Identification numbers and check digit schemes (Q2716339)

This student oriented book is intended for a wide audience, especially ``those interested in mathematics at work''. It may be, I agree, ``an ideal text for a liberal arts mathematics class''. The book is organized to allow students to move from simple mathematical concepts and check digit schemes to more complex ideas.NEWLINENEWLINEThe mathematical topics are elementary check digit systems (airline tickets, ISBN, UPC, IBM-schemes), hashing functions (e.g.\ assigning drivers license numbers), culminating in Verhoeff's scheme and cryptographic tools (Caesar and other substitution ciphers, RSA).NEWLINENEWLINEEach section starts with preliminary activities, followed by definitions and properties with proofs, examples, exercises, group activities and writing assignments (sometimes to compare different schemes) and hints for further reading. The lessons are structured under an educational point of view, as is the overall concept: to introduce number theoretic concepts (prime numbers, modulo arithmetic), the discussion of permutations, symmetry groups (plane and rigid motions) and group theory (definitions, Cayley table, order of elements).NEWLINENEWLINEFrom the perspective of mathematical content, objections to a few passages can be raised, for instance concerning the scheme of German money (the letters were at fixed positions) and the omission of important articles in the bibliography (as for instance the article of Ecker and Poch). Despite that I can conclude:NEWLINENEWLINEThe text is so well drafted and elaborated that it is a pleasure to read, even for an expert. I highly recommend this book.