Mathematical Modeling is an interactive course taught by Mr. Regele, which focuses on building a strong foundation in mathematical learning habits. In class, students work together in small groups on difficult problems, and then present their solutions to the rest of the class. By presenting findings in front of the entire class, students are able to strengthen their own understanding of the concepts, while also sharing new ideas and methods with the rest of the class. Homework assignments are thought-provoking, and rely upon the student putting their strongest efforts towards building solutions. These skills are translated into the project work, where mathematical modeling techniques are employed to model real-world problems and situations, such as hiring high school teachers, or optimizing the power bank configuration of a self-sufficient house. I find this class extremely fascinating, and am proud to share my work with you here below.

HiMCM (High School Mathematical Competition in Modeling) is a competition where teams of no more than 4 high schoolers come together to model a real-life situation using an array of techniques. At MAMS, we had 4 days to brainstorm and write up our solutions for a problem involving a self-sufficient house, which we needed to provide a power bank for. This power bank was to be comprised of any type and combination of batteries, and our job was to optimize for the best possible combination given the energy requirements of the house resident. We found numerous ways to optimize for this energy requirement, explained in the paper attached below.

One of the first examples of a real-world situation we had to model was The Epsilon High School Problem. For this problem, we were given data about the student enrollment at Epsilon High School, which was being expanded. Given the number of teachers for each subject, and the number of students enrolled in those subjects, we were asked to work in small groups and find the most optimal combination of teachers to hire. Attached below is our solution.

One of the softwares we use to aid with our mathematical modeling is Mathematica, from Wolfram Alpha. Using Mathematica, we can work with larger sets of data, and run computations which we can then visualize. The Hanford Problem was a problem for which we found the line of best fit of a set of data. The Mathematica file used to visualize the data is shown below.