The Ph.D. in Systems Science and Mathematics is an academic doctoral degree designed mainly for full-time students interested in an academic, laboratory, and/or industrial research and development career in a specialized area of systems, control, or applied mathematics. 

 

 

Students pursuing the degree Doctor of Philosophy in Systems Science and Mathematics must complete a minimum of 72 credit hours of post-baccalaureate study consistent with the residency and other applicable requirements of Washington University and the Graduate School of Arts and Sciences. These 72 units must consist of at least 36 units of coursework and at least 24 units of research, and may include work done to satisfy the requirements of a master’s degree in a related discipline. Up to 24 units may be transferred to Washington University from another institution.

 

There are seven stages to the completion of the requirements for the degree Ph.D. in Systems Science and Mathematics. Each candidate for the degree must:

 

 

The Ph.D. degree should ordinarily take no more than five years to complete, for students who enter the program with a baccalaureate degree. While individual circumstances will vary, the typical timeline will be as follows:

 

            Year 1:             Coursework and written qualifying examination

            Year 2:             Coursework, preliminary research, research advisory committee selection

            Year 3:             Coursework and preliminary research examination

            Year 4:             Research

            Year 5:             Research, completion of dissertation, and final oral examination

 

Students who enter the program with a master's degree may be able to shorten this timeline by one year or more.

 

 

 

The following are required core courses for Ph.D. in SSM that are specifically required by name and number:

 

ESE 520:         Probability and Stochastic Processes

ESE 551:         Linear Dynamic Systems I

ESE 553:         Nonlinear Dynamic Systems

Math 4111:      Introduction to Analysis

 

In addition, at least two courses from the following list must be taken:

 

ESE 516:         Optimization in Function Space

ESE 544:         Optimization and Optimal Control

ESE 552:         Linear Dynamic Systems II

ESE 556:         Computational Methods in Systems

 

 

All other courses used to satisfy the 36-hour coursework requirement must be technical courses at the senior level or above, and must be deemed relevant to the field of systems science and mathematics. These may include courses from the departments of Electrical and Systems Engineering; Mathematics; Physics; Biology; Computer Science and Engineering; Energy, Environmental, and Chemical Engineering; Mechanical and Aerospace Engineering; Biomedical Engineering; or other departments as appropriate. 

 

 

 

Schedule: The written qualifying examination will be given once a year, during the summer break, usually in August before the start of classes for the fall semester. SSM doctoral students are expected to take the exam after their first academic year of the program has been completed. 

Structure: The written examination will consist of three 2-hour examinations chosen by the student from a menu of 7 topics. 

Exam Topics: Each examination will cover theoretical material from both undergraduate and graduate level courses and is based on a syllabus of topics for each specific area. The areas are

1.      Signal Processing and Communication Theory.

2.      Probability and Statistics

3.      Linear Systems Theory

4.      Nonlinear Systems Theory

5.      Optimization and Computational Methods

6.      Electromagnetic Engineering

7.      Electronic Devices and Circuits

Grading: Students will receive one of three grades on the exam as a whole: Pass, Marginal Performance, or Fail.   An exam grade of Pass will be considered evidence of satisfactory progress in the first year of the Ph.D. program.

Retake Policy: Students awarded a Marginal Performance on the first attempt may take the examination a second time after one year's time. Students retaking the examination must take the entire examination, but may change topics if they wish. Students who fail the exam on the first attempt will not be allowed to retake the exam, and will be asked to leave the doctoral program. Students not awarded a Pass on the second attempt will be asked to leave the doctoral program.

 

The preliminary research examination is an oral examination in which students make a presentation on their preliminary research and closely related topics, then field questions from the Research Advisory Committee (see description below) in a closed session. Students are expected to show satisfactory progress in the initial stages of a program of original and creative research, to demonstrate mastery of the state-of-the-art in their particular field of interest, and to present tentative plans for the next stages of the research.

 

 

The residency requirement applies to all students pursuing Ph.D. degrees at Washington University. During the satisfactory completion of 72 credit hours, at least 48 credit hours must be earned at Washington University. At least one academic year as a student taking full-time coursework (at least nine units in the Fall and nine units in the Spring) is required.   Although circumstances may vary, the Department of Electrical and Systems Engineering encourages full-time study throughout completion of the degree requirements. Any exception to the residency requirement must be approved by the Dean of the Graduate School of Arts and Sciences.

 

 

Ph.D. students must accumulate at least 14 hours of teaching at the basic level, and four hours of teaching at the advanced level. This teaching requirement is met through teaching laboratories, help sessions, lectures in undergraduate classes, and graduate seminars.

Doctoral Dissertation

Working closely with his or her research supervisor and the Research Advisory Committee (see description below), the candidate will be expected to make an original contribution to knowledge in some branch of the field of systems science and mathematics. The work must be of sufficient scope and quality to be publishable, perhaps as several individual papers, in recognized archival engineering, science, or mathematical journals. The completed body of work will be written in the form of a doctoral dissertation, which upon acceptance becomes a publicly available document archived by the Washington University libraries.

 

 

At the completion of his or her dissertation, the candidate will make a one-hour presentation of the key research results in a public forum, and then field questions from the Dissertation Examination Committee (see description below) in a closed session.

 

All tenured or tenure-track faculty members of the Department of Electrical and Systems Engineering are participants in this doctoral program and may serve as academic advisors, research supervisors, and/or doctoral committee members. Senior faculty members may also serve as academic advisors, research supervisors, and/or doctoral committee members, with the approval of the Dean of the School of Engineering and Applied Science and the Dean of the Graduate School of Arts and Sciences.

 

            The academic advisor is the faculty member who oversees the progress of the student and is responsible for ensuring that all program requirements are met. The academic advisor must be a tenured or tenure-track faculty member in the Department of Electrical and Systems Engineering.

           

            The research supervisor is the faculty member who works most closely with the student in carrying out the dissertation research. Tenured or tenure-track faculty members at Washington University, either within or outside of the Department of Electrical and Systems Engineering, may serve as research supervisor. Ordinarily, if the research supervisor is a faculty member in the ESE Department, that person serves as academic advisor as well.

 

            There are two committees associated with the each doctoral candidate, both chaired by the academic advisor. These are:

 

1.      Research Advisory Committee. The Research Advisory Committee comprises three tenured or tenure-track faculty members from the Department of Electrical and Systems Engineering. The Research Advisory Committee is appointed in the student's second or third year and is responsible for overseeing all aspects of the student's doctoral work, including conducting the preliminary research examination, signing the Title, Scope, and Procedure of Dissertation form, and reading and approving the dissertation. Additional faculty members from any part of Washington University may be included. If the research supervisor is from outside the ESE Department, then he or she must be included on this committee.

 

2.      Dissertation Examination Committee. The Dissertation Examination Committee is a panel of at least six, five of which should be tenured or tenure-track faculty members, including at least four from the ESE Department, and at least two from outside the ESE Department, that conducts the final oral examination. Ordinarily this committee comprises the Research Advisory Committee and three additional members. Faculty members from outside of Washington University may serve on this committee, with the approval of the Dean of the Graduate School of Arts and Sciences.