Math modeling is taught by Mrs. Burns, and this class is really interesting because we tackle difficult problems that string lots of ideas together. The course focuses on modeling problems with applications to the real world.
HiMCM, or the High School Mathematical Contest in Modeling, is a 48-hour competition where students in small groups create mathematical models regarding a real-life problem. For HiMCM 2022, my group chose Problem 2: Climate Change. I worked alongside Peter Liang and Jenny Shaughnessy. Specifically, we were asked to analyze how fast CO2 levels are increasing through time and the relationship between CO2 levels and global temperature. We settled on this problem due to my fascination with climate change. I thought it would be interesting to analyze trends, as problems like climate change become increasingly important in our era. Tackling this problem reminded me of the times during the early pandemic when I would analyze COVID-19 cases (for my personal amusement) and make (rather morbid) predictions about the severity of the virus in the future.
Here is a rundown of what we were given and how we approached the problem. We were given data on historical CO2 levels as well as historical global temperature levels. We first graphed both datasets in Google Sheets. We noticed that the graph for global CO2 vs. time was roughly quadratic. Logically, this made sense because as time goes on, humans release more CO2 to sustain society. Since the growth rate is increasing, our data looks roughly quadratic (“roughly” because the rate of change of temperature was not entirely constant). We originally used Sheets’ built-in graphing tools to give us a quadratic regression, but we soon realized the data it was giving us was not precise enough. So, we used Python to get more accurate equations for the regression.
However, the temperature vs. time graph was more interesting. We noticed that the temperature fluctuates every few years. To model this, we added a sine wave to the linear regression by calculating the average amplitude and period of the “waves” in our original data. We were also curious as to why such a periodic pattern even exists. We originally hypothesized that the fluctuations in temperature were due to seasonal plant growth, but then realized that the average period of about 3 years matched more closely with El Niño.
Overall, doing HiMCM was a really enjoyable experience and also served as a great bonding experience with my peers!
Another interesting problem we worked on was the birthday problem. The task for this problem was to find the day of the week for any given birthday. I worked with Joshua Schnee and Luke Pepin to devise a model that can calculate the day of the week for any birthday after 1900. Our idea was to find the day of the week for a fixed date, and then add until reaching the date of the birthday. We calculated the day of the week of Dec. 31, 1899, which was a Sunday. We then used modular arithmetic to find how to shift the day to account for the number of regular/leap years that have passed by, the birthday’s month, and the date.
It was exciting to see everyone’s perspective on the problem. Some other groups chose some fixed dates whose dates are easy to remember. This method, called the Doomsday Method, allows users to calculate the date of their own birthday in seconds. However, the cost of this is that it has a significant learning curve. Our model, while harder to remember, is more easily accessible to those without experience calculating their birthdays.
I liked this problem because it was a practical problem and a very useful puzzle to think about.