial Theorem 1.3 Early Number Theory 2 Divisibility Theory in the Integers 2.1 The Division Algorithm 2.2 The Greatest Common Divisor 2.3 The Euclidean Algorithm 2.4 The Diophantine Equation ax+by=c 3 Primes and Their Distribution 3.1 The Fundamental Theorem of Arithmetic 3.2 The Sieve of Eratosthenes 3.3 The Goldbach Conjecture 4 The Theory of Congruences 4.1 Carl Friedrich Gauss 4.2 Basic Properties of Congruence 4.3 Special Divisibility Tests 4.4 Linear Congruences 5 Fermat's Theorem 5.1 Pierre de Fermat 5.2 Fermat's Factorization Method 5.3 The Little Theorem 5.4 Wilson's Theorem 6 Number-Theoretic Functions 6.1 The Functions ƒä and ƒã 6.2 The Mobius Inversion Formula 6.3 The Greatest Integer Function 6.4 An Application to the Calendar 7 Euler's Generalization of Fermat's Theorem 7.1 Leonhard Euler 7.2 Euler's Phi-Function 7.3 Euler's Theorem 7.4 Some Properties of the Phi-Function 7.5 An Application to Cryptography 8 Primitive Roots and Indices 8.1 The Order of an Integer Modulo n 8.2 Primitive Roots for Primes 8.3 Composite Numbers Having Prime Roots 8.4 The Theory of Indices 9 The Quadratic Reciprocity Law 9.1 Euler's Criterion 9.2 The Legendre Symbol and Its Properties 9.3 Quadratic Reciprocity 9.4 Quadratic Congruences with Composite Moduli 10 Perfect Numbers 10.1 The Search for Perfect Numbers 10.2 Mersenne Primes 10.3 Fermat Numbers 11 The Fermat Conjecture 11.1 Pythagorean Triples 11.2 The Famous ¡§Last Theorem¡¨ 12 Representation of Integers as Sums of Squares 12.1 Joseph Louis Lagrange 12.2 Sums of Two Squares 12.3 Sums of More than Two Squares 13 Fibonacci Numbers 13.1 The Fibonacci Sequence 13.2 Certain Identities Involving Fibonacci Numbers 14 Continued Fractions 14.1 Srinivasa Ramanujan 14.2 Finite Continued Fractions 14.3 Infinite Continued Fractions 14.4 Pell's Equation 15 Some Twentieth-Century Developments 15.1 Hardy, Dickson, and Erdos 15.2 Primality Testing and Factorization 15.3 An Application to Factoring: Remote Coin-Flipping 15.4 The Prime Number TheoremIllustratedYesDewey Decimal512.7Target AudienceCollege AudienceSeriesInternational Series in Pure and Applied MathematicsCopyright Date2002AuthorDavid M. BurtonEdition Number5Edition DescriptionRevised EditionLc Classification NumberQa241.B83 2002Lccn2001-030785
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Number of Pages: 432 Pages
Publication Name: Elementary Number Theory
Language: English
Publisher: McGraw-Hill Higher Education
Subject: Number Theory
Item Height: 0.8 in
Publication Year: 2001
Features: Revised
Item Weight: 25.1 Oz
Type: Textbook
Author: David M. Burton
Subject Area: Mathematics
Item Length: 9.5 in
Item Width: 6.6 in
Series: International Series in Pure and Applied Mathematics
Format: Hardcover
