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

Ph.D. students will take written exams on both 400- level algebra and analysis. The exams will be given during the week before classes begin in the fall and in the spring. Each part of the exam lasts four hours.

New students may take either or both of the Tier 1 exams in August when they 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.

Syllabi, references, and sample problems for these exams are available on the Department of Mathematics web site.

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.

The student will:

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

The review 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.
• A faculty endorsement.
• Written personal statement by student.
• Student’s 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 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.
• Lower grades indicate unsatisfactory work.

Students are able to accelerate their 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 their first year. The review committee will treat this as favorable for a student’s case.

Students who do not receive 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 at least one additional semester of support in order to do so.

After passing the Tier 2 review, students 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, students 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.