**Qualifying Requirement for the Math PhD. **The requirement is meant to ensure that students have the foundational breadth to develop their early career research program, and is meant to provide some guidance as they begin their graduate studies. Students are required to “qualify” in four graduate courses (from the list below) in (at least) three distinct areas. Example: Math 601, 620, 621, 631.

- Algebra & Number Theory
- Analysis & Probability
- Computational & Applied Mathematics
- Differential Equations
- Geometry & Topology

To "qualify in Math XXX" a student must demonstrate **comprehensive proficiency** in the course material (see syllabi below). Whether or not this proficiency has been achieved will be assessed by the faculty instructor at the end of the course. (This assessment is distinct from the course grade.)

If qualifying credit is not given, a student may appeal the decision to the DGS. The course instructor, DGS, and mentor will review the student's progress and discuss options for possible remedies.

**Timeline.** Assuming that a student has the prerequisites for these courses, the expectation is that they will complete the requirement before the beginning of their second year (by July 31).

- Those students who are missing prerequisites will have an extended timeline. In such cases, the student will develop a plan (in consultation with their mentor) outlining their path to complete the qualifying requirement (no later than the end of the second year) and submit to the DGS before the first day of classes.

**Testing-out of 601 and 631.** We offer a Qualifying Exam in these two courses in August (roughly the equivalent of the course final exam). If a student passes the exam, then they get credit for “qualifying” in the course.

**Oral exam option. ** Some students may be better served by having the option to qualify in a subject that is not among our QE courses. Such students can replace qualifying in a course with an oral exam on the subject. This should be a well-planned and thought-out part of the student’s first-year studies, and should not become an obstacle to student progress in completing the qualifying requirement. To that end the student must make the following arrangements no later than February 15th of their first year:

- Consult with the mentor and the DGS to form an exam committee of two faculty.
- Write an exam syllabus (in consultation with the exam committee), and submit to the DGS for approval.
- Schedule a (tentative) date for the oral exam. The exam must take place before the start of the student's second year (by July 31).

**Mentor's role. ** In consultation with their faculty mentor, each incoming student will develop a tentative plan/roadmap for completion of the qualifying requirement, and submit to the DGS/DGSA no later than August 31. This could be as simple as “I plan to qualify in Math 601, 620, 621, 631."

**Last Day of Class.** The Academic Calendar schedules graduate courses to end a week before undergraduate courses. This is NOT mandatory: instructors of graduate courses may continue their courses to the last day of undergraduate classes. (The intention to extend must be made clear in the syllabus at the beginning of the semester.) Instructors of Qualifying Eligible courses are in particular encouraged to take advantage of this extra time.

**Qualifying Eligible Courses & Syllabi. **The Qualifying Eligible courses have a set syllabus (listed above), regular, graded homeworks and a comprehensive final exam. At the end of the semester, the instructor will determine whether or not the enrolled Math PhD students "qualified in the course". This assessment of qualification is distinct from the course grade.