Chip-Firing Analysis of Stabilization Behaviors, Hitting Times, and Candy-Passing Games

Math can be an intimidating field. To work on some problems, one must know decades or centuries of background before one can even understand the question. However, what tends to get lost in all of that is that math can be fun, even for the relatively uninitiated. There are problems in mathematics that are discrete (essentially, self-contained) and with some combination of background research, mathematical thought, and appropriate mentoring, they are easily within reach of the high school student. During my sophomore and junior years in high school, I did work in discrete mathematics, outside the standard (albeit accelerated) math curriculum. I never had an official mentor; mostly I worked alone, but I was always able to enlist the aid of my teachers and some college professors whom I contacted, as well as similarly minded friends (both in high school with me and also some college students) who could review my work. In the summer of 2007, I was privileged to have the opportunity to attend the Research Science Institute (RSI) at MIT. Every year at RSI, 80 rising high school seniors are brought in from all around the world to conduct research for six weeks in the Boston area. They are each paired with mentors in the area who work in the student’s fields or related fields