Sunday 8 July 2012

Buy Elementary Number Theory: Book


Book Summary of Elementary Number Theory

Elementary Number Theory, Seventh Edition, is written for 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.

About the Author
David M. Burton University of New Hampshire

Table of Contents
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 Erdos
    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
    Answers to Selected Problems
    Index

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