Topic > Check Digit Patterns - 1142

In an age where information is increasingly transmitted through electronic formats, maintaining accuracy is critical. Whether it's information as simple as a book borrowed from a library or as important as a bank account number, maintaining consistency when transmitting information is critical to preventing monetary or organizational errors. To maintain consistency across various information transfers, number theory-based check digit schemes are used to detect when errors occur. This article will examine the value of check digit schemes in light of their application and mathematics. To begin with, a basic understanding of check digit patterns reveals the value of this application of number theory. Check digit patterns exist in almost all identification numbers. Authors Pommersheim, Marks, and Flapan (2010) noted that common examples of check digit patterns exist in ISBN numbers, airline tickets, money orders, and bar codes on retail items. From these examples, it is clear that check digit patterns are a common application of number theory that has a subtle impact on everyday life. This impact is found in the function of check digit schemes. In summarizing this function, mathematics professor Joseph Kirtland (2001) noted that “most check digit schemes add one or more extra digits, called check digits, to the identification number and then use the digits to check for errors subsequent to the transmission of the number" (p. 5). From the author's overview, the impact of check digit schemes is found in the prevention of errors that accompany their use. By implementing a check digit scheme in a computer or scanner, the device can quickly check the validity of an identification number and report or copy electronic devices. Furthermore, the programs prevent errors in libraries, commerce and identification. Finally, the mathematics of the check digit patterns is interesting and contributes to the detection of various transfer errors. Understanding check digits is helpful in understanding the modern world. The average person has various forms of identification and engages in many activities that use identification. Ensuring correct identification is critical to preventing monetary or identity errors. Works Cited Kirtland, J. (2001). Identification numbers and check digit schemes. Washington: Mathematical Association of America. Pommersheim, J. E., Marks, T. K., & Flapan, E. L. (2010). Number Theory: A lively introduction with proofs, applications, and stories. Hoboken, NJ: Wiley.Wheeler, M.L. (1994). Check digit schemes. The math teacher, 87(4), 228-230.