Preliminary Examination

The preliminary examination is a key step required by the Graduate School for  all students in PhD programs to be passed before the end of their third year. In Mathematics, this is an oral exam establishing whether a student is well-prepared and making progress in their chosen research direction towards their thesis.

The format of prelim should be tailored to be appropriate for each student's work and may include questioning on topics from advanced course work and a presentation of the student's research plans and current results.

From the Graduate School Bulletin (2021-22):

"The obligatory milestone examinations for PhD students are the preliminary and dissertation examinations. The requirements for the composition of the committee are the same, regardless of the examination, though its individual members may change over time. This committee also typically serves as an advisory committee to the student during his or her studies, and should be appointed to reflect research expertise that is helpful in guiding and evaluating the student’s research project. This committee must include at least three Graduate Faculty members from the major field of study, and at least one from a minor area, being from outside the degree program or from a clearly differentiated subfield within the degree program. At least two members of the committee, including the chair, must be faculty in the degree-sponsoring department or program. A majority of the committee must be Duke University faculty members, except in the case of joint PhD programs with other universities. This committee, with all members participating, will determine a program of study and administer the preliminary examination. The student’s milestone committee, either the same or with some or all members replaced as needed, will also examine the dissertation and administer the final examination." 


  • The chair of the prelim exam committee is your research/thesis advisor. They must be primary or secondary Math graduate faculty. You can have co-advisors.
  • The committee must have 4 (or more) members with at least two Math graduate faculty. Other committee members can be from other departments, or (with approval) can be experts from other institutions (subject to Graduate School approval as a term member of the committee).
  • The members of the committee should be oriented to "guiding and evaluating the student's research project" and should be open to serving in this advisory role.
  • The composition of the committee should be discussed and agreed on by the student and advisor.
  • Submitting the Graduate School's committee approval form to the DGSA is the first step in planning for the exam. This form must be APPROVED by the Graduate School at least 30 days ahead of the exam (submit it as soon as you decide on the committee members!). You do not need to select an exam date or determine the exam syllabus for this form. One member of the committee (not the advisor or co-advisor) must be listed as the "Minor Area Representative" (MAR) -- representing an important background area (but not the primary topic of the planned research).

Planning for the exam

  • Submit the committee approval form.
  • Working with your research advisor, write the syllabus to be covered for the major and minor topics of the exam. This should outline the scope of areas and key topics connected to your research. This can be a one to two page outline listing relevant reference books or articles and must be approved by all of the committee members and submitted to the DGS (email to phd-program@math)  one month before the exam. The syllabus should state if the planned format for the exam will include a research presentation or just questions on the syllabus areas.
  • You should coordinate schedule availability with all of the committee members (ex: when2meet or doodle) to determine a date and time for the exam (allow for at least a two-hour time block). Then contact the DGSA or other staff to reserve a room in the Physics or Gross buildings for the exam (a conference room or meeting room is sufficient).
  • The exam must be taken no later than the Spring of the third year, but you are encouraged to complete it as early as recommended by your advisor. You should be registered during the semester in which you take the preliminary exam. With permission of the committee, the exam can be conducted during the break between semesters but only if you are registered for the term before or the semester following the break.