abstract algebra
list of potential projects
crystallographic groups / tilings of the plane
geometric constructions w/ruler & compasss
history of algebra and the people behind it
cayley graphs
symmetry groups of the platonic solids
rubik's cube (2x2 or 3x3 depending on how ambitious you are feeling
burnside's lemma (also called burnside's counting theorem
sl(2,r) and mobius transformations
algebraic coding theory
quotient space
group actions (class equation
relationship between cycle type and conjugacy classes in symmetric group
sylow groups
anything that interests you