Department of Mathematics
Duke University : Graduate School : Dept of Math : Math Graduate program
Qualifying exams

The Qualifying Exams

The qualifying exam is part of the process used by the Mathematics Department to satisfy the Graduate School requirements for the Master of Arts degree. This examination consists of two components:

  1. Written exams in basic analysis and linear algebra
  2. Oral exams on two graduate-level topics


1. The written qualifying exams on basic analysis and linear algebra (at undergraduate level) are administered in August (just before fall term begin), January (just before spring term begin) and May (after the end of the spring term).

  • The topics covered by the exams are given in the syllabus lists:
  • Recent written qualifying exams
  • Students who do not pass the exam should work to become more prepared to retake the exam or remedy their deficiencies through coursework and faculty mentoring.
  • Students are normally expected to pass both the basic analysis and linear algebra written exams by May of their first year.
  • A Pre-qual Prep (PQP) program is offered to help students review and prepare before the written exams.


2. The oral qualifying exam is a two-hour examination on two graduate-level topics given by a committee of two members of the graduate faculty.

  • The two graduate level topics for the oral qualifying exam are chosen from the following list of seven: These links describe syllabus topics and suggested reading for each. The amount of material covered on each topic corresponds roughly to the content of a one semester introductory graduate level course. Many of the typical oral exam questions probe the student's ability to apply the general theory to specific examples.
  • The oral qualifying examination may not be taken before the student has passed the written qualifying examinations.
  • The oral qual is usually.or in the summer It must be passed before the beginning of the spring semester of the second year of study.
  • The process for setting up the oral qual exam:
    1. Select two topics from the list of seven.
    2. Contact the DGS to have the DGS appoint an exam committee. You may list any preferences or requests for Profs. for the exam.
    3. You will be informed by the DGS on the Profs for the exam. You can then contact the Profs to work out the date and time for the exam. The exam usually takes place in a faculty office.
    4. When you talk to the professors who will give you the exam, make sure you understand what they expect you to know.
    5. When you are agreed on a date and time for the exam, contact the DGS-Assistant to give them the date and time, AT LEAST ONE WEEK before the exam date.
    6. It is good to email your examiners a day or two before the exam to make sure they remember.
  • Students that do not ultimately pass the oral qualifying exams at Ph.D. level will not continue in the Ph.D. program.

The purpose of the oral qualifying examination is to determine if the student has mastered relevant beginning-graduate coursework at a level needed to continue on to advanced-level coursework and research leading to the Ph.D. (with the preliminary exam coming at that stage). There are several possible outcomes of the oral qualifying exam:

  • Passing both topics at the Ph.D. level - the qualifying exam requirements are then complete.
  • Falling short of passing one or both topics at the Ph.D. level will be categorized into two levels:
    • Passing at the Master's level.
    • Failing.
    The committee may decide to allow students who do not pass a topic at the Ph.D. level to retake the exam (in front of the full committee) once more.
  • Decisions of the committee will be entered on the Math Dept Oral Qual Form.

Duke University : Graduate School : Dept of Math : Math Graduate program