Pearson eText -- Elementary Number Theory -- Access Card
7th Edition
Published on 4. June 2022
Software
Product license key
944 pages
978-0-321-95652-1 (ISBN)
Description
Elementary Number Theory helps you push your understanding to new heights with the strongest exercise sets, proofs and examples. Applications are integrated throughout. Connections with abstract algebra help those who have already studied it, and lay the groundwork to understand key ideas if you're taking abstract algebra in the future.? Computational exercises and computer projects are available? for ?Maple,? Mathematica, Sage Math and the? book's ?many ?online resources.?
The 7th Edition offers a presentation that's easier to learn from,? while incorporating advancements and? recent? discoveries in ?number theory.? Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed. Several? hundred? new exercises enhance the text's exercise sets.
Elementary Number Theory helps you push your understanding to new heights with the strongest exercise sets, proofs and examples. Applications are integrated throughout. Connections with abstract algebra help those who have already studied it, and lay the groundwork to understand key ideas if you're taking abstract algebra in the future.? Computational exercises and computer projects are available? for ?Maple,? Mathematica, Sage Math and the? book's ?many ?online resources.?
The 7th Edition offers a presentation that's easier to learn from,? while incorporating advancements and? recent? discoveries in ?number theory.? Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed. Several? hundred? new exercises enhance the text's exercise sets.
The 7th Edition offers a presentation that's easier to learn from,? while incorporating advancements and? recent? discoveries in ?number theory.? Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed. Several? hundred? new exercises enhance the text's exercise sets.
Elementary Number Theory helps you push your understanding to new heights with the strongest exercise sets, proofs and examples. Applications are integrated throughout. Connections with abstract algebra help those who have already studied it, and lay the groundwork to understand key ideas if you're taking abstract algebra in the future.? Computational exercises and computer projects are available? for ?Maple,? Mathematica, Sage Math and the? book's ?many ?online resources.?
The 7th Edition offers a presentation that's easier to learn from,? while incorporating advancements and? recent? discoveries in ?number theory.? Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed. Several? hundred? new exercises enhance the text's exercise sets.
More details
Edition
7th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
ISBN-13
978-0-321-95652-1 (9780321956521)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Person
About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.?
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,? 7th Edition and other books.?
About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.?
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,? 7th Edition and other books.?
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,? 7th Edition and other books.?
About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.?
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,? 7th Edition and other books.?
Content
The Integers
Numbers and Sequences
Diophantine Approximation
Sums and Products
Mathematical Induction
The Fibonacci Numbers
Divisibility
Integer Representations and Operations
Representations of Integers
Computer Operations with Integers
Complexity of Integer Operations
Greatest Common Divisors
Greatest Common Divisors and Their Properties
The Euclidean Algorithm
Linear Diophantine Equations
Prime Numbers
Prime Numbers
The Distribution of Primes
The Fundamental Theorem of Arithmetic
Factorization Methods and the Fermat Numbers
Congruences
Introduction to Congruences
Linear Congruences
The Chinese Remainder Theorem
Polynomial Congruences
Systems of Linear Congruences
Applications of Congruences
Divisibility Tests
The Perpetual Calendar
Round-Robin Tournaments
Hashing Functions
Check Digits
Some Special Congruences
Wilson's Theorem and Fermat's Little Theorem
Pseudoprimes
Euler's Theorem
Arithmetic Functions
The Euler Phi-Function
The Sum and Number of Divisors
Perfect Numbers and Mersenne Primes
Moebius Inversion
Partitions
Cryptography
Character Ciphers
Block and Stream Ciphers
Exponentiation Ciphers
Public Key Cryptography
Cryptographic Protocols and Applications
Primitive Roots
The Order of an Integer and Primitive Roots
Primitive Roots for Primes
The Existence of Primitive Roots
Discrete Logarithms and Index Arithmetic
Primality Tests Using Orders of Integers and Primitive Roots
Universal Exponents
Applications of Primitive Roots and the Order of an Integer
Pseudorandom Numbers
The EIGamal Cryptosystem
An Application to the Splicing of Telephone Cables
Quadratic Residues
Quadratic Residues and Nonresidues
The Law of Quadratic Reciprocity
The Jacobi Symbol
Euler Pseudoprimes
Zero-Knowledge Proofs
Decimal Fractions and Continued Fractions
Decimal Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Factoring Using Continued Fractions
Nonlinear Diophantine Equations and Elliptic Curves
Pythagorean Triples
Fermat's Last Theorem
Sum of Squares
Pell's Equation
Congruent Numbers and Elliptic Curves
Elliptic Curves Modulo Primes
Applications of Elliptic Curves
The Gaussian Integers
Gaussian Integers and Gaussian Primes
Greatest Common Divisors and Unique Factorization
Gaussian Integers and Sums of Squares
Numbers and Sequences
Diophantine Approximation
Sums and Products
Mathematical Induction
The Fibonacci Numbers
Divisibility
Integer Representations and Operations
Representations of Integers
Computer Operations with Integers
Complexity of Integer Operations
Greatest Common Divisors
Greatest Common Divisors and Their Properties
The Euclidean Algorithm
Linear Diophantine Equations
Prime Numbers
Prime Numbers
The Distribution of Primes
The Fundamental Theorem of Arithmetic
Factorization Methods and the Fermat Numbers
Congruences
Introduction to Congruences
Linear Congruences
The Chinese Remainder Theorem
Polynomial Congruences
Systems of Linear Congruences
Applications of Congruences
Divisibility Tests
The Perpetual Calendar
Round-Robin Tournaments
Hashing Functions
Check Digits
Some Special Congruences
Wilson's Theorem and Fermat's Little Theorem
Pseudoprimes
Euler's Theorem
Arithmetic Functions
The Euler Phi-Function
The Sum and Number of Divisors
Perfect Numbers and Mersenne Primes
Moebius Inversion
Partitions
Cryptography
Character Ciphers
Block and Stream Ciphers
Exponentiation Ciphers
Public Key Cryptography
Cryptographic Protocols and Applications
Primitive Roots
The Order of an Integer and Primitive Roots
Primitive Roots for Primes
The Existence of Primitive Roots
Discrete Logarithms and Index Arithmetic
Primality Tests Using Orders of Integers and Primitive Roots
Universal Exponents
Applications of Primitive Roots and the Order of an Integer
Pseudorandom Numbers
The EIGamal Cryptosystem
An Application to the Splicing of Telephone Cables
Quadratic Residues
Quadratic Residues and Nonresidues
The Law of Quadratic Reciprocity
The Jacobi Symbol
Euler Pseudoprimes
Zero-Knowledge Proofs
Decimal Fractions and Continued Fractions
Decimal Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Factoring Using Continued Fractions
Nonlinear Diophantine Equations and Elliptic Curves
Pythagorean Triples
Fermat's Last Theorem
Sum of Squares
Pell's Equation
Congruent Numbers and Elliptic Curves
Elliptic Curves Modulo Primes
Applications of Elliptic Curves
The Gaussian Integers
Gaussian Integers and Gaussian Primes
Greatest Common Divisors and Unique Factorization
Gaussian Integers and Sums of Squares