The term project part of the course consists of working with a group
of four other students on a paper about a mathematical topic
which you will present to the class.
Class
presentations should be about 25 minutes long, so that
we can have two presentations on a given day. The combination
of your presentation and the paper you write with other
members of your project team will count for 25 per cent
grade.
Please have
a look at the list of projects below and e-mail me an ordered
list of your first three choices. I will then put people in
touch with other class members interested in the same project.
We will also set up a time so that everyone can meet with me
to discuss their project.
If you think of a mathematical project not on this list
which you'd like to pursue, that would be fine. Please
e-mail me about what you have in mind and we will meet to
discuss this.
In 2012 a group of students in math 210 decided to study the prevalence of the golden ratio in a particular painting by Mondrian. They modeled what the distribution of heights in comparison to widths in a painting which contained ``random" rectangles. They then compared this distribution with what the rectangles they saw in a painting of Mondrian. This gave some support to the idea that Mondrian did favor the golden ratio.
Here is their in-class presentation
Here is a write-up of their work.
This problem is to determine to what extent the parameters in a 3 by 3 payoff matrix can be determined from knowing the optimal strategies in the two person zero sum game defined by this matrix. This is a natural question to ask when trying to understand from the behavior of the players what their motivations are. Suppose in the B.S. model discussed in homework #4, one allows the credibility constant c and the lying constant \ell to be different from each other. For which values of c and \ell are the values of c and \ell determined by the optimal strategies of the two players? You might first want to analyze the analogous problem for the 2 by 2 truth versus lying game.
This project is about one model for how to make a choice from among a sequence of alternatives being considered. Imagine that you can interview a sequence of candidates for a job of some kind. After each interview you either have to decide to choose the candidate just interviewed or move on the next, and if you move on then you can't return to choose an earlier candidate. What is the best strategy to use if you want to maximize the chances of ending up with the best candidate? What if you want to maximize the expected rank of the candidate you choose? Here is a Survey on the secretary problem. Here is a More advanced article.