SIAM News Blog

Advancing SIAM’s Mission with the COMAP Mathematical Contest in Modeling

By John Chrispell, Nathan Gibson, Kathleen Kavanagh, and Ben Galluzzo

The Consortium for Mathematics and Its Applications (COMAP) has been promoting mathematical modeling and creative problem-solving through its undergraduate contest, the Mathematical Contest in Modeling (MCM), since 1980. SIAM supports the MCM by awarding two “Outstanding” teams with the SIAM Award in the Mathematical Contest in Modeling. Each student member of the winning team receives a cash prize of $500 and a one-year student membership with SIAM. Participating MCM teams, comprised of up to three students each, work over a long weekend to propose a solution to a broad, open-ended, and often messy real-world problem. Recent contest questions have focused on the opioid crisis, disaster relief, online marketing strategies, and the fishing industry.

Over the years, the MCM has seen a dramatic increase in participation from China. In 2020, the nation hosted the vast majority of both participating and winning teams; only 264 of the total 13,753 teams were from the U.S. Although mathematical modeling is not predominantly integrated into most U.S. math curriculums, it is arguably one of the most powerful tools for workforce development (see Figure 1). COMAP’s MCM can serve as a rewarding pathway for SIAM members and student chapters to provide undergraduate students with engaging math modeling opportunities.

Coaching strategies to prepare students vary widely across colleges and universities. At Clarkson University, where a team of sophomores earned a Mathematical Association of America prize for their solution in 2009, COMAP training takes place over roughly eight weeks. Students earn one course credit for completing the training, competing in the contest, and submitting a solution. The training focuses on the individual components of the modeling process—defining a concise problem statement, making assumptions, identifying variables, building a model, and analyzing the solution—before leading up to solving a full modeling challenge. Students also practice technical writing each week. Training begins in October, includes a longer collaborative modeling assignment over winter break, and continues for a few weeks in the spring semester until the MCM commences in February.

Clarkson often recruits potential participants from the Advanced Placement calculus II course (for first-year students) and the introductory math modeling course, as these early encounters can spark students’ interest in applied mathematics. Some participating students have even added mathematics as a double major or proceeded to complete undergraduate research in mathematics. Many teams that are recruited from Clarkson’s modeling class compete in subsequent years as well.

Figure 1. Overview of the mathematical modeling process. SIAM provides several freely-available handbooks to help eager students get started. Figure courtesy of [1].

Students that have previously participated in the MCM generally serve as the most effective recruiters. At the Indiana University of Pennsylvania, the preceding year’s competitors speak to potential participants each fall and describe both their experiences and the research topics from the last competition. Students often start to form teams during their sophomore year and frequently continue to partake until they graduate. To support students during the competition, the Department of Mathematical and Computer Sciences supplies keyed-access workspaces and ensures that the students have 24-hour access to these spaces throughout the contest. Faculty promote the event by discussing it in class and commending students who participate. They set aside a special mathematical modeling library, provide books that students can use during the MCM, and contribute ample amounts of food over the course of the weekend.

Students at Oregon State University (OSU) have been participating in the MCM since 2006 and achieved “Meritorious Winner” status for their first attempt. As with other schools, OSU’s Department of Mathematics makes rooms available, issues after-hours passes, and offers written preparation materials to supplement the resources on COMAP’s homepage. After the event, the Math Club hosts a special seminar during which participants can choose to present their solutions. All successful participants receive their official certificates during the year-end departmental awards ceremony.

OSU has no background requirements for MCM participation; students from all majors and years are welcome to partake. Past teams have consisted of freshmen through seniors whose majors ranged from math and engineering to other facets of science. The main requirements are a desire to compete and a commitment to working with teammates, often from different disciplines. These are of course the same characteristics that many employers seek, and the experience makes for excellent interview material. However, the secret to OSU’s success—modest as it may be—is undoubtedly the university’s writing-intensive mathematical modeling course. Repeated practice in writing about math, and applied math in particular, reinforces the notion of mathematics as a language into which real-world problems are translated for abstraction and efficient solution. Courses on the history of mathematics may also provide exposure to math modeling, as numerous fields of mathematics originated with attempts to describe and solve real-world phenomena.

After the competition and regardless of the outcome, many student teams use their work as the foundation for their first presented talks at regional conferences. In this way, the COMAP experience serves as a gateway into the academic research process.

We strongly encourage SIAM members to get involved with the MCM. At some universities, SIAM student chapters organize the training efforts — students can even be coaches! Registration for the 2021 competition—which is scheduled for February 4-8, 2021—is already open, and teams can collaborate remotely. If you are interested in serving as a judge, more information about judging opportunities is available online

[1] Bliss, K.M., Kavanagh, K.R., & Galluzzo, B.J. (2014). Math Modeling: Getting Started and Getting Solutions. Philadelphia, PA: Society for Industrial and Applied Mathematics.

John Chrispell is an associate professor of mathematics at the Indiana University of Pennsylvania. Nathan Gibson is an associate professor of mathematics at Oregon State University. Kathleen Kavanagh is a professor of mathematics at Clarkson University and the Vice President for Education at SIAM. Ben Galluzzo is an associate professor of mathematics at Clarkson University.

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