After completing this program, students should:
- have a substantial and deep background in their mathematical specialty, in preparation for significant independent research through and beyond the completion of the Ph.D. thesis.
- have the skills required to learn, adapt, develop, and use new mathematical ideas, in preparation for a lifetime of sustained scholarly activity.
- have the capacity to write mathematics clearly, meeting accepted standards of the professional research literature.
- have the ability to present mathematical lectures and seminars to a wide range of audiences, meeting accepted standards of the profession.
- have the capacity to read current technical research literature within and related to the students' areas of specialization.
- have sufficient breadth of background to be a literate member of the broader mathematical community.
- have the ability to teach and begin mentoring their own students.