Identification Numbers And Check Digit Schemes

by Joseph Kirtland

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.

174 pages, Paperback

First published March 29, 2001

Reviews

[Charles · Rating 5 out of 5]

This book is an ideal text for a liberal arts math class and there are two primary reasons for this. The first is that the mathematics is not difficult, with a bit of direction, even those that struggle with algebra will be able to understand it. The second reason is that the content demonstrates in many ways how mathematics is used to manage transactions. By demonstrating the role of the check digits in identification codes, the student can easily see and understand how valuable math is. Much of the content requires only a knowledge of basic arithmetic.
A secondary reason is the inclusion of a large number of exercises, including some that are designed for a short writing assignment. This is a valuable addition for classes where the students are often expected to write about what they have learned.
Writing effective and understandable books for liberal arts classes in mathematics is challenging, yet with this book Kirtland makes it look easy.