# Mathematical Modeling

Mathematical modeling is a course taught by Mr. Regele where we learn to look at different problems mathematically and think logically through our process. We also apply mathematical modeling to tackle different real-world problems. In November, we formed teams of 4 and took part in a 36-hour math competition to solve one of these real-world problems. We started the year by solving some PCMI problem sets. More recently, we started the Exeter 2 and 3 problem sets, while simultaneously solving the Fibonacci, Pascal, and Factorial problems. Throughout the year, we also complete Mathematica assignments to learn more about the tool to use for different applications.

## HiMCM 2021

HiMCM was a 36-hour math competition I did with a group of 4 in November 2021. We were given 36 hours to choose a prompt, develop a mathematical model, and assemble a 20 page paper detailing our solution. My team (Team 11619) chose Problem B, a prompt based around solving and modeling the water shortages in Lake Mead, and developing a plan to alleviate the problem through a water reclamation plan. For our first night, our team mostly focused on completely understanding the question and brainstorming modeling ideas. On the second day, we really dove in and developed our model further. That night, we officially started drafting our paper and worked until 4:00 AM in the morning to write a majority of its components (I’m not sure it was completely necessary, but it was fun nonetheless). The last day was spent writing the summary and finalizing the paper. Although the 36 hours period felt short and extremely stressful in the moment, looking back, HiMCM was an incredibly rewarding experience with my friends. In all, I am really proud of the work we managed to produce. ## Mathematica

Below is an example of a Mathematica assignment from math class. Mathematica assignments usually involve a modeling problem or data set we need to analyze and model using the application. I really like doing Mathematica assignments because I always learn more about the tool and its various functions. In the Hanford Part 1 assignment, we were tasked with calculating the Least-Square Line Regression of the given set of data without using the “Fit” function. I particularly enjoyed this assignment since we first derived the Least Square Regression line in class together and then finished the problem on Mathematica for homework. Take a look at my writeup down below!