The Linear Algebra Method

Katie Johnson, UNL

Meeting Time: February 22, 2011, 2:00-2:50pm

Abstract: Oftentimes in discrete math, we will use vectors or matrices to represent structures we are studying, such as incidence vectors or adjacency matrices. Rarely, however, do we use all that Linear Algebra has to offer while working with them. I plan to exhibit several proof techniques, that will involve looking at dimension, rank, and orthogonality, and use these techniques to prove theorems that are mostly set theoretic, but also include a Ramsey graph construction.