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Elementary Number Theory, 7th 요약정보 및 구매

사용후기 0 개
지은이 David M. Burton
발행년도 2001-08-01
판수 7판
페이지 448
ISBN 9780071289191
도서상태 품절
판매가격 48,000원
포인트 0점
배송비결제 주문시 결제

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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.

    

  • Preface 

    New to this Edition 
    1 Preliminaries 
    1.1 Mathematical Induction 
    1.2 The Binomial Theorem 

    2 Divisibility Theory in the Integers 
    2.1 Early Number Theory 
    2.2 The Division Algorithm 
    2.3 The Greatest Common Divisor 
    2.4 The Euclidean Algorithm 
    2.5 The Diophantine Equation 

    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 Binary and Decimal Representations of Integers 
    4.4 Linear Congruences and the Chinese Remainder Theorem

    5 Fermat's Theorem 
    5.1 Pierre de Fermat 
    5.2 Fermat's Little Theorem and Pseudoprimes 
    5.3 Wilson's Theorem 
    5.4 The Fermat-Kraitchik Factorization Method 

    6 Number-Theoretic Functions 
    6.1 The Sum and Number of Divisors 
    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 

    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 Primitive 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 Introduction to Cryptography 
    10.1 From Caesar Cipher to Public Key Cryptography 
    10.2 The Knapsack Cryptosystem 
    10.3 An Application of Primitive Roots to Cryptography 

    11 Numbers of Special Form 
    11.1 Marin Mersenne 
    11.2 Perfect Numbers 
    11.3 Mersenne Primes and Amicable Numbers 
    11.4 Fermat Numbers 

    12 Certain Nonlinear Diophantine Equations 
    12.1 The Equation 
    12.2 Fermat's Last Theorem 

    13 Representation of Integers as Sums of Squares 
    13.1 Joseph Louis Lagrange 
    13.2 Sums of Two Squares 
    13.3 Sums of More Than Two Squares 

    14 Fibonacci Numbers 
    14.1 Fibonacci 
    14.2 The Fibonacci Sequence 
    14.3 Certain Identities Involving Fibonacci Numbers

    15 Continued Fractions 
    15.1 Srinivasa Ramanujan 
    15.2 Finite Continued Fractions 
    15.3 Infinite Continued Fractions 
    15.4 Farey Fractions 
    15.5 Pell's Equation 

    16 Some Recent Developments 
    16.1 Hardy, Dickson, and Erd�s 
    16.2 Primality Testing and Factorization 
    16.3 An Application to Factoring: Remote Coin Flipping 
    16.4 The Prime Number Theorem and Zeta Function Miscellaneous Problems 

    Appendixes 
    General References 
    Suggested Further Reading 

    Tables

  • David M. Burton

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