Qualifying Exams

The Qualifying Examination is an oral exam given by a committee of three faculty members. Each student chooses three qualifying exam topics and discusses the content with suitable examiners. The topics must be in distinct, relatively broad areas of mathematics. The major topic is usually chosen in consultation with the prospective thesis advisor. After passing the qualifying exam, students must designate a thesis advisor, most often the examiner in the major topic.

In Applied Mathematics, single-semester graduate courses qualify as minor topics, and a breadth requirement is imposed separately. In Pure Mathematics, each minor topic should correspond either to an advanced graduate course (where "advanced" means "having another graduate course as prerequisite", in which case the prerequisite is implicitly included as well), or to a less advanced graduate course supplemented with a minimum of 30% of a semester's worth of additional material arranged with the examiner. If either minor topic is related to the major topic, it should be covered deeply enough to contain sufficient disjoint material and the other minor topic should be largely unrelated.

The exam can be taken as soon as the student feels ready, usually by the end of the third semester. Students have two chances to pass but must do so by the last day of the fourth semester.

Instructions

At least one month prior to the examination, students must obtain approval of the examination topics and the composition of the examining committee as follows.

Students must submit by e-mail to Bjorn Poonen (for Pure Mathematics) or to Michel Goemans (for Applied Mathematics), with a copy to the examiners:

• Approximate Date of Exam
• Major Topic; Examiner; Description by course number(s) and/or subject matter from text or readings (only required for the major topic if the Examiner is outside the department)
• Minor Topic 1; Examiner; Description by course number(s) and/or subject matter from text or readings
• Minor Topic 2; Examiner; Description by course number(s) and/or subject matter from text or readings

Scheduling the Qualifying Exam

Having obtained approval by return e-mail, students should pick up two scheduling forms from the Graduate Mathematics Office and obtain signatures on these forms from each examiner. The examination usually takes place in the office of an examiner. Students are responsible for making all the scheduling arrangements.

Reporting the Results of the Qualifying Exam

Students should bring a report form (obtained from the Graduate Math Office) to the quals. This form is to be signed by the major examiner at the completion of the quals and then returned to the Graduate Math Office.