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The Resource Elementary Number Theory with Programming, (electronic book)

Elementary Number Theory with Programming, (electronic book)

Label
Elementary Number Theory with Programming
Title
Elementary Number Theory with Programming
Creator
Contributor
Subject
Language
eng
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
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Lewinter, Marty
Dewey number
512.7
LC call number
QA241 .L384 2015
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Meyer, Jeanine
http://library.link/vocab/subjectName
Computer programming
Label
Elementary Number Theory with Programming, (electronic book)
Instantiates
Publication
Copyright
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
  • The Möbius Function -- The Riemann Zeta Function -- Exercises -- Chapter 7 The Euler Phi Function -- The Phi Function -- Eulerś Generalization of Fermatś Little Theorem -- Phi of a Product of m and n When gcd(m,n)>1 -- The Order of a (mod n) -- Primitive Roots -- The Index of m (mod p) Relative to a -- To Be or Not to Be a Quadratic Residue -- The Legendre Symbol -- Quadratic Reciprocity -- When Does x2=a (mod n) Have a Solution? -- Exercises -- Chapter 8 Sums and Partitions -- An nth Power Is the Sum of Two Squares -- Solutions to the Diophantine Equation a2+b2+c2=d2 -- Row Sums of a Triangular Array of Consecutive Odd Numbers -- Partitions -- When Is a Number the Sum of Two Squares? -- Sums of Four or Fewer Squares -- Exercises -- Chapter 9 Cryptography -- Introduction and History -- Public-Key Cryptography -- Factoring Large Numbers -- The Knapsack Problem -- Superincreasing Sequences -- Exercises -- Answers or Hints to Selected Exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Index -- EULA
Control code
EBC1896027
Dimensions
unknown
Edition
1st ed.
Extent
1 online resource (224 pages)
Form of item
online
Isbn
9781119062769
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2016. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
Elementary Number Theory with Programming, (electronic book)
Publication
Copyright
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
  • The Möbius Function -- The Riemann Zeta Function -- Exercises -- Chapter 7 The Euler Phi Function -- The Phi Function -- Eulerś Generalization of Fermatś Little Theorem -- Phi of a Product of m and n When gcd(m,n)>1 -- The Order of a (mod n) -- Primitive Roots -- The Index of m (mod p) Relative to a -- To Be or Not to Be a Quadratic Residue -- The Legendre Symbol -- Quadratic Reciprocity -- When Does x2=a (mod n) Have a Solution? -- Exercises -- Chapter 8 Sums and Partitions -- An nth Power Is the Sum of Two Squares -- Solutions to the Diophantine Equation a2+b2+c2=d2 -- Row Sums of a Triangular Array of Consecutive Odd Numbers -- Partitions -- When Is a Number the Sum of Two Squares? -- Sums of Four or Fewer Squares -- Exercises -- Chapter 9 Cryptography -- Introduction and History -- Public-Key Cryptography -- Factoring Large Numbers -- The Knapsack Problem -- Superincreasing Sequences -- Exercises -- Answers or Hints to Selected Exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Index -- EULA
Control code
EBC1896027
Dimensions
unknown
Edition
1st ed.
Extent
1 online resource (224 pages)
Form of item
online
Isbn
9781119062769
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2016. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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