Mathematics Logo

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.

Each minor topic should correspond to a single-semester graduate subject or equivalent content. The major topic should go into significantly greater depth. 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.

In order for a student to pass the qualifying exam, at least one faculty member must be willing to serve as thesis advisor. Therefore students are strongly encouraged to talk to a potential advisor when assembling their qualifying exam committee to confirm in advance that there is a faculty member willing to serve as advisor if the student passes.


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 Bill Minicozzi (for Pure Mathematics) or to Jon Kelner (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 file the following forms, complete with all signatures, to Math Academic Services.

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 the Report on Qualifying Examination Form to the quals. This form is to be signed by the three examiners at the completion of the quals and then returned to the Math Academic Services office.