Professor Thibodeaux and senior student Savannah Logan '14, worked on a project to investigate relationships between derivatives and algebraic structures called zero divisors. They first derived a formula for the number of zero divisors in the set of upper triangular matrices whose entries are from some subset of the whole numbers. They then determined the rate at which this number grows as a function of the size of the matrices and the size of the subset of whole numbers. Those rates were then compared with the derivatives of those functions, as is done with marginal cost and revenue in economics. Finally, using Gronwall’s inequality, a result was presented concerning when it is appropriate to use derivatives to approximate these discrete quantities.