The oral exam (also known as the PhD preliminary exam, as opposed to our prelims which is also known as the Graduate Preliminary Exam) offers an opportunity to determine whether a candidate is ready for and likely to succeed in a research career. In order to pass, the student needs to demonstrate three criteria:
ability to master core material (relevant to planned research, and tested mostly by the major part of the exam);
ability to quickly pick up new material from an unrelated area (which is important if and when new developments necessitate such expansion; tested mostly by the minor part of the exam); and
ability to work productively with a potential advisor.
The Ph.D. Oral Exam Committee: This committee is appointed by the Graduate Group Chair after consultation with the student. It consists of three or more faculty members, at least two of whom are tenured members of the department. The syllabi for the exam are agreed upon by the committee and the student, with the approval of the Graduate Group Chair. The Graduate Group Chair notifies the mathematics faculty of the exam (date, time, place, committee members, reading lists). All faculty are to be explicitly invited, and each faculty member who attends the exam is a full voting member of the Exam Committee.
Scheduling the Ph.D. Oral Exam: To take this exam, the student should have passed the Prelim Exam (also known as the Graduate Preliminary Exam) and be in good standing. The student also should have taken at least six graduate mathematics courses (including those taken elsewhere). The student discusses in advance the topics, syllabi and the composition of the oral exam committee with the Graduate Group Chair, whose written approval is needed. The exam is to be taken by the end of the student's second academic year in the program. A one or two semester extension may be requested from the Graduate Group Chair in the case of students who took mostly 500-level courses in their first year.
If the Ph.D. Oral Exam is not passed on the first try, it may be taken just once more, and this must occur before the end of the following semester. Passing the Ph.D. Oral Exam on the second try, at the latest, is a requirement for remaining in the Ph.D. program.
With the approval of the oral exam committee and the graduate chair, the minor part of the exam can be substituted by a written thesis. In exceptional cases, as discussed below, it might be possible instead to substitute a thesis for the major part of the exam (but not for both parts). In either case, this thesis should be comparable, in quality, length and style, to a Masters thesis. It is typically expository in nature, but may also be a research paper or collection of papers. Committee members should approve such a substitution if they are convinced that writing it will adequately demonstrate that the student has accomplished the three criteria above. Thus, a thesis written in lieu of the minor should demonstrate the candidate’s ability to learn and assemble all ingredients needed for a particular problem or set of problems with which the student was not very familiar previously. A thesis written in lieu of the major should demonstrate broad understanding of the basics of the subject as well as ability to apply them to specific problems. But in this situation it is also crucial to establish the student’s ability to work productively and effectively with the potential advisor, so sufficient interactions between them must take place to establish this. Permission to substitute a thesis for the major part of the exam will therefore be given only in exceptional circumstances.