Elementary Number Theory with Programming (eBook)

Marty Lewinter, Jeanine Meyer (Autoren)

eBook Download: PDF

2015
John Wiley & Sons (Verlag)
978-1-119-06279-0 (ISBN)

Infos

A highly successful presentation of the fundamental concepts of number theory and computer programming

Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area.

Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes:

• Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas
• Select solutions to the chapter exercises in an appendix
• Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set
• A related website with links to select exercises
• An Instructor's Solutions Manual available on a companion website

Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.

Marty Lewinter, PhD, is Professor Emeritus of Mathematics at the State University of New York, Purchase College. The author of three books and more than 80 articles, he is Executive Director of Mathematics at American Digital University Services.

Jeanine Meyer, PhD, is Professor of Mathematics/Computer Science at the State University of New York, Purchase College. She is the author of six books as well as numerous journal articles.

Inhalt

Chapter I: Pythagoras: "Everything is number"

This first chapter presents several definitions for classes ofnumber, including triangular and perfect. The programs include onefor factoring numbers and one to test a conjecture up to a fixedlimit

Chapter II: Proof

The second chapter focuses on primes as well as approaches forsolving Pell equations. The programs include examples that countsteps to compare two different approaches

Chapter III: Pascal's Triangle

The third chapter focuses on factorial. It also presentsPascal's Triangle. The programs include examples thatgenerate factorial using iteration and using recursion and thusdemonstrate and compare important techniques in programming

Chapter IV: Divisors and Primes

The fourth chapter returns to factoring, demonstrating thealgorithm for producing the greatest common divisor of two numbers.The programs include one that uses the algorithm to produce the GCDof a pair of numbers and a program to produce the primedecomposition of a number

Chapter V: Modular Arithmetic

The fifth chapter presents mod equations. One program checks ifa mod equation is true and another determines the solvability of amod equation and then solves an equation that is solvable by abrute force approach

Chapter VI: Number Theoretic Functions

The sixth chapter is again on factoring and also the Taufunction. The programs include two distinct approaches tocalculating the Tau function

Chapter VII: Euler's Phi Function

The seventh chapter presents the Euler Phi function and otherfunctions. The programs demonstrate two approaches to calculatingthe Phi function

Chapter VIII: Sums and Partitions

The eighth chapter presents partitions, including binarypartitions. The exposition explains the central role of binaryrepresentation in computing and the programs produce the binarypartition using a built-in function and also using the mathematicalapproach explained in the chapter

Chapter IX: Cryptography

The ninth chapter presents codes from very old to modern day.The programs include different ways to generate counts of lettersand also Fermat factoring

Answers or hints to selected exercises

Sample programs at the end of each chapter. You canaccess working examples of the sample programs at thewebsite: http://faculty.purchase.edu/jeanine.meyer/numbertheory/

Rezensionen

"It consists of nine chapters, all including the corresponding programs along with their mathematical content. The mathematical structure is also interesting and well-formed starting from special numbers, primes and Pell equation, to Pascal's triangle, prime decomposition and modular arithmetic and finishing with number-theoretic functions, the Euler Phi-function, sums and partitions and the classical application to cryptography. It is also remarkable that the main scope of the programs is defined before their use from the reader, providing him the best orientation for his study." (Zentralblatt MATH 2016)

Produkt-Details

• Erscheint lt. Verlag: 6.5.2015
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Technik
• Schlagworte: computer programming • Computer Science • cryptography • divisors and prime decomposition • Euler's Phi function • fibonacci sequence • Informatik • Kryptographie • <p>number theory • Mathematics • Mathematik • modular arithmetic • number theoretic functions • Number Theory • Pascal's triangle • special numbers • sums and partitions</p> • the Pell equation • triangle numbers • Zahlentheorie
• ISBN-10: 1-119-06279-9 / 1119062799
• ISBN-13: 978-1-119-06279-0 / 9781119062790