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Primality Testing for Beginners
 
Lasse Rempe-Gillen University of Liverpool, Liverpool, United Kingdom
Rebecca Waldecker Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Primality Testing for Beginners
Softcover ISBN:  978-0-8218-9883-3
Product Code:  STML/70
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-1445-0
Product Code:  STML/70.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-9883-3
eBook: ISBN:  978-1-4704-1445-0
Product Code:  STML/70.B
List Price: $108.00 $83.50
Primality Testing for Beginners
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Primality Testing for Beginners
Lasse Rempe-Gillen University of Liverpool, Liverpool, United Kingdom
Rebecca Waldecker Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Softcover ISBN:  978-0-8218-9883-3
Product Code:  STML/70
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-1445-0
Product Code:  STML/70.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-9883-3
eBook ISBN:  978-1-4704-1445-0
Product Code:  STML/70.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 702014; 244 pp
    MSC: Primary 11;

    How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience.

    Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.

    Readership

    Undergraduate students interested in number theory, cryptography, and computer science.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part 1. Foundations
    • Chapter 1. Natural numbers and primes
    • Chapter 2. Algorithms and complexity
    • Chapter 3. Foundations of number theory
    • Chapter 4. Prime numbers and cryptography
    • The AKS algorithm
    • Chapter 5. The starting point: Fermat for polynomials
    • Chapter 6. The theorem for Agrawal, Kayal, and Saxena
    • Chapter 7. The algorithm
    • Appendix A. Open questions
    • Appendix B. Solutions and comments to important exercises
  • Reviews
     
     
    • The authors can be congratulated on making an important recent result accessible to a very wide audience.

      Ch. Baxa, Monatsh Math
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 702014; 244 pp
MSC: Primary 11;

How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience.

Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises.

Readership

Undergraduate students interested in number theory, cryptography, and computer science.

  • Chapters
  • Introduction
  • Part 1. Foundations
  • Chapter 1. Natural numbers and primes
  • Chapter 2. Algorithms and complexity
  • Chapter 3. Foundations of number theory
  • Chapter 4. Prime numbers and cryptography
  • The AKS algorithm
  • Chapter 5. The starting point: Fermat for polynomials
  • Chapter 6. The theorem for Agrawal, Kayal, and Saxena
  • Chapter 7. The algorithm
  • Appendix A. Open questions
  • Appendix B. Solutions and comments to important exercises
  • The authors can be congratulated on making an important recent result accessible to a very wide audience.

    Ch. Baxa, Monatsh Math
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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