Symmetry and Representations of Finite Groups

June 21 - July 2

TIME: MWF 12:30 pm - 2:00 pm


The Theory of Partitions

July 7 - July 16

TIME: MWF 12:30 pm - 2:00 pm


At the beginning of the twentieth century, P.A. MacMahon developed an operator method to study problems in the theory of partitions. While obviously powerful, the method was extremely cumbersome algebraically. Now in the age of computer algebra systems, it is being revived. There is now an implementation in Mathematica in a program called Omega. The topic of partitions begins with the fundamental question: How many ways can you write a given integer as sums of positive integers? In trying to answer this question we will be led to a variety of intriguing discoveries including some of those found by India's great, enigmatic genius, Srinivasa Ramanujan. The basics of this method will be covered in the course, and the students will be given access to the relevant software. Students will be encouraged to use Omega for course-related projects.