  We classify right-veering homeomorphisms of the once-punctured torus using
the Burau representation of the 3-strand braid group. We show that reducible
and periodic mapping classes in B_3 can be identified as right-veering by
consideration of the reduced version of the Burau representation. Given any
element beta in B_3, we give a method to quickly determine its action on the
generators of the fundamental group of the 3-times punctured disk. This action
which determines whether beta is right-veering, left-veering, or neither.
