Elementary Number Theory
(Sprache: Englisch)
Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical...
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Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
Inhaltsverzeichnis zu „Elementary Number Theory “
<h1> Elementary Number Theory, 7e, by David M. Burton </h1><h1> Table of Contents </h1><h2> Preface </h2><h2> New to this Edition </h2><h2> 1Preliminaries </h2><h4> 1.1Mathematical Induction </h4><h4> 1.2The Binomial Theorem </h4><h2> 2Divisibility Theory in the Integers </h2><h4> 2.1Early Number Theory </h4><h4> 2.2The Division Algorithm </h4><h4> 2.3The Greatest Common Divisor </h4><h4> 2.4The Euclidean Algorithm </h4><h4> 2.5The Diophantine Equation </h4> <h2> 3Primes and Their Distribution </h2><h4> 3.1The Fundamental Theorem of Arithmetic </h4><h4> 3.2The Sieve of Eratosthenes </h4><h4> 3.3The Goldbach Conjecture </h4><h2> 4The Theory of Congruences </h2><h4> 4.1Carl Friedrich Gauss </h4><h4> 4.2Basic Properties of Congruence </h4><h4> 4.3Binary and Decimal Representations of Integers </h4><h4> 4.4Linear Congruences and the Chinese Remainder Theorem </h4><h2> 5Fermat's Theorem </h2><h4> 5.1Pierre de Fermat </h4><h4> 5.2Fermat's Little Theorem and Pseudoprimes </h4><h4> 5.3Wilson's Theorem </h4><h4> 5.4The Fermat-Kraitchik Factorization Method </h4><h2> 6Number-Theoretic Functions </h2><h4> 6.1The Sum and Number of Divisors </h4><h4> 6.2 The Möbius Inversion Formula </h4><h4> 6.3The Greatest Integer Function </h4><h4> 6.4An Application to the Calendar </h4><h2> 7Euler's Generalization of Fermat's Theorem </h2><h4> 7.1Leonhard Euler </h4><h4> 7.2Euler's Phi-Function </h4><h4> 7.3Euler's Theorem </h4><h4> 7.4Some Properties of the Phi-Function </h4><h2> 8Primitive Roots and Indices </h2><h4> 8.1The Order
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of an Integer Modulo n </h4><h4> 8.2Primitive Roots for Primes </h4><h4> 8.3Composite Numbers Having Primitive Roots </h4><h4> 8.4The Theory of Indices </h4><h2> 9The Quadratic Reciprocity Law </h2><h4> 9.1Euler's Criterion </h4><h4> 9.2The Legendre Symbol and Its Properties </h4><h4> 9.3Quadratic Reciprocity </h4><h4> 9.4Quadratic Congruences with Composite Moduli </h4><h2> 10Introduction to Cryptography </h2><h4> 10.1From Caesar Cipher to Public Key Cryptography </h4><h4> 10.2The Knapsack Cryptosystem </h4><h4> 10.3An Application of Primitive Roots to Cryptography </h4><h2> 11Numbers of Special Form </h2><h4> 11.1Marin Mersenne </h4><h4> 11.2Perfect Numbers </h4><h4> 11.3Mersenne Primes and Amicable Numbers </h4><h4> 11.4Fermat Numbers </h4><h2> 12Certain Nonlinear Diophantine Equations </h2><h4> 12.1The Equation </h4><h4> 12.2Fermat's Last Theorem </h4><h2> 13Representation of Integers as Sums of Squares </h2><h4> 13.1Joseph Louis Lagrange </h4><h4> 13.2Sums of Two Squares </h4><h4> 13.3Sums of More Than Two Squares </h4><h2> 14Fibonacci Numbers </h2><h4> 14.1Fibonacci </h4><h4> 14.2The Fibonacci Sequence </h4><h4> 14.3Certain Identities Involving Fibonacci Numbers </h4><h2> 15Continued Fractions </h2><h4> 15.1Srinivasa Ramanujan </h4><h4> 15.2Finite Continued Fractions </h4><h4> 15.3Infinite Continued Fractions </h4><h4> 15.4Farey Fractions </h4><h4> 15.5Pell's Equation </h4><h2> 16Some Recent Developments </h2><h4> 16.1Hardy, Dickson, and Erdös </h4><h4> 16.2Primality Testing and Factorization </h4><h4> 16.3An Application to Factoring: Remote Coin Flipping </h4><h4> 16.4The Prime Number Theorem and Zeta Function </h4><h2> Miscellaneous Problems </h2><h2> Appendixes </h2><h2> General References </h2><h2> Suggested Further Reading </h2><h2> Tables </h2><h2> Answers to Selected Problems </h2><h2> Index </h2>
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Bibliographische Angaben
- Autor: David Burton
- 2010, Maße: 16,5 x 23,6 cm, Kartoniert (TB), Englisch
- Verlag: McGraw-Hill Higher Education
- ISBN-10: 0071289194
- ISBN-13: 9780071289191
Sprache:
Englisch
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