Several schemes use modular arithmetic to append a check digit to product identification numbers for error detection. Some schemes are discussed, including ones for money orders and library books. Then a foolproof method is presented. (MNS)

Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin…

These proceedings include two lectures followed by working group and topic group contributions in reduced format. The two lectures were by Heinrich Bauersfeld, speaking on contributions to a fundamental theory of mathematics learning and teaching, and Henry Pollak, speaking on the relationship between applications of mathematics and the teaching…