Applied 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 applied mathematics content. Students must pass three written exams for the following core subjects:

Applied Probability
Real Analysis
Partial Differential Equations

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

At least one of the screening examinations 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 two or three 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 (10 pages minimum) should include: introduction, statement of the problem, literature survey, methodology, summary of preliminary results, proposed research, references, appendix (including one or two fundamental references). This should be submitted to the department at least one week before the qualifying examination.

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.

These must include
MATH 794a Doctoral Dissertation Units: 2
MATH 794b Doctoral Dissertation Units: 2

And six courses from the following:

MATH 502b Numerical Analysis Units: 3
MATH 505b Applied Probability Units: 3
MATH 507b Theory of Probability Units: 3
MATH 509 Stochastic Differential Equations Units: 3
MATH 520 Complex Analysis Units: 3
MATH 525b Real Analysis Units: 3
MATH 530b Stochastic Calculus and Mathematical Finance Units: 3
MATH 532 Combinatorial Analysis Units: 3
MATH 541b Introduction to Mathematical Statistics Units: 3
MATH 542 Analysis of Variance and Design Units: 3
MATH 545 Introduction to Time Series Units: 3
MATH 547 Mathematical Foundations of Statistical Learning Theory Units: 3
MATH 550 Statistical Consulting and Data Analysis Units: 3
MATH 555b Partial Differential Equations Units: 3
MATH 565a Ordinary Differential Equations Units: 3
MATH 574 Applied Matrix Analysis Units: 3
MATH 580 Introduction to Functional Analysis Units: 3
MATH 585 Mathematical Theory of Optimal Control Units: 3
If a student receives a grade of B- or lower in any of the required courses, the requirement can be waived upon passing the screening exam for the course at the master’s level or higher.

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 below B will not be accepted and at most one grade of B will be accepted.

Dissertation Committee 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.