# University of Minnesota Student Chapter’s Math Modeling Contest

Each fall semester since 2015, the SIAM Student Chapter at the University of Minnesota has held a local mathematical modeling contest. This modeling contest is designed to encourage undergraduate students to get more involved in the math community at the University of Minnesota, raise awareness for the international Mathematical Contest in Modeling, and recruit teams to participate in the international competition.

The Mathematical Contest in Modeling (MCM) is a five-day international competition held in late January or early February, in which teams of undergraduates and high school students use mathematical modeling to solve open-ended, real world problems. Students participate in teams of up to three members, and the competition is conducted remotely. On the first day of the competition, teams select a problem to work on from the MCM website and, over the remainder of the competition, design a model addressing the issues raised in the problem statement. The team’s submission at the end of the competition consists of a solution paper which restates the problem in the students’ own words, explains any assumptions that are made in the solution, describes the model and results, and discusses the strengths and weaknesses of the model in light of any model testing, sensitivity analysis, or error analysis that was conducted. These solution papers are usually upwards of twenty pages in length. The team must also submit a summary of their solution, usually addressed to a technical lay person.

The MCM gives undergraduates and high school students the opportunity to practice and enhance their skills in modeling real life problems using mathematics they have learned in their classes. They get experience solving problems where there is no one “correct” solution with the added bonus that it looks great on a resume. Additionally, the competition shows students that you must be able to work collaboratively and as a team to be successful in mathematics. The team format is one factor that is attributed to the high proportion of women participating in the MCM (42% in 2018) relative to other national and international math competitions.

Compared to the international MCM, the local contest run by the UMN SIAM Student Chapter is a low key affair. Students still compete in teams of up to three members, but the format of the competition is adjusted to better suit the UMN student body and encourage first-time participants. Usually, teams are presented with only one problem on which they can work (the problem given in Fall 2017 appears at the end of this article), and are given about a week to prepare their submission. Because the competition is held at the end of fall semester when UMN students are busy taking midterms and preparing for finals, teams are asked to submit a proposal up to three pages in length about how they would address the problem if it were given in the real MCM competition. They must also submit a one page personal statement about why the team members want to participate in the international contest. Team proposals are reviewed by a panel of student chapter officers and graded on both the mathematical content and writing quality.

Using chapter funds, the top two to three teams from the local competition are sponsored to take part in the international competition. In the roughly two months between the two competitions, chapter officers provide the teams with feedback on how they could improve their work and help the top teams prepare for the international competition. These officers also register the students for the international competition and serve as their advisors.

Chapter officers organize all parts of the local competition, from writing the problem to advertising in addition to the judging and mentoring components outlined above. Officers actively recruit participants by giving short presentations in math, statistics, and science classes where students learn techniques that may make them successful in the international competition. Furthermore, if a student is interested in participating in the local competition but does not have a full group, chapter officers will connect interested parties so that a full group can be formed.

The local competition is a great opportunity for graduate students to gain experience mentoring and for undergraduates to learn about using mathematics outside of a classroom setting. We have found this to be a useful and rewarding event at the University of Minnesota. If you have any further questions about our local competition, we would love to hear from you. Send us an email at siam@umn.edu. Also, be sure to check our website. For more information on the international MCM, please visit their website.

### Local MCM Competition Problem Fall 2017: Say It Ain’t Snow

Your local Minneapolis government has caught the Math Bug and realized that their snow plowing strategy is inefficient. They have hired a team of quantitatively inclined people (that’s you!) to come up with a better method. But hurry! Winter is coming! You can operate up to X snow plows at any given time and need to plow part of a city street system for as little money as possible. In the figure are four neighborhoods of Minneapolis, with major roads in bold. It is in the interest of the neighborhood to plow the bold streets first. Plows cost Y dollars per mile plus Z dollars per hour to operate. It takes, on average, W hours to clear a single lane of a cubic kilometer of snow.

Your task, should you choose to accept it, is to come up with and analyze a plowing model for a small
region of the city. Your model should answer some, **but not all**, of the following questions:

- What other variables do you need to take into account to have the optimal strategy?
- When should the plowing start? In particular, what does the start time depend on?
- How do you determine whether or not you need to plow?
- Consider the costs and benefits of salting vs. plowing. Note: it costs \(S\) dollars per mile (\(S>Y\)) plus \(T\) dollars per hour (\(T<Z\)) to operate a salt truck, and salting is only effective for small quantities of snow.
- If you make a mistake in the determination on whether or not to plow, what are the costs? What do these costs depend on? Are you more worried about sending out plows too often or not often enough?
- How do your strategies change as you get close to going over budget?
- How does your model scale to the entire city?
- How should you balance the safety of plow and salt truck operators vs. the need to plow the city, in particular for emergency vehicles?
- Explicitly address and justify any assumptions, approximations, or simplifications you make in your model and analysis.

*Know of any high school students interested a math modeling competition? Check out the SIAM-organized MathWorks Math Modeling Challenge*.