Applied Mathematics (PhD)

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Application deadline: December 1

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

Screening Procedure

The screening examination consists of four examinations covering the subject content of: MATH 502a Numerical Analysis or MATH 555a Partial Differential Equations ; MATH 505a Applied Probability (or, at the student’s discretion, MATH 507a Theory of Probability ); MATH 525a Real Analysis ; and MATH 541a Introduction to Mathematical Statistics .

The department offers the examinations twice a year, at the end of summer and at the beginning of the spring semester. All four parts of the screening examination must be attempted by the end of the third semester (not counting summer sessions) in the program. The students may take each of the exams as many times as they wish, but three of the exams must be successfully completed by the end of the fourth semester (not counting summer sessions) and all four must be successfully completed by the end of the sixth semester in the program. 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 consisting of an adviser and four other faculty members, including at least one from another department.

Qualifying Examination

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 1 week before the qualifying examination.

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

Course Requirements

The student must complete, with no grade lower than B, a minimum of 60 units of courses carrying graduate credit and approved by the qualifying exam 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 504a Numerical Solution of Ordinary and Partial Differential Equations Units: 3
MATH 504b Numerical Solution of Ordinary and Partial Differential Equations 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 555a Partial Differential Equations Units: 3
MATH 565a Ordinary Differential Equations Units: 3
MATH 574 Applied Matrix Analysis Units: 3
MATH 576 Applied Complex Analysis and Integral Transforms Units: 3
MATH 580 Introduction to Functional Analysis Units: 3
MATH 585 Mathematical Theory of Optimal Control 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 of B (A = 4.0) or lower will not be accepted and, at most, two grades of B will be accepted. A PhD candidate may petition the department for transfer of additional credit, after he or she passes the qualifying examination.

Foreign Language Requirement

The student must demonstrate a reading comprehension of mathematics in one language (other than English) in which there is a significant body of research mathematics (such as Chinese, French, German, Japanese and Russian) by passing a written examination, administered by the Mathematics Department, in translation of mathematical content.

Dissertation

Following passage of the screening examination and approval of a dissertation topic by the qualifying exam committee, the student begins research toward the dissertation under the supervision of the dissertation committee. The primary requirement of the PhD is an acceptable dissertation based on a substantial amount of original research conducted by the student.

Research Areas

Opportunities for research are available from the faculty in several areas of applied mathematics with an emphasis on: computational biology, control theory, financial mathematics, mathematical neurosciences, numerical analysis, optimization, scientific computing, statistical genetics, statistics and stochastic differential equations.