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(link is external), the Bendheim Center for Finance(link is external), the Andlinger Center for Energy and the Environment(link is external), the Princeton Environmental Institute(link is external), and the Center for Statistics and Machine Learning(link is external). 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:
ORF 522 Linear and Nonlinear Optimization
ORF 523 Convex and Conic Optimization
ORF 524 Statistical Theory and Methods
ORF 525 Statistical Learning and Nonparametric Estimation
ORF 526 Probability Theory
ORF 527 Stochastic Calculus
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.
Information on the Oral Exam
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.
Qualifying for the M.A.:
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.
Dissertation and FPO:
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.
For Ph.D. candidates, tuition and fees during a student’s regular period of enrollment are provided in full from a student’s graduate student financial support, in the form of tuition support from fellowships, assistantships, or external sources.
The annual stipend amount provided to Ph.D. candidates during their regular enrollment is intended to support a single graduate student based on estimated costs. Master’s students or students with spouses and/or dependents may require additional resources to support their living expenses