Kelly Black, Ph.D., Department of Mathematics, University of Georgia
Dr. Black was the 2016 pre-triage lead judge, a triage judge group leader, and a judge in the contention round in Philadelphia
The questions in the 2016 Moody’s Mega Math Challenge (M3 Challenge) asked student teams to examine the economic advantages of different car sharing programs. The first question required the teams to determine what proportions of drivers can be classified as low, medium, or high in terms of the amount of time they use their car and the distance they drive. The second question required the teams to examine four different ways for a company to implement a car sharing program and determine the participation rates for each program. The final question required students to adjust their results for the second question and accommodate the inclusion of self-driving cars as well as cars that make use of alternative energy sources.
The models that student teams submitted this year tended to be simpler compared to previous years. The primary difference was that the teams tended to provide more analysis and insight into their models. This is a welcome development, and it is encouraging to see greater attention paid to this important aspect of modeling.
Modeling is a recursive practice. We generally start with simple models followed by close introspection and analysis, and we then follow up with small changes and additions to our models to account for unforeseen behaviors. This cycle is generally repeated until a model has been more fully developed and something new comes along to catch our eye.
More specific observations with respect to this year’s Challenge are given in the commentary that follows. The first three sections focus on each of the three questions in order. After the three sections for each question, an additional section is given that provides some general notes about modeling.