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Elementary Number Theory with Applications

ISBN-10: 0123724872
ISBN-13: 9780123724878
Edition: 2nd 2007
Authors: Thomas Koshy
List price: $110.00
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Description: This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy  More...

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Book details

List price: $110.00
Edition: 2nd
Copyright year: 2007
Publisher: Elsevier Science & Technology Books
Publication date: 5/8/2007
Binding: Hardcover
Pages: 800
Size: 7.75" wide x 9.25" long x 1.50" tall
Weight: 3.498
Language: English

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

Preface
A Word to the Student
Fundamentals
Fundamental Properties
The Summation and Product Notations
Mathematical Induction
Recursion
The Binomial Theorem
Polygonal Numbers
Pyramidal Numbers
Catalan Numbers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Divisibility
The Division Algorithm
Base-b Representations (optional)
Operations in Nondecimal Bases (optional)
Number Patterns
Prime and Composite Numbers
Fibonacci and Lucas Numbers
Fermat Numbers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Greatest Common Divisors
Greatest Common Divisor
The Euclidean Algorithm
The Fundamental Theorem of Arithmetic
Least Common Multiple
Linear Diophantine Equations
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Congruences
Congruences
Linear Congruences
The Pollard Rho Factoring Method
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Congruence Applications
Divisibility Tests
Modular Designs
Check Digits
The p-Queens Puzzle (optional)
Round-Robin Tournaments (optional)
The Perpetual Calendar (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Systems of Linear Congruences
The Chinese Remainder Theorem
General Linear Systems (optional)
2 x 2 Linear Systems (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Three Classical Milestones
Wilson's Theorem
Fermat's Little Theorem
Pseudoprimes (optional)
Euler's Theorem
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Multiplicative Functions
Euler's Phi Function Revisited
The Tau and Sigma Functions
Perfect Numbers
Mersenne Primes
The Mobius Function (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Cryptology
Affine Ciphers
Hill Ciphers
Exponentiation Ciphers
The RSA Cryptosystem
Knapsack Ciphers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Primitive Roots and Indices
The Order of a Positive Integer
Primality Tests
Primitive Roots for Primes
Composites with Primitive Roots (optional)
The Algebra of Indices
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Quadratic Congruences
Quadratic Residues
The Legendre Symbol
Quadratic Reciprocity
The Jacobi Symbol
Quadratic Congruences with Composite Moduli (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Continued Fractions
Finite Continued Fractions
Infinite Continued Fractions
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Miscellaneous Nonlinear Diophantine Equations
Pythagorean Triangles
Fermat's Last Theorem
Sums of Squares
Pell's Equation
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Appendix
Proof Methods
Web Sites
Tables
Factor Table
Values of Some Arithmetic Functions
Least Primitive Roots r Modulo Primes p
Indices
References
Solutions to Odd-Numbered Exercises
Fundamentals
Divisibility
Greatest Common Divisors
Congruences
Congruence Applications
Systems of Linear Congruences
Three Classical Milestones
Multiplicative Functions
Cryptology
Primitive Roots and Indices
Quadratic Congruences
Continued Fractions
Miscellaneous Nonlinear Diophantine Equations
Credits
Index

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