Codes, cryptography and algorithms · Maths EE idea · Accessible

Check digits: which errors do they catch?

A research question to start from

Which typing errors are always detected by the ISBN-10 and ISBN-13 check-digit systems, and why does the choice of modulus matter?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

Precise, provable statements about detection, with a design comparison.

Mathematics you would need

Modular arithmetic
Weighted sums
Prime vs composite moduli
Error types (single digit, transposition)

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Prove ISBN-10 detects all single errors and adjacent transpositions.
Show which transpositions ISBN-13 misses.
Compare other systems (for example bar codes or bank numbers).

Scope and difficulty

Accessible. Accessible.

Pitfalls

Descriptive essay.
Claims tested on a few examples only.

Where to start reading

Search a library catalogue or a university's open lecture notes for: ISBN check digit error detection proof modulus 11; transposition errors. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.