This award supports two undergraduate researchers working under the supervision of the principal investigator on problems in two areas of mathematics. In the first, number theory, the students will consider convergents of continued fractions reduced by an integer, with special attention paid to cases involving very small periods. Work will also be done in graph theory. Here the research will focus on polynomial invariants: distinguishing graphs by Tutte polynomials and unimodality of Whitney numbers. If the schedule permits, studies of network reliability will also be conducted.