Winter Term 2000
The World According to Mathematics
similarities and interplay between them. We first will look at some mathematical examples,
and then we will discuss an excerpt from a book by G.H. Hardy, a twentieth century
mathematician.
check-sum reports an error Z≠0:
[10a+9b+8c+7d+6e+5f+4g+3h+2i+j](mod11)=Z.
Off-by-one errors: If one of the digits of the transmitted ISBN is one
one less:the digit with the multiplier congruent to -Z(mod11)is
wrong.
ISBN are, in order from left to right,uand v, then Zis congruent to (u–
v)(mod 11).
Suppose further that the result of applying the ISBN algorithm to 0-679-79181-X
yields Z = 3. Verify that the error-correction theorem above gives the correct
information about where the error occurs.
79171-X. Suppose further that the result of applying the ISBN algorithm to 0-579-
79171-X yields Z = 2. Verify that the error-correction theorem above gives the
correct information about where the error occurs.
71971-X. Suppose further that the result of applying the ISBN algorithm to 0-679-
71971-X yields Z = 3. Verify that the error-correction theorem above gives the
correct information about where the error occurs.