#### Latin Squares

INSTRUCTOR: Gary Mullen

COURSE SUMMARY:

Latin squares are n × n matrices based upon n distinct symbols and with the additional properties that each row and each column contains each of the n symbols exactly once. Inspite of their simplicity, they have many very interesting properties and connections to other areas of mathematics. In addition, they have numerous applications. In this REU course we will discuss some constructions for sets of latin squares and generalizations of latin squares as well as some of their properties and applications.

#### Regular solids and symmetry in three and four dimensions

INSTRUCTOR: Adrian Ocneanu

COURSE SUMMARY:

The quaternion group, or SU(2), is arguably the most important non commutative group in mathematics and physics. Acting by rotations of three dimensional space, it has subgroups related to the symmetries of the Platonic solids. We shall discuss these structures, related to many areas of mathematics and physics, and will illustrate their connection with four dimensional regular solids as illustrated by the new sculpture in the mathematics department.

Suggested reading: the first chapters from Quaternions & Octonions by Conway and Smith