The Math Department “qualifying exam” is comprised of a 3-tier system designed to help determine as quickly and efficiently as possible whether students have mastered basic graduate level mathematics, exhibit the necessary abilities and self-discipline, and have prepared themselves to pursue the independent research necessary for the Ph.D. within a 2 to 3 year period.
Tier-1: Comprehensive 400-level written exams
Ph.D. students will take a 2-part written exam on 400-level Analysis and Algebra. These exams will be given the week before classes begin in the fall and in the spring. New students may take either or both of the Tier-1 exams in August when they first arrive. A student is allowed to try each exam each time it is offered, but s/he 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.
Tier-2: Committee Review
Each spring, the Graduate Policy Committee will review the record of every Ph.D. student who has either:
- Completed 2 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 their first year.
The committee will decide which students may continue toward Ph.D. candidacy. The committee’s considerations will include:
- Performance on the Tier-1 exams
- Performance in 500 level coursework
- Student’s academic advisor’s report (see below)
- Written personal statement by student
- Student’s performance of assistantship duties
- Student’s performance on A.I. English exams (if applicable)
As indicated above, students can accelerate their progress in the program by passing the Tier-1 exams on entrance into the program and electing the Tier-2 review at the end of their first year. The review committee will treat this as favorable for their case. Students who do not get a recommendation to continue will be encouraged to complete the M.A. degree. If they have financial support at the time of review, they will be entitled to one additional semester of support.
Tier 3: Oral exam
After the Tier-2 review, students must arrange and pass a Qualifying Oral Exam before beginning their 4th year. The student will seek the direction of a faculty member as scientific advisor a “tentative Ph.D. advisor” for this exam. The faculty member will assign a reading list consisting of texts and research level papers; this material will comprise the “major topic” of the exam. The student will also propose a minor area, to be approved by the Director of Graduate Studies. If and when the advisor feels the student is ready for the exam, the advisor will arrange for a 3-member faculty committee to administer the exam. These exams are projected to last approximately 2 hours, and one of the committee members must be qualified to examine the student in the minor area, where the student must demonstrate 500-level mastery. In order to pass the exam, the student 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), and
- Identify a faculty member willing to serve as Ph.D. advisor. This will typically, but not necessarily, be the faculty member who organized the exam.
Two aspects of the Graduate Program that directly support this 3-tiered system below are:
- A faculty advisor will be assigned to every entering student. The advisor will be expected to follow the student’s progress in both coursework and instructional duties, and to write a short report for the Tier-2 review committee at the appropriate time.
- Grades in 500-level courses will be given and evaluated according to the following guidelines:
- A grade of “A” means that, based on the student’s work in that course, the instructor believes the student will succeed in being admitted to Ph.D. candidacy.
- A grade of “B” means that the student’s work in that course is satisfactory, but the instructor has reservations (based on that work) about the student’s ability to be admitted to candidacy.
All students must maintain at least a “B” average in their 500-level coursework, in accordance with currently published departmental and university guidelines.
Tier-1 exams are administered the week before classes begin in August and the week before classes begin in January and will be allotted 4 hours (the intention is that time should not be a serious constraint).
Students may not take M800 before they pass their Tier 1 exams, except during summer terms. Students who have passed the Tier 1 exams but not the Tier 3 exam may take up to 3 hours of M800 each semester. Exceptions to this rule may be granted with the permission of the Director of Graduate Studies.