Elementary Number Theory with Applications, Second Edition

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 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 "In revising his undergraduate text, Koshy incorporates new sections and exercises dealing with the latest discoveries and reinvigorates the standards in number theory, as well. - Elementary Number Theory is the only number theory text that shows the student how modular systems can be employed to create beautiful designs, tying the theory to both geometry and art. - This text is ideal for undergraduate mathematics and computer science students, and any instructor teaching a course in number theory will find the content to be ideally suited for their current curricula. - "The second edition of Elementary Number Theory features real-world applications of number theory, used in computer security and is the only text that covers barcodes, ZIP codes, ISBNs, EAN, and VIN. - It is loaded with pedagogical features including many fully worked examples, graded exercises, chapter summaries, and computer exercises. This is a well-organized, non-intimidating book written with students in mind. - Koshy also keeps the instructor in mind, allowing maximum flexibility in chapter selection based on the course length and students' needs."--Jacket Content: Fundamentals Divisibility Theory Canonical Decompositions Linear Diophantine Equations and Congruences Congruence Applications Systems of Linear Congruences Three Classical Milestones Multiplicative Functions Cryptology Primitive Roots and Indices Quadratic Congruences Nonlinear Diophantine Equations Appendix A.1 Proof Methods Appendix A.2 Web Sites Tables: Factor Table Values of Some Arithmetic Functions Least Primitive Roots Modulo Primes Indices References Solutions to Odd-Numbered Exercises Includes sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. This title covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes.