Lafayette College’s Summer 2013 REU will run from Sunday, June 9, 2013 until Saturday, August 3, 2013.   Participants are expected to be continuing their undergraduate education in the Fall of 2013, and NSF regulations require that only U.S. citizens and permanent residents are eligible to participate.  Each participant will receive free housing and a \$3,200 stipend.

There will be three projects, listed below.  In order to apply to the program you will need to

• upload a copy of a current transcript (unofficial transcripts are acceptable).
• arrange for two letters of recommendation to be submitted to the website.

The deadline for applications is March 1, 2013.  For other questions about the REU, please send an email to mathreu@lafayette.edu

You can get to the application page through this link.

Project 1

General Area: Discrete Mathematics
Topic: The colored cubes puzzle

Given a palette of six colors, there are exactly 30 distinct ways to color a cube so that each face consists of one color.  The colored cubes puzzle is easy to state: given an arbitrary collection of n3 colored cubes, when can these cubes be stacked into a larger n x n x n cube so that each n x n face is one color?  It turns out that there is a solution to the colored cubes puzzle whenever n > 2.  A proof of this result and a number of open problems can be found in this paper.

Based on the group’s interests, we’ll explore some of the open problems that come from the colored cubes puzzle.  Some background in discrete mathematics/ combinatorics will be helpful.  Programming experience might also be useful, but is not required.

Project 2

General Area: Combinatorics
Topic:  Graphs, matroids, polynomials

How many ways can you color the countries on a map so that no countries sharing a common border receive the same color?  This classic counting problem is solved by a polynomial defined on a graph, the chromatic polynomial.  We will study generalizations of this polynomial to matorids (which generalize graphs), and other combinatorial structures, like rooted graphs, and partially ordered sets.

The questions we will study will depend on the interests of the group, but a background in combinatorics or discrete math would help.  So would some computer programming skills, but that is not a requirement.  There are lots of open questions in areas that should be accessible, and you will learn something about matroids, probably from a new book.

Project 3

General Area: Abstract Algebra, Discrete Mathematics
Topic: SET®, Geometry and Groups