As expressed by the Dean of Graduate Studies, the Doctoral Qualifying Examination is not only a major benchmark in the student's career, but a point at which the faculty must reflect with wisdom on the student's general qualifications for a respected position as an educator or leader as well as the student's preparation in a special area of study. The intended outcome of this examination is a unanimous decision by the committee based on:

• Relevant portions of the student's previous academic record;
• Performance on specific parts of the examination; and
• Overall evaluation of the student's performance and potential for scholarly research as indicated during the examination.

GGAM Guideline for the Student:

Prior to the Qualifying Exam, the student must identify a Ph.D. thesis advisor selected from among GGAM faculty and constitute a Qualifying Exam committee with 5 members. At least one member of the exam committee must be from outside GGAM, and at least three members should be GGAM faculty. The student’s Ph.D. advisor can be a member of the committee.

Approximately five to six weeks before the Qualifying Exam, the student must submit the Qualifying Exam application to the office of Graduate Studies through the Graduate Coordinator.

Four weeks before the exam, the student must submit a carefully written Qualifying Exam proposal to the GGAM chair. The proposal will contain three parts: a research plan (A), a syllabus (B), and a bibliography (C)

(A) The research plan is a description of the research projects that will constitute the student's Ph.D. thesis. The research plan may not exceed 10 pages

A typical format of this part of the proposal includes:

• An Introduction: This section provides background, motivation, and context regarding the research projects.
• Aims of the proposed work: This section includes key goals, preliminary results, and future work.
• Methodology: This section presents the tools, ideas, or computations that are or will be part of the work.

(B) The second part of the proposal is a syllabus of relevant mathematical topics that were selected to aid on the research plan. It is understood that there is a connection between the syllabus topics proposed and the research plan. Typically the syllabus will include four or five topics with specific references to books, papers, or courses. This part of the proposal uses a maximum of 2 pages. The student will be asked questions on these topics which are meant to provide tools and skills useful to the research plan.

The student will describe how each topic of the syllabus connects to the proposed research (e.g., link to the methods used in the projects, include citations to books and papers or courses). It is important that the coursework described in the syllabus is actually tested in the exam; see the rationale below.

(C) The bibliography collects information about relevant books, papers, and software that will be used in the research project or the syllabus. There is no limit in the number of pages.

The proposal must be developed in close consultation with the student’s Qualifying Exam committee. The Ph.D. advisor must have approved the document before submission. The GGAM chair and GGAM Executive committee will review the proposal and make suggestions and recommendations. The GGAM executive committee will approve once the proposal satisfies breadth and depth standards. We stress that the proposal must be submitted at least a month prior to the exam.

EXAMPLE QE PROPOSAL

GGAM Guideline for Qualifying Exam committees:

As part of the qualifying exam proposal, students prepare a detailed syllabus of coursework material. GGAMEXEC reviews the proposal and approves it if it satisfies a breadth and depth requirement. It is very important that the coursework is actually tested in the exam; see the rationale below.

The following is a recommended breakdown of a qualifying exam; the actual time for each portion of the exam is left to the discretion of the chair.

• 90 minutes research talk and discussion regarding research
• 10 minutes break
• 60 minutes questions on the syllabus
• 10 minutes deliberation

The candidate should aim for a 40 minutes research presentation, which leaves up to 50 minutes for discussion. Often it is the case that questions are asked during the research presentation. The chair should attempt to keep track of the time spent during the research talk to ensure that enough time for discussion is spent during the 90 minutes allocated.

Rationale:

It is very important that a thorough examination of coursework is included in the exam, no matter how strong or weak a candidate’s performance in the research component. Many of our students study very hard for the qualifying exam and may be disappointed if no (or too few or too shallow) coursework questions are asked, while other students may be motivated by a consistently thorough coursework examination to study harder for the qualifying exam. Studying for the qualifying exam will counter the oft-observed phenomenon that the material of a course is forgotten quickly after the finals have been written. Also, knowing the tools and methods of a broader field of study reduces the risk of getting stuck in a particular research direction.

A break between the research and coursework portions of the examination is strongly suggested. It serves as an opportunity for the candidates to refresh themselves, and then focus on the coursework examination. At the same time, it serves as a reminder to the committee that satisfactory performance in the research and coursework portions are two separate necessary conditions for passing the exam.