Qualifying Exams (written and oral)

Each of the four graduate programs within the Department of Mathematics and Statistics has its own distinct examination requirements. Written qualifying examinations are offered in the week before the beginning of the fall and spring semesters. Sign ups are offered during the previous semester. Students new to the program may sign up for examinations by emailing the GPM, although we can not guarantee that the exam schedule will accommodate their plans. In the fall semester, the Advanced Calculus/Linear Algebra exam is offered during the second week of classes instead of the week before.

The examination committee for each exam will report the results in detail to the GAC, which will then make the final decision about passing or failure. In some cases when a student does not pass, but in the opinion of the GAC, no purpose would be served by requiring the student to retake all or part of the exam, the GAC may offer alternative ways for the student to qualify for the PhD. These could include: an oral exam (which may cover additional material), additional coursework, or potentially other options as well.

A student who changes programs within the Department may apply past exam results to the new program. For example, a student who moves from the Statistics MS program to the Statistics PhD program may apply any Basic exams which they passed at the PhD level to their PhD program exams.

Syllabi for the exams detailed below are contained in the Graduate Handbook. Past exams may be found on the department web page.

Failure to complete any exams by the time limits given below will result in termination of the student in their program at the end of that semester (usually the spring semester).

Applied Mathematics MS

The Applied Mathematics MS program currently has no examination requirements.

Statistics MS

Students in the Statistics MS program must either complete at least one credit of Statistical Consulting (typically STAT 598C) or pass two exams at the MS level from among the three Basic exams: Applied Statistics, Probability, Statistics. These exams must be completed by January of the student’s second year in the program. There is no penalty for attempting and not passing the third exam.

Statistics PhD

Students in the Statistics PhD program must pass all three Basic exams (Applied Statistics, Probability, Statistics) at the PhD level by January of the student’s second year. After completing those exams, statistics PhD students take a written exam on advanced statistics and an oral exam on statistics literature. The written exam has two versions, one covering advanced probability theory and statistics and asymptotic theory, and the other covering advanced probability theory and statistics and linear models. The advanced statistics exam version I is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 705. The advanced statistics exam version II is based on advanced topics in Stat 607 and Stat 608, and topics from Stat 725. The two versions are offered in alternate years depending on which of Stat 705 and Stat 725 is offered in a year.

For the literature-based oral exam, students need to select an exam committee consisting of three faculty, one of whom is designated as the chair. With the committee’s help, they will then choose a topic for the exam. This can be the topic of a previous oral exam (the Statistics Coordinator will have a list of past exam topics), or another topic chosen in consultation with the primary faculty member and agreed to by the two secondary faculty. Students are then given references on the chosen topic to read. The exam is in the form of an oral presentation and responding to questions in front of the exam committee.

In order to take the literature-based exam, a student is responsible for forming an exam committee by the end of September for a January exam, or by the last day of spring classes for an August exam. The GPM and the SCA must be notified of the committee members and topics by that date. Decisions on passing the exam are by unanimous consent of the exam committee, to be confirmed by the GAC. After the GAC makes its determination, the student will be notified of the result via a memo from the GPD sent by the GPM. A student who does not pass will have one more chance to pass the literature-based exam. The second attempt may be on the same or a different topic.

Mathematics PhD

Students in the Mathematics PhD program must pass three written exams by January of the student’s second year. One of these exams must be Advanced Calculus/Linear Algebra, which the student is expected to begin taking in their first semester and continue taking until passed. The remaining two exams may be chosen from among Algebra, Analysis, Applied Mathematics, Stochastics, Topology. (With the approval of the GPD, Mathematics students may also take the written Advanced Statistics exam in place one of these two exams.) These correspond to the regularly offered 600-level course sequences. Students are allowed to take up to three exams during any exam period. There is no penalty for attempting and not passing additional exams.

After completion of the written exams, students should begin to prepare for the oral examination. This examination may be attempted at most twice and must be passed by the mid-semester date of the student’s sixth semester in the program.

1. By the mid-semester date of a student’s fifth semester, they must name a three person exam committee of faculty in the department. One member will be designated as the chair. At most one member of the committee can be a Visiting Assistant Professor.
2. The student and the committee will draw up a list of topics for the exam and agree on a date and time for examination.
   1. The list should be roughly equivalent to 6 credits worth of material selected from 9 credits worth of courses.
      1. Typically the 9 credits will break down as 3 credits from a second year course, 3 from a reading course with a member of the committee and 3 from either source.
      2. The topic list will then be further refined to reflect approximately two thirds of the material from each course.
   2. The committee member(s) responsible for second year course material need not be the actual instructor of the course which the student took, although they should be qualified to teach it.
   3. A template topic form can be obtained from the GPM. The completed form must be provided to the GPM at least one month before the scheduled exam date. The GPM will provide it to the GPD and all committee members for approval.

The examination itself will be governed by the following rules:

1. The exam may be a combination of a presentation by the student and questions from the committee, with the presentation portion not to exceed thirty minutes; or it may consist entirely of questions.
2. The exam length will be between ninety minutes and two hours depending on the judgment of the committee.
3. The committee will decide after the exam on a recommendation to the GAC. A passing recommendation must be a unanimous decision of the committee.
   1. The chair of the committee shall promptly submit a short (approximately one half to one page) review of the exam to the GAC explaining the recommendation.
   2. The GAC will determine whether or not to accept the recommendation of the committee. The GAC retains the ultimate authority to determine the results of the exam but expects to override the committee’s recommendation only in unusual circumstances.
   3. The GPM will send the student a memo from the GPD with the final decision of the GAC.