Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office of Graduate Education.

The Ph.D. degree results from following a program of study in mathematics or in applied mathematics. In either case, the student’s program of study must include:

• At least six, four-credit (nonthesis) graduate mathematics courses (i.e., those with numbers MATH-6xxx or MATP-6xxx).
• At least one three- or four-credit course at the graduate (6000) level outside the department (i.e., not coded MATH or MATP and not cross listed with any department course), selected in consultation with the math adviser.
• At least two-thirds of the total credit hours, excluding thesis, must contain the suffix numbers 6000—6999 with the further limitation that no more than 21 credits hours of 4000—4990 courses are allowed.

All doctoral students must pass a written preliminary exam as well as an oral qualifying examination, and complete an oral candidacy presentation.

In addition, the course MATH-6591 Research in Mathematics is strongly suggested. Any deviations from these requirements must have the approval of the Department’s Graduate Committee.