Ph.D. in Operations Research
|Major Code: 9074||Degree Awarded: Doctor of Philosophy|
|Age Restriction: N||Admission status: graduate|
|Delivery Mode/s: classroom only||Location/s: main campus|
|Admission Materials: 3 letters of recommendation, résumé, objectives|
The doctor of philosophy program provides a more advanced level of education, as well as demonstrated ability to perform independent research. These additional strengths should qualify the graduate for vital positions of leadership in industry, business, government and academia.
An applicant for the doctoral program will normally have completed a master's degree in operations research or a related discipline. If the master's degree is not in operations research, then the student will be required to take the core courses for Florida Tech's master's degree in operations research. These courses may be used toward fulfilling the credit requirements for the Ph.D. in operations research. Students will also be required to pass a written qualifying examination equivalent to Florida Tech's master's final program examination.
General admission requirements and the process for applying are presented in the
The degree of doctor of philosophy (Ph.D.) is conferred primarily in recognition of the breadth of scientific accomplishment and the power to investigate scientific problems independently, rather than for the completion of a definite course of studies. Every course in a student's program of study is evaluated not only as to content, but also as to the way in which it complements other courses and furnishes breadth and depth to the program. The work should consist of advanced studies and scientific research that lead to a significant contribution and knowledge of a particular area.
The doctoral program in operations research requires a minimum of 72 semester credit hours after the bachelor's degree or 42 semester credit hours after the master's degree. Students entering the Ph.D. program with a bachelor's degree must follow the master of science degree requirements listed above for 30 semester credit hours. Students entering the Ph.D. program with a master's degree in operations research, or continuing doctoral students with 30 credit hours equivalent to master's degree requirements in operations research must take must take six 5000- or 6000-level mathematics course onsite at Florida Tech (equivalent to 18 semester credit hours).
A course used for a master's degree cannot be used to fulfill the doctoral requirements. Transfer course substitutions must be approved by the department head. All students must successfully complete a preliminary examination; a series of three qualifying written examinations and one oral examination; and present and orally defend a written dissertation proposal.
In addition, all students must successfully complete a virtual written grant proposal and defend it orally; submit a written dissertation and defend it orally; and complete a minimum of 24 semester credit hours of dissertation research.
The individual doctoral program of study must be approved by the student's doctoral committee and the program chair. Students who have not taken
The doctoral program in operations research does not fall within the traditional boundaries of a single discipline. The scope is broad and interdisciplinary. Consequently, every course in a student's program of study is evaluated in terms of how it complements other courses and provides breadth and depth to the program. Considerable latitude is permitted in course selection, provided the core requirements for operations research/mathematics/computation are met. The remaining courses are selected in collaboration with the doctoral committee according to the interests and research objectives of the student.
MTH 5301 Numerical AnalysisCredit Hours: 3Includes Gaussian elimination and solution of linear systems of equations, root finding methods, systems of nonlinear equations, interpolation, numerical integration, initial value problems for ODEs and fast Fourier transform.
MTH 5320 Neural NetworksCredit Hours: 3Introduces architectures, algorithms and applications. Includes single and multilayer perceptrons, counterpropagation, Kohonen self-organization, adaptive resonance theory, neocognition, probabilistic neural networks and Boltzmann machines with and without learning, recurrent neural networks.
ORP 5050 Discrete System SimulationCredit Hours: 3Covers the principles of building and using a discrete event simulation; construction and statistical testing of random variate generators; statistical analysis and validation of results; design of simulation projects; and variance reduction methods.Requirement(s):Instructor approval or prerequisite course
Each student must take a preliminary examination by the end of the first year (offered twice a year). The examination includes the calculus sequence, linear algebra and probability/statistics, and may be retaken only once. A passing grade on the preliminary examination is 80 percent, and students who score 60-80 percent will continue with the master's program.
Before acceptance to the first proposal defense, students must take the series of qualifying comprehensive examinations (three written, two-hour examinations and one oral examination) on three topics chosen with the approval of their major advisor, and based on the student's coursework. Written examinations must be taken within one week, followed by the oral examination within two weeks after passing the written examinations. Passing grades for each of the qualifying examinations is 75 percent and a failed examination should be retaken within three weeks. Any examination may be retaken only once. Students who fail the written qualifying examination series may earn a master's degree on passing a final program examination. Further examination and committee requirements include:
- Examinations taken after completion of coursework.
- At least 60 days before the examination series, the examination committee must be formed, the corresponding document signed by all committee members and the department head, and filed with the graduate school.
- The examination series must be taken within a three-week period.
- The oral examination should include advanced topics in the area(s) of the proposed research at the discretion of student's advisor.
The doctoral dissertation includes:
- Two proposals
- Dissertation coursework (a minimum of 24 credit hours)
The first proposal will be based on forthcoming research. A proposal defense must be preceded by at least three credit hours of research (six hours are recommended). A student can take as many hours as needed for the completion of the proposal defense. However, only a maximum of nine credit hours will be counted toward the dissertation. A minimum of 15 credit hours of dissertation must be taken after the proposal defense.
At least 60 days before the proposal defense, the dissertation committee must be formed unless it is identical to the examination committee. In the former case, a corresponding document signed by all dissertation committee members must be filed with the graduate school. On successful oral defense of the proposal, the student is allowed to continue their research.
Before the dissertation defense, the student defends the second proposal, which must include a virtual submission of a written grant proposal to a funding agency (such as NSF) and approved by the dissertation committee, followed by an oral presentation and discussion. The topic of the research must be related to the dissertation.
The dissertation is expected to represent original research that expands the boundary of knowledge in modern mathematics. Before the defense, the student is expected to present at a conference and have at least one paper published or accepted for publication in an established academic journal with ranking.
The dissertation must be written and orally defended. A written thesis of the dissertation must be sent to each committee member at least 30 days before the scheduled defense.