Math Modeling Contests

The Montana Math Modeling Challenge (MMMC) is a 24-hour regional modeling contest for undergraduate students. In 2008, the University of Iowa hosted the first such regional contest, (called the Midwest Mathematical Modeling Competition, or MMMC), which involved 13 teams from 5 different schools.  Since then, dozens of schools have hosted these 24-hour Mathematical Modeling Challenges.  This year's contest will be the fifth time that Carroll has hosted the MMMC.

Feedback and interaction. The MMMC is designed to provide students with multiple forms of immediate feedback on their solutions. Additionally as an on-site contest, student participants have the opportunity to interact with peers from other institutions as well as observe different solution approaches presented by other teams. In brief, the MMMC differs from other contests in the following ways:

1. All student teams work on their solutions at a regional host site.
2. Teams have only 24 hours to prepare a solution to one of the given problems.
3. Each team prepares a brief oral presentation of their model and a one-page summary of their results.
4. An advisory panel reviews and provides feedback for summaries; students peer-review the oral presentations.

Yes. Teams of students from first-year through fourth-year with varying mathematical backgrounds have all successfully developed solutions. Please take a look at a few question sets and solutions from past contests as a gauge of question difficulty.

Question sets:

• MMC 2008
• MMC 2009
• MMC 2010
• MMC 2011
• MMC 2012
• MMC 2013
• 2015 MMMC Problems
• 2016 MMMC Problems
• 2017 MMMC Problems

MMMC Contest Rules

Contest Rules

Participants in the MMMC are expected to follow the spirit of the rules used by COMAP in the MCM/ICM contests. Most notably, students will be bound by the following two rules:

1. Teams may use any inanimate source of data or materials --- computers, software, references, web sites, books, etc., however all sources used must be credited. Failure to credit a source will result in a team being disqualified from the competition.
2. Team members may not seek help from or discuss the problem with their advisor or anyone else, except other members of the same team. Input of any form from anyone other than student team members is strictly forbidden. This includes email, telephone contact, personal conversation, communication via web chat or other question-answer systems, or any other form of communication.

Summary Sheet

• At the top of your summary sheet list the title and team number only. Do NOT list any group member names or institution information.
• The summary should be no more than two pages in length and should be single spaced with a 12 point font.
• Teams may submit an additional sheet listing the references used to create their model.

A summary should clearly describe your approach to the problem and, most prominently, what your most important conclusions were. The summary should inspire a reader to learn the details of your work.

10-Minute Presentation

• Clearly state (in your own words) which problem you are solving and how you plan to solve it.
• List and provide rationale for all assumptions you make in solving your problem.
• List all variables used in your model.
• If applicable, justify your choice of model by comparing it to other models.
• Discuss your model's strengths and weaknesses. Use pictures, charts, diagrams, etc. to explain your problem and your solution methods.
• Try to avoid reading text off the screen.
• Discuss future goals and ideas concerning your problem.

The Mathematical Contest in Modeling (MCM) and its sister contest, the Interdisciplinary Contest in Modeling (ICM) are international competitions sponsored by COMAP that ask teams of three undergraduates to spend a weekend modeling an applied mathematics problem. These competitions provide great opportunities for students to focus on problem solving skills in a real-world environment. Problems come from research areas of applied mathematics related to many fields – business, environmental sciences, and sports are a few examples. Student teams are given 96 hours to analyze a single open ended problem, develop a model of the problem, solve the model, and write a report. Carroll’s faculty meet with student teams weekly in the months before the competition to help them prepare for the unique nature of this international contest.

COMAP's Mathematical Contest in Modeling (MCM) successfully encourages teamwork, creativity and written exposition. However, one (logistically necessary) element that many students remark is lacking from this competition is adequate feedback -- both from the micro perspective "What do the judges really think of my team's paper?" to the macro "How did other teams answer this question?" This contest was designed in response to the aforementioned student concerns and has been developed to meet the following objectives:

• Encourage independent thinking.
• Promote collaboration.
• Develop mathematical communication abilities.
• Prepare student teams to participate in the MCM.
• Create a unique mathematical community.

HELENA – A team of Carroll College students recently ranked among the top in the world in the annual Mathematical Contest in Modeling (MCM)/Interdisciplinary Contest in Modeling (ICM) sponsored by the Consortium for Mathematics and Its Applications (COMPAP). Three Carroll College teams competed in the February competition with one team placing in the top three percent of all participants worldwide.

The MCM/ICM is a unique international contest for undergraduate students. It challenges teams of students to clarify, analyze, and propose solutions to open-ended real-world problems. Students participate as team members rather than as individuals, creating an environment for sharing knowledge and skills. Student teams are given 100 hours to analyze a single open-ended problem, develop a model of the problem, solve the model, and write a report.

This year, a total of 26,112 teams from nearly 20 countries and regions across the globe participated in the competition. Carroll College had nine students volunteer to compete in three teams of three students.

Carroll’s top-performing team was ranked as “Finalist,” placing them in the top 3% of all teams. Only eight U.S. teams earned ranks of "Finalist" or better. One Carroll team was ranked as “Honorable Mention,” placing them in top 24% of teams, and one team was ranked as “Successful Participant.”

• MCM Problem C, Finalist:  Sabrina Crooks, Shirley Davidson, Madeline Norton
• ICM Problem A, Honorable Mention:  Keaton Blair, Connor James, Milos Vukadinovic
• ICM Problem A, Successful Participant:  Ethan Mancini, Iain Scott, Makenzie Jahn

Read more about the 2021 MCM/ICM teams

Carroll teams have placed in the top 1% in the MCM/ICM in 2003, 2006 and 2010. Learn more about the competition.

Carroll ICM and MCM Teams