Since my last blog, I have been working on three different projects: Modeling the Future, Science Fair (Abstract Algebra), and M3 Challenge, another mathematical modeling competition. In this blog, I will talk about all three competitions I have been working on. For Abstract Algebra, I will also use part of my paper to talk about Lagrange’s Theorem.
To those who don’t know or don’t remember, Modeling the Future is a mathematical competition that requires us to focus on a potential cure of a pervasive disease. We need to analyze the cure and talk about its impact on the insurance industry. MTF was certainly an interesting competition. However, as the school robotics schedule did not match with the team’s meeting schedule, our team failed to submit a paper. Despite the failure of completing Part II, I still think the process was meaningful. We did a lot of research on Alzheimer’s Disease and its genetic solutions. More importantly, the group sat down and brainstormed on the math models. If you are interested in our math model, please visit my last blog.
On the past Saturday (March 2nd), I participated in another mathematical modeling competition: M3 Challenge. In this competition, I paired up with four other Westtown students and worked on a series of problems for 14 consecutive hours. This year, we looked at drug abuse. In question 1, we needed to predict the percentage of high school students who vape and compare that with the percentage of high school students who smoke cigarettes. Through logistic regression, our prediction was only 2 percents away from the real value in the year of 2017. Furthermore, we found as more teenagers start to vape, the smoking population (including those who vape) are decreasing.
Question 2 was certainly the main dish for M3 Challenge. In this question, we needed to predict the number of drug users among 300 high school seniors. In specific, we were asked to consider Nicotine, Alcohol, Non-Prescribed Opioids, and Marijuana. In this part, we constructed our own model and equations to make the prediction. We considered variables including Gender, Family Genetics, Income, and Parental Education. Eventually, we estimated 51 would drink, 32 would smoke marijuana, 30 would smoke nicotine products, and 24 would use non-prescribed opioids out of the 300 high school seniors. I am not sure if our results match with the reality, so tell me what you think in the comment!
Finally, we were asked to build a metric in question 3 to rank which drug out of the four in question 2 has the worst impact on the user. After considering physical damage, physical dependence, psychological dependence, spending, and crime, we found marijuana has the biggest impact, followed by opioids, alcohol, and nicotine. If you are wondering why nicotine has the smallest impact out of the four drugs, please remember that smoking cigarettes cause the least crime in comparison to drinking alcohol or using marijuana. In this question, we used the Analytical Hierarchy Process (AHP) to make predictions.
M3 Challenge this year was an awesome experience. The limitation of fourteen consecutive hours is tight, but also makes sure all teammates are fully devoted toward the task. If you are a Junior or Senior next year and are interested in solving real-life issues using math models, please make sure to consider M3 Challenge! The registration is free and the seats are unlimited. All I can tell you is you will be proud of your final paper after a whole day of hard work!
At the end of the blog, I would like to provide some updates on my independent math project for the science fair. In the past two weeks, I finished my paper and finalized it with T. Susan, my instructor. Now, I am working on my poster and hopefully will have it ready before I depart for spring break. As you may know, science fairs usually prefer projects with profound real-life implication, so I am very uncertain what the judges will think about my project on Abstract Algebra. All I can do is to do my best job on the preparations and try my best on the day of competition. As I said at the beginning of this blog, I am using part of my paper to talk about Lagrange’s Theorem. Before you start, remember Lagrange’s Theorem is a theorem in Group Theory. A group is a set that has closure, associativity, an identity element, and an inverse element. If you want to review this part, please visit my last blog.
Conrad, K. (n.d.). ORDERS OF ELEMENTS IN A GROUP. Retrieved March 3, 2019, from https://kconrad.math.uconn.edu/blurbs/grouptheory/order.pdf
Humke, P. D. (2002, April 5). Lagrange’s theorem: Statement and proof. Retrieved February 6, 2019, from St. Olaf College website: https://www.stolaf.edu//people/humke/COURSES/AASyllabus/LaGrange.pdf
Lynn, B. (n.d.). Lagrange’s theorem. Retrieved February 6, 2019, from Applied Cryptography Group, Stanford University website: https://crypto.stanford.edu/pbc/notes/group/lagrange.html
M3 Math Modeling Challenge [Photograph]. (n.d.). Retrieved from https://m3challenge.siam.org/
Sandoiu, A. (n.d.). How drug mortality rates vary across the United States [Photograph]. Retrieved from https://www.medicalnewstoday.com/articles/321329.php