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The ORFE program places a strong emphasis on quantitative methods and mathematical modeling. Students in ORFE develop a unique set of skills that build upon a solid foundation in probability, statistics, and optimization.
The theoretical foundations of ORFE are of central importance in many complex problems in engineering and science. Students and faculty in ORFE work in a broad range of application areas, such as finance, energy, health, risk analysis, biostatistics, genomics, machine learning, operations research, stochastic networks, signal and image processing, automated vehicle control systems, optimal design of engineered systems, and homeland security.
ORFE faculty is renowned within the field. They have won numerous awards for their research and are fellows of the major scientific societies in their research areas. Graduates of the Ph.D. program work in academia, research organizations, and industry. Many of them have taken positions at top universities.
The department offers two degree programs: the Doctor of Philosophy (Ph.D.) in Operations Research and Financial Engineering, and a Master of Science in Engineering (M.S.E.). These programs provide a great deal of flexibility for students in designing individual plans of study and research according to their needs and interests. The department is a major participant in the Master of Finance (M.Fin.) program offered through the Bendheim Center for Finance.
The Ph.D. is formulated to prepare students for research and teaching. The aim of the program is to provide a strong disciplinary background in one of the core areas of research in the department. The emphasis is on the theoretical foundations, mathematical models, and computational issues in practical problem solving. Current teaching and research activities include probability and stochastic processes, stochastic analysis, mathematical statistics, machine learning, analysis of big data, linear and nonlinear optimization, stochastic optimization, convex analysis, stochastic networks and queueing theory, mathematical and computational finance, and financial econometrics. Application areas of current interest to faculty include finance, energy, health, biostatistics, genomics, machine learning, and engineering problems.
The departmental faculty are affiliated with a number of interdisciplinary programs and centers, including the Program in Applied and Computational Mathematics, the Bendheim Center for Finance, the Andlinger Center for Energy and the Environment, the Princeton Environmental Institute, and the Center for Statistics and Machine Learning. Students may combine their departmental work with courses and research opportunities offered by such programs and centers and also by other departments including Computer Science, Economics, and Mathematics.
By the end of the first year, the student is expected to narrow his or her area of doctoral research and choose an appropriate adviser. The second year of study starts with a qualifying examination and is spent with advanced course work, research projects, and preparation for the general examination. The general examination is normally taken at the end of the second year.
Beyond the general examination, the completion of a dissertation usually takes two to three years. Upon acceptance of the dissertation by the department, the candidate for the Ph.D. takes the final public oral examination, which is primarily a defense of the dissertation.
The student, in consultation with an informal faculty adviser and the director of graduate studies, develop a course plan. A typical plan consists of six courses, emphasizing the foundations of the program, probability, statistics, and optimization.
The following are considered core courses:
Qualifying exams in these areas will be offered in September of the student’s second year.
Each student must satisfy qualifying requirements in 4 of the 6 core classes. If a student’s grade in a core course taken in the first year is A- or better, the student is exempt from taking the qualifying exam in that area. Before the exam, the student must have acquired demonstrated competence in real analysis at the level of MATH 314.
The optimization exams are based on ORF 522 and ORF 523. The probability exams are based on ORF 526 and ORF 527. The statistics exams are based on ORF 524 and ORF 525.
The results of the qualifying exam are determined by a vote of the faculty.
By the end of the first year, the student is expected to narrow his or her area of doctoral research and choose an appropriate adviser.
ORFE students take the general exam in April or May of their second year. By that time, the students have met the qualifying examination requirements, have taken and passed ORF 509, have taken or are currently enrolled in ORF 510 and have passed with a B+ or higher two advanced courses. The student must have shown adequate progress on research and an acceptable level of understanding of his or her area of specialization.
The general exam consists of two parts, a written and an oral part, both covering the student’s primary area of specialization. The written part requires taking and passing with a B+ or higher two approved advanced courses at the graduate (500) level beyond the 4 core classes counted for the qualifying exam. These two courses must be approved by the student’s adviser and the DGS.
For each student, an examining committee is selected by the student and adviser. It has to be approved by the department chair. The committee consists of the student’s adviser and two additional ORFE faculty or affiliated faculty. The committee will administer the oral exam, evaluate the student’s performance in research and overall knowledge of his/her field, and make a recommendation to the department faculty. A departmental faculty vote determines the final outcome. The oral exam may be up to 2 hours in length.
Before the exam, the student is required to submit a comprehensive written report on the research conducted in ORF 509-510. It is due one week before the exam takes place. The report serves as the basis for the student’s presentation. The purpose of the presentation is to explain the research the student has done so far and plans to do in the future. Examining faculty may ask questions on the presentation and on any other material deemed appropriate for a comprehensive examination.
The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination. It may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.
Upon completion and acceptance of the dissertation by the department, the candidate will be admitted to the final public oral (FPO) examination.
The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.
The ORFE department is geared towards educating students whose ultimate goal is to get a Ph.D. The admission rate for the M.S.E. degree is very low. Applicants interested in an M.S.E. degree from ORFE are urged to identify and contact a faculty member in whose area of research they would like to work. Admission will be based on not only qualifications of applicant, but also requires support of at least one faculty member who expresses an interest to supervise the applicant. Students enrolled in this program are eligible for financial support in the form of research or teaching assistantships if such funds are available. Applicants who are primarily interested in a Master's degree in Finance should apply for the Master in Finance at the Bendheim Center for Finance. The School of Engineering provides more information regarding the Master of Science in Engineering program.
The M.S.E. program has a strong research focus reflected in the requirement of a thesis. The M.S.E. degree is usually completed within two academic years of full-time study.
The course requirements are fulfilled by successfully completing ten one-semester courses, two of which are required research courses (ORF 509 and 510).
The M.S.E. program has a strong research focus reflected in the requirement of a thesis. Upon completion and acceptance of the thesis by the department, the candidate will be admitted to the final defense, administered by at least two faculty members.
Rene A. Carmona
Alain L. Kornhauser
William A. Massey
René A. Carmona
John M. Mulvey
Warren B. Powell
K. Ronnie Sircar
Robert J. Vanderbei
Ramon van Handel
Amir Ali Ahmadi
Yacine Aït-Sahalia, Economics
Markus K. Brunnermeier, Economics
Weinan E, Mathematics
Sanjeev R. Kulkarni, Electrical Engineering
H. Vincent Poor, Electrical Engineering
Paul D. Seymour, Mathematics
Christopher A. Sims, Economics
Yakov G. Sinai, Mathematics
John D. Storey, Lewis-Sigler Institute for Integrative Genomics
Wei Xiong, Economics
Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.