# Projects

Students had to write a final paper on the topic of the last talk. This included handing in a paper outline, a first draft, a second draft (if necessary) and a final draft. Papers had to be written in LaTeX. The final paper was worth 25% of the total course grade.

Sperner's Lemma and Fair Division Problems (PDF) by Suthee Ruangwises. Used with permission.
Abstract
This paper is a seminar paper that summarizes Francis Edward Su's paper "Rental harmony: Sperner's lemma in fair division" in 1999. In this paper we introduce and prove Sperner's Lemma. Then, we introduce the fair division problem and an algorithm based on Sperner's lemma that can solve some variants of the fair division problem.

Making Money from Fair Games: Examining the Borel-Cantelli Lemma (PDF) by Sammuel Cannon. Used with permission.
Abstract
In this paper we discuss and prove the Borel-Cantelli Lemma. We then show two interesting applications of the Borel-Cantelli Lemma. These include a method by which one can profit from a series of games that individually have an expected value of zero, defying intuition regarding linearity of expectation, as well as displaying that a sequence of 100100 straight coin flips of heads will occur with probability one if one flips a fair coin into infinity.