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Invitation to Number Theory: Second Edition
 

Revised and updated by John J. Watkins and Robin Wilson

MAA Press: An Imprint of the American Mathematical Society
Now available in new edition: NML/51
Click above image for expanded view
Invitation to Number Theory: Second Edition

Revised and updated by John J. Watkins and Robin Wilson

MAA Press: An Imprint of the American Mathematical Society
Now available in new edition: NML/51
  • Book Details
     
     
    Anneli Lax New Mathematical Library
    Volume: 492017; 134 pp

    Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.

    In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  • Table of Contents
     
     
    • Cover
    • Preface to the Revised Edition
    • Introduction
    • History
    • Numerology
    • The Pythagorean Problem
    • Figurate Numbers
    • Magic Squares
    • Primes
    • Primes and Composite Numbers
    • The Sieve of Eratosthenes
    • Mersenne Primes
    • Fermat Primes
    • Divisors of Numbers
    • The Fundamental Factorization Theorem
    • Divisors
    • Problems Concerning Divisors
    • Perfect Numbers
    • Amicable Numbers
    • Divisors and Multiples
    • Greatest Common Divisor
    • Relatively Prime Numbers
    • Euclid's Algorithm
    • Least Common Multiple
    • The Pythagorean Theorem
    • Preliminaries
    • Solving the Pythagorean Equation
    • Pythagorean Triangles
    • Related Problems
    • Fermat's Last Theorem
    • Number Systems
    • Numbers for the Millions
    • Other Systems
    • Comparing Number Systems
    • Early Calculating Devices
    • Computers and their Number Systems
    • Cryptarithms
    • Congruences
    • What is a Congruence?
    • Properties of Congruences
    • The Algebra of Congruences
    • Powers of Congruences
    • Fermat's Little Theorem
    • Euler's Phi Function
    • Applying Congruences
    • Checking Computations
    • The Days of the Week
    • Tournament Schedules
    • Prime or Composite?
    • Cryptography
    • Secret Codes
    • Caesar Ciphers
    • Vigenère Ciphers
    • Public Key Ciphers
    • Solutions to Selected Problems
    • References
    • Index
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     
    • [I]t is full of interesting things and is worth showing to bright students.

      Allen Stenger, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 492017; 134 pp

Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.

In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  • Cover
  • Preface to the Revised Edition
  • Introduction
  • History
  • Numerology
  • The Pythagorean Problem
  • Figurate Numbers
  • Magic Squares
  • Primes
  • Primes and Composite Numbers
  • The Sieve of Eratosthenes
  • Mersenne Primes
  • Fermat Primes
  • Divisors of Numbers
  • The Fundamental Factorization Theorem
  • Divisors
  • Problems Concerning Divisors
  • Perfect Numbers
  • Amicable Numbers
  • Divisors and Multiples
  • Greatest Common Divisor
  • Relatively Prime Numbers
  • Euclid's Algorithm
  • Least Common Multiple
  • The Pythagorean Theorem
  • Preliminaries
  • Solving the Pythagorean Equation
  • Pythagorean Triangles
  • Related Problems
  • Fermat's Last Theorem
  • Number Systems
  • Numbers for the Millions
  • Other Systems
  • Comparing Number Systems
  • Early Calculating Devices
  • Computers and their Number Systems
  • Cryptarithms
  • Congruences
  • What is a Congruence?
  • Properties of Congruences
  • The Algebra of Congruences
  • Powers of Congruences
  • Fermat's Little Theorem
  • Euler's Phi Function
  • Applying Congruences
  • Checking Computations
  • The Days of the Week
  • Tournament Schedules
  • Prime or Composite?
  • Cryptography
  • Secret Codes
  • Caesar Ciphers
  • Vigenère Ciphers
  • Public Key Ciphers
  • Solutions to Selected Problems
  • References
  • Index
  • Back Cover
  • [I]t is full of interesting things and is worth showing to bright students.

    Allen Stenger, MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.