Math Models and Competitions

I have always been expecting a way to explore some interesting math areas that I could hardly learn and research in a normal high school math classroom. Therefore, it is a great opportunity for me to take the Math Independent Research, where I can look deeply into the two areas that I love. In other words, I will divide my energy into two different math topics: Math modeling and math competition problem solving.

For math modeling, I will start to learn more about the math modeling skills applied in different areas and sorts of situations with my mentor in China, while I will continue working on our Moody’s Math Challenge (a math modeling competition where a practical problem is asked to be solved) paper from last school year. I plan that I will have completed a better-written paper by the end of October and have known more about math modeling. In November and December, I will try writing a new math modeling paper, hopefully about Westtown solar panel power generation system on top of the Athletic Center.

For math competition problem solving, I will find sample problems and questions from different Math Competitions that Westtown students, including me, are planning to take next year. I would take some past exams from competitions such as the Harvard-MIT competition and the AMC. The materials I will use are going to be problems and questions from the past years’ Math competition. I will focus on the skills of problem solving while I spend time practicing past questions. At the end of this process, I would have a better sense of the types of problems on these exams, and later, have a brief outline of these exams. It would be really helpful if I can present a list of things that we should prepare for math competitions at the end of the semester.

During this summer, I started to do some preparation works on both of the two areas. My mentor for math modeling had given me some introduction and general information on math modeling skills. Information includes the common type of problems in math modeling area and varied ways of setting up math models in different situations. I went over the Moody’s Math Challenge paper of our team with my mentor, but we did not start to improve it right away. Instead we figured that it would be better for me to read more similar papers in the catalogue in order to analyze the common points. With the new school year coming up right now, I am going to wrap up some more comparable papers. I will soon start to work on the Moody’s Math Challenge paper.

I also went to the other mentor of mine for math competition problems solving. Instead of heading straight into the past exams and problems of math competitions in America, my mentor showed me some typical math competitions in China. They might be similar in a huge part, if not the same. I had a taste on problems from various catalogs in Chinese math competitions. My mentor agreed with me that it might be a good starting point to try organizing math competition problems in America with the catalogs in China. In this way, I might get an extra chance to look into the differences of the emphasis of the math competitions in America and China. I will keep researching on and studying about the Chinese catalogs at the beginning of this school year. Later, I would try moving onto the preparation for Harvard-MIT problem sets.

I am really looking forward to the Math Independent Research class this year.

—— Shuangcheng Du

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