The most critical portion of completing a Ph.D. in Mathematics is the completion of a dissertation in a chosen field of Mathematics. That is, the completion of a original and scholarly contribution to Mathematics. Each Ph.D. candidate has a dissertation advisor from her/his chosen field to provide guidance during the research and writing of the dissertation. At Syracuse University, we have a diverse choice of possible research areas: Algebra, Analysis, Applied Mathematics, Combinatorics, Geometry & Topology, Probability, Statistics, and Mathematics Education.