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Identification Numbers and Check Digit Schemes

Identification Numbers and Check Digit Schemes

by Joseph Kirtland

Catalog Code: IDN
Print ISBN: 978-0-88385-720-5
184 pp., Paperbound, 2001
List Price: $44.50
Member Price: $35.50
Series: Classroom Resource Materials

No Longer Available

Identification numbers, used to encode information pertaining to products, documents, accounts, or individuals, are recorded onto documents, typed or scanned into computers, sent via the Internet, or transmitted in some other fashion millions of times a day. Given the heavy reliance on these numbers to transmit information and the possibility that a transmission error may occur, many add an extra digit or check digit that is used to determine if the identification number has been transmitted incorrectly. The mathematical process, called a check digit scheme, is used by the receiver of the number, independent of the sender, to recognize when a transmission error has occurred. This book presents the mathematics behind a variety of check digit schemes used today. Special attention is given to the airline ticket, United States Post Office money order, UPC, ISBN, IBM and Verhoeff schemes. Topics from number theory, set theory, and group theory are not only used to develop the schemes presented, but are used to develop topics from cryptography (RSA) and symmetry.

Table of Contents

1. Identification Numbers and Check Digit Schemes
2. Number Theory, Check Digit Schemes, and Cryptography
3. Functions, Permutations, and Their Applications
4. Symmetry and Rigid Motions
5. Group Theory and the Verhoeff Check Digit Scheme
6. Bibliography

About the Author

Joseph Kirtland received his Ph.D. in mathematics from the University of New Hampshire. His main mathematical interest is finite group theory, and he has published a number of articles in the area of both finite and infinite group theory. Professor Kirtland joined the faculty at Marist College in 1992. A highly respected teacher, he has been selected six times by students for the Faculty Recognition Award in the School of Computer Science and Mathematics. In the fall of 2000, he was presented with the Board of Trustee’s Distinguished Teaching Award. He has been active in the Metropolitan New York section of the Mathematical Association of America. He and his wife Cindy have two children, Timmy and Betsey.