### Ph.D. Examinations

#### Ph.D. Preliminary Examinations

Students entering the Ph.D. program must pass two of the following written and/or oral examinations:

- Prelim AN: A two-hour Ph.D. Preliminary Examination in Analysis on material similar to that in Math 5307.
- Prelim LA: A two-hour Ph.D. Preliminary Examination in Linear Algebra on material similar to that in Math 5333.
- Prelim STAT: A two-hour Ph.D. Preliminary Examination in Statistics on material similar to Math 5312 & Math 5313.

Students are expected to pass Preliminary Exams within the first year to maintain their GTA stipend. Only students in Statistics & Data Science tracks are allowed to take Prelim STAT.

All of the Ph.D. Preliminary Examinations are offered twice a year in January and August.

#### List of Prelim Dates for January 2021

- Tuesday, January 12, 2021, 10:00 am - 12:00 noon

Prelim: Linear Algebra - Thursday, January 14, 2021, 10:00 am - 12:00 noon

Prelim: Analysis - Friday, January 15, 2021, 10:00 am - 12:00 noon

Prelim: Statistics

**For Jan. 2021 online exams, please email Dr. Ren-Cang Li to register.**

Requests for disability accommodations should be submitted informally to the Chair of the Graduate Affairs Committee. Documentation authorizing said disability will be required from the Office of Disabilities.

#### Diagnostic Evaluation

A diagnostic evaluation of a Ph.D. student is performed by a committee of three composed of the potential advisor and two other faculty members in the related area for the purpose of making sure the student is ready for his/her dissertation research in the chosen area.

Before the evaluation, the student should ask the potential advisor about the evaluation range and then the potential advisor will give the student a list of research papers or a list of mathematical questions, or equivalent from which questions are derived. The potential advisor chairs the evaluation.

To be qualified to take a diagnostic evaluation, the student must already have passed two Prelim exams and must also be in good academic standing.

Diagnostic evaluation must occur as soon as possible after passing two Prelim exams and must be completed by the end of the 3rd long semester for PhD student, and by the end of the 4th long semester for BS-PhD fast track student to be considered a Ph.D. student of good standing.

Each student can take no more than 2 attempts of the diagnostic evaluation.

#### Ph.D. Comprehensive Examination

Students must pass a Ph.D. Comprehensive Examination. The content and format (oral/written) of this examination will be at the choosing and under the sole direction of the student's Ph.D. Dissertation Committee, but it should be after the completion of a majority of the core requirements.

For an oral presentation by the student before the comprehensive examination committee, the student will prepare and make a brief presentation of a research proposal or a report based on a research paper related to his or her dissertation area.

The presentation will be followed by questioning from the committee members. Questions will likely focus on, but not be restricted to, one or more components of the following:

- the presentation (i.e., the research proposal or report)
- the specialized field of the proposed dissertation area
- current research periodicals/monographs related to the presentation
- general core courses of the Ph.D. curriculum

Written presentation/examinations are similar in coverage except that they are conducted in written form.

A student will be allowed to take the Comprehensive Examination a maximum of two times, but a repeat must be done no later than the following long semester.

GRANDFATHERING: Those Ph.D. students who entered the program prior to Spring 2007 may choose between the format described here and the old format.

#### Ph.D. Dissertation Examination

Students in every degree plan must pass a final Ph.D. oral examination based on his or her doctoral dissertation.

For inquiries about the Ph.D. Program in Mathematics, send an email to the Mathematics Graduate Program Advisors.