The Mathematical Contest in Modeling and Interdisciplinary Contest in Modeling are international competitions sponsored by COMAP that ask teams of up to three undergraduates to spend a weekend modeling an applied mathematics problem.
In the MCM, teams receive short descriptions of two open-ended problems. One of the problems has a continuous flavor (e.g. engineering, differential equations or physics) and the other has a discrete flavor (e.g. computer science, graph theory or combinatorics). Teams choose one of the two problems to work on, and may use any inanimate aids (books, computers, research papers, etc.). Their job is to scope the problem, develop a model, apply their model, and analyze their model in a complete report. They have only 96 hours to do this—approximately 6 p.m. on a Thursday until 6 p.m. the next Monday.
In the ICM, teams receive a short description of a single interdisciplinary problem which affects a quantitative situation in mathematics, operations research, systems engineering, security (industrial, information, or physical), and resource and environmental protection and management. Again, they may use any inanimate aids as they spend their weekend scoping their problem, developing a model, applying their model, analyzing their model and writing a complete report. This contest takes place during the same weekend in early February.
Here is a page of resources compiled by Dr. Mark Parker and Dr. Kelly Cline from Carroll College. Check out the MCM/ICM problems page if you are interested in looking over the problems from previous years. Also, check out Carroll College professor Dr. Kelly Cline's Guide to the MCM, for a past Outstanding Winner's perspective on the MCM competition.
Each year, COMAP designates the top 1-2% of all papers as Outstanding Winner, the next 15% or so are designated Meritorious and the remainder of the top 50% are designated Honorable Mention. Those teams that survived the weekend with a viable product comprise the next 50% Successful Participant.
Contact Gary Olson for additional information.