Revised and updated by John J. Watkins and Robin Wilson
| eBook ISBN: | 978-1-4704-4403-7 |
| Product Code: | NML/49.E |
| List Price: | $50.00 |
| MAA Member Price: | $37.50 |
| AMS Member Price: | $37.50 |
Revised and updated by John J. Watkins and Robin Wilson
| eBook ISBN: | 978-1-4704-4403-7 |
| Product Code: | NML/49.E |
| List Price: | $50.00 |
| MAA Member Price: | $37.50 |
| AMS Member Price: | $37.50 |
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Book DetailsAnneli Lax New Mathematical LibraryVolume: 49; 2017; 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.
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Table of Contents
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Cover
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Preface to the Revised Edition
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Introduction
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History
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Numerology
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The Pythagorean Problem
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Figurate Numbers
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Magic Squares
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Primes
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Primes and Composite Numbers
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The Sieve of Eratosthenes
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Mersenne Primes
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Fermat Primes
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Divisors of Numbers
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The Fundamental Factorization Theorem
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Divisors
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Problems Concerning Divisors
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Perfect Numbers
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Amicable Numbers
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Divisors and Multiples
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Greatest Common Divisor
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Relatively Prime Numbers
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Euclid's Algorithm
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Least Common Multiple
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The Pythagorean Theorem
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Preliminaries
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Solving the Pythagorean Equation
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Pythagorean Triangles
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Related Problems
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Fermat's Last Theorem
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Number Systems
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Numbers for the Millions
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Other Systems
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Comparing Number Systems
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Early Calculating Devices
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Computers and their Number Systems
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Cryptarithms
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Congruences
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What is a Congruence?
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Properties of Congruences
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The Algebra of Congruences
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Powers of Congruences
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Fermat's Little Theorem
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Euler's Phi Function
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Applying Congruences
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Checking Computations
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The Days of the Week
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Tournament Schedules
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Prime or Composite?
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Cryptography
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Secret Codes
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Caesar Ciphers
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Vigenère Ciphers
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Public Key Ciphers
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Solutions to Selected Problems
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References
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Index
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Back Cover
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Additional Material
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Reviews
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[I]t is full of interesting things and is worth showing to bright students.
Allen Stenger, MAA Reviews
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
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- Additional Material
- Reviews
- Requests
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
