Identification Numbers and Check Digit Schemes（ISBN=）

　　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.
　　? Applies mathematics to everyday life ? Pedagogical introduction
to important branch of mathematics ? Encourages students to write
papers to crystallize their understanding

Introduction;
1. Identification numbers and check digit schemes;
2. Number theory, cryptography, and check digit schemes;
3. Functions, permutations, and their applications;
4. Symmetry and rigid motions;
5. Group theory and applications.