As articulated by the Dean of Graduate Studies, the Doctoral Qualifying Examination marks a pivotal milestone in a student's academic journey. It is a moment when faculty must thoughtfully assess the student’s overall qualifications for a future role as an educator or leader, as well as their preparedness within a specialized area of study.
The intended outcome of the examination is a unanimous decision by the committee, based on:
- Relevant portions of the student’s academic record
- Performance on designated sections of the examination
- A comprehensive evaluation of the student’s potential for scholarly research as demonstrated during the exam
The Qualifying Exam should be completed by the sixth quarter and no later than the end of the ninth quarter after admission to the Ph.D. program.
GGAM Guidelines for Students
Committee Formation & Advisor Selection
Before scheduling the Qualifying Exam, the student must select a Ph.D. dissertation advisor from GGAM faculty and form a committee of five members. At least one member must be from outside GGAM, and at least three must be GGAM faculty. The advisor may serve on the committee.
Application Timeline
- 5–6 weeks before the exam: Submit the Qualifying Exam application to the Office of Graduate Studies via GradSphere.
- 4 weeks before the exam: Submit a detailed proposal, reviewed and approved by the Ph.D. advisor, to the Graduate Program Coordinator.
Qualifying Exam Proposal Components
The proposal must be written in close collaboration with the committee and approved by the Ph.D. advisor prior to submission. It must include:
(A) Research Plan (max 10 pages)
Describes the Ph.D. research projects in three sections:
- Introduction: Background, motivation, and context
- Aims: Key goals, preliminary results, future direction
- Methodology: Tools, theories, and computations involved
(B) Syllabus (max 2 pages)
Outlines four to five relevant mathematical topics that support the research plan. Each topic should:
- Clearly connect to the proposed research
- Include citations to relevant texts or courses. Students will be examined on these topics, which should be selected to strengthen the research foundation.
(C) Bibliography (no page limit)
A curated list of relevant books, papers, and software that inform either the research plan or the syllabus.
The GGAM Chair and Executive Committee will review the proposal and may offer feedback. Final approval requires that the proposal meet the program’s standards for depth and breadth. Proposals must be submitted at least one month before the exam.
A sample Qualifying Exam Proposal is available for reference [HERE].
GGAM Guidelines for Exam Committees
The student-prepared syllabus must reflect adequate breadth and depth and be directly tested during the examination.
Suggested Exam Format
- 90 minutes: Research presentation and discussion
- 10 minutes: Break
- 60 minutes: Syllabus-based questions
- 10 minutes: Committee deliberation
The research presentation should last ~40 minutes, allowing for up to 50 minutes of discussion. The committee chair should track time to ensure ample discussion takes place.
Rationale for Coursework Examination
A rigorous evaluation of syllabus material is essential regardless of the candidate's performance in the research portion. Thorough questioning:
- Motivates students to prepare deeply for all aspects of the exam
- Prevents the rapid loss of course material post-finals
- Equips students with broader tools and methods to avoid narrow research trajectories
The recommended break between exam sections allows candidates to recharge and refocus, while reinforcing that strong performance in both the research and syllabus portions is required to pass.