2009 COMAP: For Undergraduates Who Want to Model
The Consortium for Mathematics and its Applications (COMAP), is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.
Six Columbia students participated this past spring in the Mathematical Contest in Modeling (MCM) which challenges teams of students to clarify, analyze, and propose solutions to open-ended problems. The contest attracts diverse students and faculty advisors from over 500 institutions around the world.
Columbia participants included: Adrian Haimovich (APAM), Stephen Cox (DEES), Dan Amrhein (Physics), Boris Grinshpun (APAM), Pradeep Bandaru (APAM), & Jiang Yio (Biological sciences)
People develop mathematical models as tools to solve various problems. Predictive models are used to determine the effects of climate change, the path of a subatomic particle, the future of the economy, the winner of American Idol, and the next music track you’ll want to listen to. Optimization models are used to route information over the World Wide Web, determine optimal departure times for an airline, time traffic lights, and even create Sudoku puzzles and crosswords for the morning paper. In summary, mathematical models are important in numerous aspects of our everyday lives, many of which we take for granted.
by Boris Grinshpun, B.S. 2010, Applied Mathematics
This past February, I learned firsthand the process of developing a mathematical model when I took part in the Mathematical Contest in Modeling (MCM), an annual four-day team competition for undergraduate students. The MCM is run by the Consortium for Mathematics and its Applications (COMAP). It is highly publicized by many professional organizations, including the Society for Industrial and Applied Mathematics (SIAM), and teams from all over the globe participate. This year two teams from Columbia were organized and funded by the Columbia University chapter of SIAM.
The MCM consists of two real-world problems, a continuous problem and a discrete one. A team of three students has four days to develop a solution to one of these problems in the form of a mathematical model and to summarize the results in a paper. The paper includes a restatement of problem, the rationale behind the proposed model, the development and testing of the model, error analysis, and a discussion of the strengths and weaknesses of the model. This year, the continuous
problem asked for a model to optimally control traffic in, around, and out of a traffic circle. The discrete problem asked for a model to predict the energy consequences of the cell phone revolution over the next fifty years.
For undergraduates who are interested in participating in the MCM, here is a brief day-by-day description of my team’s experience.
Day 1: We read both questions carefully and brainstormed points that needed to be addressed and preliminary ideas for effective models. We attempted to restate both problems in such a way that the main task ahead of us was clear. We used Google extensively and searched for information on traffic circles and cell phone use. We watched YouTube videos of cars driving along traffic circles. We laughed at unfortunate drivers trying to get through the traffic circles. We drew a rudimentary traffic circle and it felt good.
Day 2: We worked on mathematizing our traffic circle word problem. We added detail to our traffic circle – more lanes, more signs, serious consideration of flow rates and traffic light timing. We worked with NetLogo (a programmable modeling environment) to create an interactive traffic circle model. We had dinner and played with Shazam, the iPhone app. After dinner we linearized the traffic circle and created a second NetLogo simulation.
Day 3: We made elaborate flow-charts and schematics using Inkscape, a vector graphics editor. We had another heated debate on how to correctly time traffic lights. We produced plots in MATLAB to describe the timing. We made an outline for our paper and proceeded to write different parts in a Google document. Before we left for the night we practiced throwing our MetroCards.
Day 4: We did last minute research while working diligently on our paper. We basked in the warm glow of our windowless room with many hours remaining until the 8 p.m. deadline. We ran short on time and wrote frantically to make the deadline. All hope seemed lost, but we just barely finished on time. The adrenalin rush wore off and we found ourselves relieved and exhausted. We celebrated with pizza.
The MCM competition is a great experience for those interested in learning to develop mathematical models to use in real-world problems. However, this competition is not only a learning experience; it is also a bonding experience. After spending four days as part of team, struggling and rejoicing as we progressed through the competition, eating meals together, exchanging stories and learning about one another’s mathematical and technical skills I felt much closer to my team members. I highly recommend this competition to people who enjoy problem solving, mathematics and team work.