Math Modeling is a very unique math class. Instead of our teacher explaining a concept at the whiteboard and then having us do several practice problems on that concept, we are given problems that help us explore the concept and learn it for ourselves. So far, we have covered number theory through card shuffling, statistics, and algebra and geometry through problems from the Phillips Exeter curriculum. In addition to this, we also learned about math modeling itself, and how to represent problems through mathematical representations. We have done several problems of the week, High School Mathematical Contest in Modeling (HiMCM), a challenge where we only have 50 hours to mathematically model a problem and write up a report on our math model, and Modeling the Future Challenge (MTFC), a long term project where we mathematicaly model something that is interesting to us.
The Epsilon project was a group project that we worked on. We had to use math modeling to determine which departments the school should hire teachers for. We had to take into account constraints of the problem, such as the maximum number of teachers that could be hired in total. We also had to take into account our goal of making the teacher distribution fair across departments and explore what fair meant. Once we understood that, we could come up with mathematical representaitons to identify the best distribution of new teachers across departments. The attached slideshow is what we presented in class to explain our problem, goal, process, and results.
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Modeling the Future Challenge (MTFC) is a long term competition that we work on as a group project in class. In this project, we are tasked to dive deeper into a topic or problem we are interested in and identify key risks, such as loss of money or loss of lives, and the best strategies to mitigate those risks through mathematic modeling. Our group chose to explore climate change, specifically the excessive carbon dioxide in the atmosphere and what risks that poses to us, our businesses, and the earth. We then look at different strategies to mitigate the risks, such as carbon recycling. The attached document is a project proposal that we worked on as part of Phase 1 of the project. In the next phase, we will be paired with a mentor and doing the actual mathematic modeling and writing up a complete report.
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