Taught by Mr. Regele.
Advanced Mathematical Modeling is a course that investigates how mathematics can be used to solve and model problems which do not have one definite solution. It differs from standard math courses taught at highschools since it doesn’t follow a textbook and it is not meant to prepare for a standardized test. Rather, we work on thinking like a mathematician thinks, and understanding the core roots of the subject. By dealing with many unfamiliar and abstract problems, we train ourselves on how we should think about problems, rather than just how to solve them. In addition to this course, I am self-studying AP Calculus BC and participating in the MAMS Math Team.
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Work Samples
HiMCM
IMMC
Easing Traffic
High School Mathematical Contest in Modeling (HiMCM)
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HiMCM is a mathematical modeling competition given internationally, with two problems for teams to pick from. At MAMS, we formed teams of 4 and were given 36 continuous hours to devote completely to the problem of choice. Our group chose a problem based on finding the best summer job for a highschool student. We chose the problem since it was very open-ended and allowed us to use a lot of creativity in our solution, which we believe is unique. Using a large online database of jobs and our proprietary questionnaire, we were able to create a working model that could be used in the real world. Our team was given the designation of Outstanding and we were given the National Council of Teachers of Mathematics Award.
(results here)
International Mathematical Modeling Challenge (IMMC)
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In the IMMC, teams of high school or undergraduate students are given a week to solve a mathematical modeling problem, similar to the HiMCM. In this contest, there are multiple problems to be addressed, all linked by a similar theme. For our year (2021), we were tasked with determining the “Greatest of All Time (GOAT)” in a variety of sports, both individual and team-oriented. Our team was selected by the U.S. panel of judges (results here) to represent our nation in the final round of judging, where we competed against 26 other nations. In the final round of judging, we were given the designation of Honorable Mention.
(results here)
Easing Traffic
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In this project we were tasked with generating a mathematical model for a problem having to do with traffic flow and speed limits, as seen at the top of the document. The purpose of this project was to help us practice with Wolfram Mathematica, a powerful modeling software. The document presents four models, with each one improving on the last in terms of accuracy and applicability. Each model comes with a graphical representation of the data generated, demonstrating the utility of Mathematica.