Graduate study in mathematics is attractive for many reasons. Centuries of careful scholarship have produced a rich tradition and intellectual depth that is unsurpassed among classical subjects of advanced study. Today, careful modes of advanced mathematical reasoning are vital to many breathtaking technological advances. Indeed, the interplay with emerging sciences and technologies has always been vital to the development of mathematical ideas. That interplay is even more intense today, with computing technology providing a level of interaction that was not possible in the past. Thus the modern world of mathematics consists both of established bodies of knowledge, distilled from the studies of scholars past and present, and of emerging areas of study and application. These advancing areas are often characterized more by unanswered questions and intellectual challenges than by established answers. The world of mathematics is not static, but is part of the same explosion of knowledge and technology that fills the headlines..
Most of our students become involved in some sort of study or research project in addition to their course work. This can range from independent study on a topic of special interest, under the direction of a faculty member, to supporting work on a faculty research project, to the doctoral dissertation of Ph.D. students.