Elementary Number Theory with Applications 2nd Edition by Koshy, Thomas – Ebook PDF Instant Download/Delivery: 0123724872,9780123724878
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ISBN 10: 0123724872
ISBN 13: 9780123724878
Author: Koshy, Thomas
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
Elementary Number Theory with Applications 2nd Table of contents:
Chapter 1. Fundamentals
1.1 Fundamental Properties
1.2 The Summation and Product Notations
1.3 Mathematical Induction
1.4 Recursion
1.5 The Binomial Theorem
1.6 Polygonal Numbers
1.7 Pyramidal Numbers
1.8 Catalan Numbers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 2. Divisibility
2.1 The Division Algorithm
*2.2 Base-b Representations (optional)
*2.3 Operations in Nondecimal Bases (optional)
2.4 Number Patterns
2.5 Prime and Composite Numbers
2.6 Fibonacci and Lucas Numbers
2.7 Fermat Numbers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 3. Greatest Common Divisors
3.1 Greatest Common Divisor
3.2 The Euclidean Algorithm
3.3 The Fundamental Theorem of Arithmetic
3.4 Least Common Multiple
3.5 Linear Diophantine Equations
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 4. Congruences
4.1 Congruences
4.2 Linear Congruences
4.3 The Pollard Rho Factoring Method
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 5. Congruence Applications
5.1 Divisibility Tests
5.2 Modular Designs
5.3 Check Digits
*5.4 The p-Queens Puzzle (optional)
*5.5 Round-Robin Tournaments (optional)
*5.6 The Perpetual Calendar (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 6. Systems of Linear Congruences
6.1 The Chinese Remainder Theorem
*6.2 General Linear Systems (optional)
*6.3 2×2 Linear Systems (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 7. Three Classical Milestones
7.1 Wilson’s Theorem
7.2 Fermat’s Little Theorem
*7.3 Pseudoprimes (optional)
7.4 Euler’s Theorem
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 8. Multiplicative Functions
8.1 Euler’s Phi Function Revisited
8.2 The Tau and Sigma Functions
8.3 Perfect Numbers
8.4 Mersenne Primes
*8.5 The Möbius Function (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 9. Cryptology
9.1 Affine Ciphers
9.2 Hill Ciphers
9.3 Exponentiation Ciphers
9.4 The RSA Cryptosystem
9.5 Knapsack Ciphers
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 10. Primitive Roots and Indices
10.1 The Order of a Positive Integer
10.2 Primality Tests
10.3 Primitive Roots for Primes
*10.4 Composites with Primitive Roots (optional)
10.5 The Algebra of Indices
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 11. Quadratic Congruences
11.1 Quadratic Residues
11.2 The Legendre Symbol
11.3 Quadratic Reciprocity
11.4 The Jacobi Symbol
*11.5 Quadratic Congruences with Composite Moduli (optional)
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 12. Continued Fractions
12.1 Finite Continued Fractions
12.2 Infinite Continued Fractions
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Chapter 13. Miscellaneous Nonlinear Diophantine Equations
13.1 Pythagorean Triangles
13.2 Fermat’s Last Theorem
13.3 Sums of Squares
13.4 Pell’s Equation
Chapter Summary
Review Exercises
Supplementary Exercises
Computer Exercises
Enrichment Readings
Appendix
A.1 Proof Methods
A.2 Web Sites
Tables
T.1 Factor Table
T.2 Values of Some Arithmetic Functions
T.3 Least Primitive Roots r Modulo Primes p
T.4 Indices
References
Solutions to Odd-Numbered Exercises
Chapter 1 Fundamentals
Chapter 2 Divisibility
Chapter 3 Greatest Common Divisors
Chapter 4 Congruences
Chapter 5 Congruence Applications
Chapter 6 Systems of Linear Congruences
Chapter 7 Three Classical Milestones
Chapter 8 Multiplicative Functions
Chapter 9 Cryptology
Chapter 10 Primitive Roots and Indices
Chapter 11 Quadratic Congruences
Chapter 12 Continued Fractions
Chapter 13 Miscellaneous Nonlinear Diophantine Equations
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