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Mathematical Modeling is a course taught by Mr. Regele here at Mass Academy. Math Modeling is a course that emphasizes open-ended problem solving and encourages critical thinking and collaboration. Computer simulations are also taught in the form of software such as Mathematica. Topics in the course are a fusion of many disciplines, including but not limited to trigonometry, geometry, algebra, and number theory. The main goal of the course is to prepare students to solve real-world problems.

All juniors compete each year in the High School Mathematical Contest in Modeling (HiMCM). HiMCM is a contest that tests the ability of high schoolers to work in groups to use math modeling to solve a real-world problem. The contest requires the solution to be communicated in a mathematical paper, and as such tests both the math and writing skills of students. The contest took place from November 3rd to November 16th, but following tradition, we completed most of the project within a 36-hour window. I was in a group with Anush, Jonah, and Rohan. Each year, there are two problems to choose from. This year, the problems were “HiMCM Problem A: Storing the Sun” and “HiMCM Problem B: Tackling the Drought.” Our group chose the former, as we thought it provided more room for creativity. The problem scenario was that we were moving to a remote region that relied on solar power. The objective of the problem was to develop a mathematical model to determine an optimal energy storage system that met the needs of a client with certain specifications. Our solution centered around a decision matrix that could determine the optimal battery out of about 30 batteries for some given parameters. Part of our solution required using these parameters along data collected from the 2015 RECS survey to estimate electricity usage in homes using a regression model. One of my teammates Jonah coded the decision matrix in Java to create an application to streamline the process. In hindsight, there were several aspects of the solution that we could have improved upon, but I am proud of the fact that we made it through the 36 hours with a final product. This was definitely an experience that will help me whenever I am writing a mathematical or scientific paper in the future.

Median-Median was a Mathematica lab we completed to learn how to construct a median-median regression line. To find a median-median regression line, data is first plotted on a scatterplot. Three equal groups are then created, and the median point of each group is found. The median point can be found by finding the median x-value and the median y-value. After this, the first and third point can be used to find the slope. Each median point is then equally weighted to find the y-intercept. The aim of this process is to determine a line that isn’t greatly affected by outliers and is a good representation of the data. In addition to learning how to compute the median-median regression line, the lab also taught me how to use conditional statements and loops in Mathematica. I heard that we will be continuing this lab in the future, and I am interested to see what modifications will be made.