The Resource Elementary Number Theory with Programming, (electronic book)
Elementary Number Theory with Programming, (electronic book)
Resource Information
The item Elementary Number Theory with Programming, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Elementary Number Theory with Programming, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 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 highlyqualified 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 wellknown 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 publicprivate 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 graduatelevel 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
 Language
 eng
 Edition
 1st ed.
 Extent
 1 online resource (224 pages)
 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  PublicKey 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
 Isbn
 9781119062769
 Label
 Elementary Number Theory with Programming
 Title
 Elementary Number Theory with Programming
 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 highlyqualified 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 wellknown 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 publicprivate 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 graduatelevel 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
 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)
 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  PublicKey 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)
 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  PublicKey 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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