Qualifying Exams

Qualifying examinations

The Mathematics qualifying exam is a three-tiered system designed to help determine as quickly and efficiently as possible whether you are ready to advance to candidacy. The exams demonstrate mastery of basic mathematics. They also indicate whether you exhibit the necessary abilities, self-discipline, and preparation to pursue the independent research needed to earn the Ph.D. degree.

Tier 1: Comprehensive written examinations

You will take two written exams, one on undergraduate Analysis topics and one on undergraduate Algebra topics; four hours are allotted for the completion of each of these written exams.

These exams will be given the week before classes begin in the fall and in the spring. You may take either or both of the Tier 1 exams in August when you first arrive. You are allowed to try each exam each time it is offered, but you must pass both exams prior to the end of the second year of study. Students pursuing a Master's Degree are not required to take the Tier 1 exams.

An archive of past Tier 1 exams can be found here.

You may not take M800 before you pass the Tier 1 exams, except during summer terms. Exceptions to this rule may be granted with the permission of the director of graduate studies.

Tier 2:  Committee review

Each spring/summer, a departmental committee will review the record of every student who has either:

  • Completed two years in the program without previous review, or
  • Passed the Tier 1 exams on entrance to the program and elects the review at the end of the first year.

You will:

  • Provide to the graduate office a personal statement that describes your plan for further study and research, including a proposal for the area of research and a topic for a minor.
  • Request an endorsement from your (interim) advisor or another faculty member. By endorsing you, the faculty member agrees to guide you to prepare for the Tier 3 exam.

The review committee will decide if you may continue toward Ph.D. candidacy. The committee’s considerations will include:

  • Performance on the Tier 1 exams.
  • Performance in 500-level coursework.
  • A faculty endorsement.
  • Written personal statement by student.
  • Your performance of assistantship duties.

In support of the Tier 2 review, grades in 500-level courses will be given and evaluated according to the following guidelines:

  • A grade of A means that, based on your work in that course, the instructor believes you will succeed in being admitted to Ph.D. candidacy.
  • A grade of B means that your work in that course is satisfactory, but the instructor has reservations (based on that work) about your ability to be admitted to candidacy.
  • Lower grades indicate unsatisfactory work.

You must maintain at least a B average in your coursework, in accordance with currently published departmental and university guidelines.

You are able to accelerate your progress in the program by passing the Tier 1 exams on entrance into the program and electing to take the Tier 2 review at the end of your first year. The review committee will treat this as favorable for your case.

If you do not receive a recommendation to continue, you will be encouraged to complete the M.A. degree. If you have financial support at the time of review, you will be entitled to at least one additional semester of support in order to do so.

Tier 3: Oral exam

After passing the Tier 2 review, you must arrange for and pass an oral examination before October of their fourth year. You seek the direction of a faculty member as a scientific advisor for this exam. The faculty member assigns a reading list consisting of texts and research-level papers; this material will comprise the major topic of the exam. If and when the scientific advisor feels that you are ready for the exam, the advisor will arrange for a three-member faculty committee to administer it.

You submit a proposal for the Tier 3 exam to the director of graduate studies for approval. It consists of topics for the major and minor area of the examination, a syllabus and a reading list for the major and minor topics, and the list of three faculty members serving as the Tier 3 committee.

These exams are projected to last approximately two hours. One of the committee members must be qualified to examine you in the minor area, where you must demonstrate 500-level mastery. In order to pass the exam, you must:

  • Demonstrate a level of mathematical ability and maturity sufficient for successfully undertaking a Ph.D. dissertation (normally in the major area of the exam).
  • Identify a faculty member willing to serve as Ph.D. advisor. This will typically, but not necessarily, be the faculty member who organized the oral exam.