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Title Elementary number theory with programming / Marty Lewinter, Jeanine Meyer.
Imprint Hoboken, New Jersey : John Wiley and Sons, Inc., [2015]


 Internet  Electronic Book    AVAILABLE
Description 1 online resource
Note Includes index.
Available only to authorized UTEP users.
Print version record and CIP data provided by publisher.
Subject Number theory.
Number theory -- Problems, exercises, etc.
Computer programming.
Genre Problems and exercises.
Contents Title Page -- Copyright Page -- Contents -- Preface -- Words -- Notation in Mathematical Writing and in Programming -- Chapter 1 Special Numbers -- Triangular Numbers -- Oblong Numbers and Squares -- Deficient, Abundant, and Perfect Numbers -- Exercises -- Chapter 2 Fibonacci Sequence, Primes, and the Pell Equation -- Prime Numbers and Proof by Contradiction -- Proof by Construction -- Sums of Two Squares -- Building a Proof on Prior Assertions -- Sigma Notation -- Some Sums -- Finding Arithmetic Functions -- Fibonacci Numbers -- An Infinite Product -- The Pell Equation -- Goldbachś Conjecture -- Exercises -- Chapter 3 Pascalś Triangle -- Factorials -- The Combinatorial Numbers n Choose k -- Pascalś Triangle -- Binomial Coefficients -- Exercises -- Chapter 4 Divisors and Prime Decomposition -- Divisors -- Greatest Common Divisor -- Diophantine Equations -- Least Common Multiple -- Prime Decomposition -- Semiprime Numbers -- When Is a Number an mth Power? -- Twin Primes -- Fermat Primes -- Odd Primes Are Differences of Squares -- When Is n a Linear Combination of a and b? -- Prime Decomposition of n! -- No Nonconstant Polynomial with Integer Coefficients Assumes Only Prime Values -- Exercises -- Chapter 5 Modular Arithmetic -- Congruence Classes Mod k -- Laws of Modular Arithmetic -- Modular Equations -- Fermatś Little Theorem -- Fermatś Little Theorem -- Multiplicative Inverses -- Wilsonś Theorem -- Wilsonś Theorem -- Wilson's Theorem (2nd Version) -- Squares and Quadratic Residues -- Lagrangeś Theorem -- Lagrange's Theorem -- Reduced Pythagorean Triples -- Chinese Remainder Theorem -- Chinese Remainder Theorem -- Exercises -- Chapter 6 Number Theoretic Functions -- The Tau Function -- The Sigma Function -- Multiplicative Functions -- Perfect Numbers Revisited -- Mersenne Primes -- F(n)=Sigmaf(d) Where d Is a Divisor of n.
Summary 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.
Other Author Meyer, Jeanine.
Other Title Print version: Lewinter, Marty, 1950- Elementary number theory with programming. Hoboken, New Jersey : John Wiley and Sons, Inc., [2015] 9781119062769
Other Title Number theory with programming