Math Modeling

Course Description

In this Math Modeling course taught by Ms. Durost, we move beyond traditional lectures to discover mathematical concepts through hands-on collaboration and complex problem-solving. The curriculum integrates number theory, statistics, algebra, geometry, and trigonometry, but applies them through a unique "discovery-based" lens where teamwork is essential to uncovering solutions. A core component of the class involves developing sophisticated mathematical models to tackle real-world challenges, which we showcase through group presentations and Problem of the Week (POW) assignments. Furthermore, we test our skills on a larger scale by participating in prestigious national competitions, including the Modeling the Future Challenge (MTFC) and the High School Mathematics Contest in Modeling (HiMCM). This approach ensures that we aren't just memorizing formulas, but are instead learning how to use math as a tool to interpret and solve the world's most pressing problems.

MTFC Project Proposal

The Modeling the Future Challenge (MTFC) is an academic competition where students act as junior actuaries to solve real-world problems using the actuarial process. Unlike traditional math competitions, the MTFC requires teams to identify a specific risk within their community, analyze complex datasets, and develop mathematical models to project future outcomes and suggest mitigation strategies. For our project, "Faster to the Flame," we focused on the critical issue of shortening firefighter response times in growing urban and suburban areas. As cities become more congested, delayed arrivals increase the risk of fatalities, injuries, and property loss. Our goal was to determine which factors contribute most to these delays and how to most efficiently reduce them.

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HiMCM Practice Paper

For this practice HiMCM (High School Mathematical Contest in Modeling), which is an international competition where teams use mathematical modeling to solve real-world problems, our team developed a quantitative algorithm to rank roller coasters based solely on measurable physical data to eliminate subjective bias. Using the COMAP 2018 dataset, we selected key variables like height, speed, and duration, and created a method to estimate missing data points through proportional relationships between track length and speed. We then normalized these variables to a 0–1 scale and applied weighted coefficients—prioritizing duration, speed, and height—to produce a standardized "Thrill Score" between 0 and 100. Through this process, we identified Steel Dragon 2000 as the top-ranked coaster and learned how to transform human perception into a reproducible mathematical framework while accounting for data gaps and model sensitivity.

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