The Department of Electrical & Systems Engineering (ESE) at Washington University in St. Louis (WUSTL) offers a PhD 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.
Degree Requirements & Timeline
Students pursuing the degree Doctor of Philosophy in Systems Science & 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 & 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 WUSTL from another institution.
There are seven stages to the completion of the requirements for the degree PhD in Systems Science & Mathematics. Each candidate for the degree must:
- Complete at least 36 hours of post-baccalaureate coursework.
- Pass a written qualifying examination, to be taken before the second academic year of the program.
- Pass an oral preliminary research examination, to be completed within two years of passing the written qualifying examination, and at least one year prior to completion of the dissertation.
- Satisfy the general residency requirement for PhD degrees offered by the Graduate School of Arts & Sciences.
- Satisfy the general teaching requirement for PhD degrees offered by the Graduate School of Arts & Sciences.
- Write a doctoral dissertation that describes the results of original and creative research in a specialization within systems science and mathematics.
- Pass a final oral examination in defense of the dissertation research.
- ESE 590 Electrical & Systems Engineering Graduate Seminar must be taken each semester.
The PhD 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 PhD 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 ESE; Mathematics; Physics; Biology; Computer Science & Engineering; Energy, Environmental & Chemical Engineering; Mechanical Engineering & Materials Science; Biomedical Engineering; or other departments as appropriate.
Courses used to satisfy the 36-hour coursework requirement must be in technical courses in electrical engineering or closely related topics. Courses are chosen jointly by the student and his or her academic advisor to meet individual educational objectives, and are subject to the approval of the Graduate Program Steering Committee. Note that neither ESE 501 or ESE 502 count toward the course requirement for this degree.
Written Qualifying Examination
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 PhD 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.
Preliminary Research Examination
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 PhD degrees at WUSTL. During the satisfactory completion of 72 credit hours, at least 48 credit hours must be earned at WUSTL. 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 ESE Department 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 & Sciences.
PhD 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.
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.
Final Oral Examination
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 & 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 & Applied Science and the Dean of the Graduate School of Arts & Sciences.
Students funded by ESE in their first year should choose their academic advisors by the summer of the first year. Academic advisors of ESE PhD students should be tenured or tenure-track faculty members in ESE or hold courtesy appointment in ESE.
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:
- 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.
- 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 & Sciences.