During the passing several weeks, including Thanksgiving break, I have quickly gone through the two Art of Problem Solving books that Math Department ordered. Overall the first book is more fundamental, while the second book really explains advanced and complicated topics. As I expected, these two books are targeted to help high school students preparing for math competitions such as AMC and AIME. Continue reading
This week is a turning point of my Math Independent Research. After I came back from the Harvard-MIT Math Tournament that was held at Boston last weekend, I have spent more time sitting down and thinking about what Westtown needs in order to achieve higher on the path of mathematics competitions. I have thought more about my role in this case, what I can and should do in order to contribute to the future Westtown Math Teams and math lovers. After considering thoroughly and talking with T. Margaret, I decided to extended my clean energy paper and focus more on math competition preparation experiences and problem solving. Therefore, I would like to do a presentation about my suggestions and vision on math competitions at Westtown.
This weekend I came to Boston to compete in the Harvard-MIT Math Tournament as one of the nineteen Westtown Math Team members. Although this was the second year that I knew about and planned to attend this tournament, it was my first time to actually come to Boston and compete, since I was injured at the last minute before the tournament last year. We took off from our school on Friday morning, reached the Philadelphia International Airport, arrived at Boston Logan Airport in the afternoon, and eventually checked into our hotel in the evening. We had a brief team meeting and went to bed early so that we would be ready for the tournament on Saturday.
This week overall is a productive week for my math independent research. I have designed an initial structure and direction for my clean energy paper by talking with T. Judy, the Director of Sustainability at our school. Besides, I have put some effort in problem solving in order to get ready for the upcoming Harvard-MIT Math Competition in Boston.
Since the beginning of the school year, I have divided my time into two parts as I have planned: working on Moody’s paper with math modeling and doing problem solving practices by myself. Overall I think that I am in the place where I planned to be, yet some small adjustments might be needed in the next quarter so that I will be able to complete my original goals at the end of semester one. Continue reading
Just to follow up a little to my conclusions at the end of my solution to the first Moody question, the prediction for plastic wastes landfilled in 100 years. In my opinion, there will certainly be technology breakthroughs in the next 100 years to solve the waste problem. For instance, the SpaceX corporation, founded by Elon Musk, is working on recyclable rockets. Continue reading
This week I wrapped up my solution for question 1 in last year’s Moody’s Math Challenge with some more thoughts coming up and more time writing them down. Just as a reminder I will repost the question 1 below:
How big is the problem? Create a model for the amount of plastic that ends up in landfills in the United States. Predict the production rate of plastic waste over time and predict the amount of plastic waste present in landfills 10 years from today.
As I mentioned in earlier blog post, I have shifted my focus to using the idea of American population growth and the amount of plastic waste landfilled per capita. To me, it is the idea of involving amount per capita that is the key to my thoughts in this question. It is common sense to me that everywhere people around us are discarding approximately the same amount of plastic everyday. Therefore, it is reasonable to calculate out the amount of plastic waste landfilled per capita in recent years and to create a model according to the trend that data shows.
This week I switched back to problem solving practices on Harvard-MIT questions, and I would like to introduce another category of problems that I have been solving: Geometry. Geometry problems frequently show up in different kinds of mathematics competitions, including the Harvard-MIT competitions. According to the archives of the General tests from recently years, three out of ten questions are geometric problems, which is a high ratio. Therefore, it is important to prepare for geometric problems in order to succeed in the exam. This week I have worked on several geometric problems from Harvard-MIT competition. Below are a couple of questions that I chose to show my solutions.
How big is the problem? Create a model for the amount of plastic that ends up in landfills in the United States. Predict the production rate of plastic waste over time and predict the amount of plastic waste present in landfills 10 years from today.
Flickr – Dan Butts photostream
When I was thinking about this question in the Moody’s Math Challenge, Markov Chain initially came into my mind. Markov Chain was first introduced to me in my Linear Algebra at Westtown School class last year as an application of a matrix in the real world. According to the Linear Algebra textbook, the Markov Chains are used as mathematical models of a wide variety of situations in biology, business, chemistry, engineering, physics, and elsewhere. Continue reading
This week, I started some preparation work for revising our team paper from Moody’s Math Challenge last spring.
According to the description on Moody’s official website, Moody’s Mega Math Challenge (M3 Challenge) is an applied mathematics competition for high school students. By asking students to solve complex, real-world issues with the power of mathematics, Moody’s Mega Math (M3) Challenge reminds high schoolers that math is more than just formulas and solving for “x.” The Internet-based contest, for which registration and participation are free, gives eleventh and twelfth grade students 14 hours to solve an open-ended, applied math-modeling problem focused on a relevant issue. Continue reading
Independent Seminar Blog 