# 2009 Research Experiences for Undergraduates

Computational Number Theory and Combinatorics

Research Projects

** Please note that some of these works are still in progress! **

## Graph NIM

This group consisted of
Sarah Legget, Stephanie Thomas, Bryce Richards and Nathan Sitaraman.
They studied a generalization of the game of NIM to graphs.
In particular they attempted to characterize which types and sizes of graphs
favor a certain player.
REU Report

## Modular Forms of weight 3/2

This group consisted of Allen Gehret, Alexa Kottmeyer and Nick Salter.
They studied modular forms of half integral weight. They focused on building
bases for spaces of modular forms of a given level and character and with
weight 3/2 which are made up of well understood modular forms.
REU Report

## Jordanizing Matrices and Collecting Coupons

This group consisted of Scott Atkinson, Jeannette Brown and Tyler Lemburg.
They studied Jordanizing matrices. Given a matrix A with Jordan form J
there are many choices of matrices P such that PAP^{-1}=J. This group
developed methods for producing matrices P which are in some sense as nice
as possible. They applied these methods to the coupon collector problems,
completely analyzing in particular the case in which two copies of each
coupon are to be collected.
REU report