Mathematics (PhD)

Application deadline: December 15

Completion of the program requires a maximum effort by the student for a minimum of four years of full-time work.

Screening Procedure

The screening procedure consists of written examinations covering core mathematics content. Student must pass three written exams chosen from among the following five core subjects:

Algebra
Analysis
PDE
Probability
Topology

The department offers the examinations twice a year, prior to the beginning of the Fall and Spring semesters.

Either the Algebra or Analysis examination must be successfully completed by the end of the second semester in the program. All of the examinations must be successfully completed by the end of the fourth semester.

The qualifying examination should follow one or two semesters after the successful completion of the screening procedure.

Qualifying Exam Committee

No later than at the end of the first semester after passing the screening procedure, the student must form a qualifying exam committee. The committee must consist of an adviser (committee chair) and four other faculty members, including at least one from another department.

Qualifying Examination

The qualifying examination consists of written and oral components.

The written portion of the qualifying examination consists of a PhD dissertation proposal. This document (6 pages minimum) should include: an introduction and overview of the area of research, a statement of the proposed research problem, literature survey, proposed approach including techniques or methods to be employed and references. No preliminary results are required. This research proposal should be submitted to the qualifying exam committee at least one week before the oral component of the exam.

The oral portion of the qualifying examination consists of a presentation of the PhD dissertation proposal and examination by the committee. The student must demonstrate research potential.

The student must register for MATH 794a in the semester immediately following successful completion of the qualifying examination.

Course Requirements

The student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit. Courses outside of the Mathematics Department must be approved by the Graduate Committee.

Required Courses

The following courses must be completed with a grade of B or higher. Students may opt to pass the written screening exam, at the PhD level, in lieu of the course.

MATH 510a Algebra Units: 3
MATH 525a Real Analysis Units: 3
MATH 540 Topology Units: 3
MATH 794a Doctoral Dissertation Units: 2
MATH 794b Doctoral Dissertation Units: 2

Additional courses

Five additional courses from the following list must also be completed:

MATH 502a Numerical Analysis Units: 3
MATH 505b Applied Probability Units: 3
MATH 507a Theory of Probability Units: 3
MATH 510b Algebra Units: 3
MATH 520 Complex Analysis Units: 3
MATH 525b Real Analysis Units: 3
MATH 532 Combinatorial Analysis Units: 3
MATH 533 Algebraic Combinatorics Units: 3
MATH 535a Differential Geometry Units: 3
MATH 535b Differential Geometry Units: 3
MATH 540 Topology Units: 3
MATH 541a Introduction to Mathematical Statistics Units: 3
MATH 555b Partial Differential Equations Units: 3
MATH 565a Ordinary Differential Equations Units: 3

Additional Requirements

Transfer of Credit

No transfer of credit will be considered until the screening examination is passed. A maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the PhD. A grade lower than B will not be accepted and at most one grade of B will be accepted.

Dissertation and Defense

Following successful completion of the screening procedure and approval of a dissertation topic by the chair of the student’s qualifying exam committee, the student proceeds with research towards the dissertation.

The student must form a dissertation committee consisting of at least three members, including the thesis advisor (committee chair) and a member outside the mathematics department. The PhD thesis, based on a substantial amount of original research conducted by the student, must be defended and approved by the dissertation committee.