Identification Numbers and Check Digit Schemes (Classroom Resource Materials)

✍ Scribed by Joseph Kirtland

• Publisher: The Mathematical Association of America
• Year: 2001
• Tongue: English
• Leaves: 190
• Edition: 1st
• Category: Library

✦ Synopsis

This book develops the mathematical skills necessary for the investigation of the increasingly pervasive codes used to identify everything from credit cards to books to supermarket goods. An important part of such codes is the check digit, which can point out when an error has been made, either accidentally in transmission, or deliberately in an attempt at fraud. Mathematics plays a crucial role in designing and verifying such check digit schemes. Beginning undergraduates and pre-university students should find this book both accessible and fun. In the process of describing the identification number schemes, the author introduces many fundamental areas of discrete mathematics, including modular arithmetic and group theory, with emphasis on their applications. A unique point of the book is the way it offers students the possibility of writing papers summarizing a given topic to improve their understanding. It also contains pointers into the literature for further reading.

✦ Table of Contents

Front Cover......Page 1
Title......Page 4
Copyright......Page 5
Acknowledgement......Page 6
Dedication......Page 8
Contents......Page 10
To the Student......Page 12
To the Professor......Page 13
1.1 Developing Identification Numbers ......Page 16
1.2 Types of Identification Numbers ......Page 17
1.3 Transmiccion Fnrors ......Page 19
1.4 Check Digits ......Page 20
2.1 Preliminaries ......Page 24
2.2 Integer Division ......Page 25
2.3 Mndulo Arithmetic ......Page 34
2.4 US Postal Money Orders ......Page 41
2.5 Airline Ticket Identification Numbers ......Page 45
2.6 The Universal Product Code Check Digit Scheme ......Page 49
2.7 The ISBN Check Digit Scheme ......Page 56
2.8 Cryptography and the RSA Public-Key System ......Page 60
3.1 Sets ......Page 76
3.2 Creating Identification Numbers ......Page 81
1.3 Functions ......Page 87
3.4 Permutations ......Page 96
3.5 The IBM Scheme ......Page 107
3.6 Graphs of Functions ......Page 113
4.1 Symmetry ......Page 120
4.2 Symmetry and Rigid Motions ......Page 127
5.1 Fundamental Concepts ......Page 136
5.2 Cayley Tables ......Page 152
5.3 Powers and Orders of Group Elements ......Page 159
5.4 The Verhoeff Check Digit Scheme ......Page 167
6 Bibliography ......Page 182
Index ......Page 188
Back Cover......Page 190