Softcover ISBN:  9780821898833 
Product Code:  STML/70 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470414450 
Product Code:  STML/70.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821898833 
eBook: ISBN:  9781470414450 
Product Code:  STML/70.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821898833 
Product Code:  STML/70 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470414450 
Product Code:  STML/70.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821898833 
eBook ISBN:  9781470414450 
Product Code:  STML/70.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 70; 2014; 244 ppMSC: 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 longstanding 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.
RempeGillen 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.
ReadershipUndergraduate 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


Additional Material

Reviews

The authors can be congratulated on making an important recent result accessible to a very wide audience.
Ch. Baxa, Monatsh Math


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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 longstanding 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.
RempeGillen 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.
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