PhD in Mathematical Modeling
Please Note: This program is currently recruiting its first class, which will begin in fall 2017.
Mathematical modeling is the process of developing mathematical descriptions, or models, of real-world systems. These models can be linear or nonlinear, discrete or continuous, deterministic or stochastic, and static or dynamic, and they enable investigating, analyzing, and predicting the behavior of systems in a wide variety of fields. Every mathematical modeling enterprise has four aspects: the content of the application field, the mathematical formulation and analysis, the analytical and computational methods (which often involve high-performance computing), and the interpretation and analysis of the results. Through extensive research, graduates of this program will have the expertise not only to use the tools of mathematical modeling in various application settings but also to contribute in creative and innovative ways to solve complex interdisciplinary problems and to communicate effectively with domain experts in various fields.
Plan of study
The degree requires at least 60 credit hours of coursework and research. The curriculum consists of three required graduate common courses, three required graduate concentration courses, a course in scientific computing and high-performance computing (HPC), elective courses focused on the student’s chosen research concentration, and a doctoral dissertation. At least 30 credit hours of coursework, including the common curriculum, is required. In addition, at least 30 credit hours of research, including the Graduate Research Seminar and an interdisciplinary internship outside of RIT, is required. At least three years of full-time study or its equivalent in the part-time study is required. Students must pass two qualifying exams (one based on common courses and one on concentration courses) by the end of their second year and a candidacy examination at least one year before completing their dissertation.
Students will develop a plan of study in consultation with an application domain advisory committee. This committee will consist of the program director, one of the concentration leads and an expert from an application domain related to the student’s research interest. The committee will ensure that each student has a roadmap for completing their degree based on the student’s background and research interest. The plan of study may be revised as needed.
Elective courses for the mathematical modeling program are available from within the School of Mathematical Sciences; in addition, the program makes use of elective courses from the doctorate programs in astrophysical sciences and technology, imaging science, color science, and computing and information sciences, as well as courses from additional graduate programs at RIT. These programs provide application domain-specific courses that can be of interest for particular research projects.
Admission to candidacy
The program director serves on the Ph.D. in Mathematical Modeling Admissions Committee, a committee with representatives selected in consultation with the concentration leads.
Each student must pass two qualifying examinations in order to begin thesis work. Their purpose is to determine whether the student has sufficient knowledge of modeling principles, mathematics, and computational methods to conduct doctoral research. The examinations will be administered by a committee that is appointed by the mathematical modeling program director. Students must pass the examinations in order to continue in the Ph.D. program.
The first exam will be based on the Numerical Analysis I and the Mathematical Modeling courses. The second exam will be based on the student’s Concentration Foundation courses and additional material deemed appropriate by the committee. The qualifying examinations will be administered twice each year, typically during winter break and after graduation in the spring.
When a student has developed an in-depth understanding of their dissertation research topic, the Dissertation Committee administers an examination to determine if the student will be admitted to candidacy for the doctoral degree. This examination must be completed at least one year before the student can graduate. The purpose of the examination is to ensure that the student has the necessary background knowledge, command of the problem, and intellectual maturity to carry out the chosen research topic. The examination may include a review of the literature, preliminary research results, and proposed research directions for the completed dissertation. Requirements for the candidacy exam include both a written dissertation proposal and the presentation of an oral defense of the proposal.
Dissertation research adviser
After the student passes the qualifying examinations, the student chooses a dissertation research adviser. In practice, many students will have made this choice, de facto, before the exams, and for such students, this step in the program will simply be an administrative formality.
Once a student has chosen a dissertation adviser, the student, with the advice of the adviser, forms a dissertation committee consisting of four members, including the dissertation adviser. The committee will include, in addition to the dissertation research adviser, one other member who is a member of the SMS faculty and an external chair. The external chair must be a member of the RIT faculty who is not an affiliated faculty of the mathematical modeling program. The fourth committee member must not be a member of the RIT faculty. We expect that committee members who are not members of the RIT faculty will be industrial scientists, engineers, or other researchers, or they can be researchers at other universities or research institutes; however, we impose no particular restrictions on the fourth committee member. The mathematical modeling program coordinator must approve, as committee members, persons who are not members of the RIT faculty. The main duties of the Dissertation Committee are administering both the candidacy exam and final dissertation defense. In addition, the Dissertation Committee should assist the student in planning and conducting their dissertation research and provide guidance during the writing of the dissertation.
Upon entry to the program, students are assigned an academic adviser from the program faculty. By their second year, students declare a Ph.D. adviser. This faculty member will also serve as their primary academic adviser. Upon the formation of the dissertation committee, typically by the end of the student’s third year, the members of the committee will remain in regular contact with the student to ensure steady progress towards completion. The student’s committee will meet once per semester to discuss the progress of the student.
Final examination of the dissertation
The final dissertation examination may be scheduled after the dissertation has been written and distributed to the committee. The Dissertation Committee must also consent to administer the final examination. Copies of the dissertation must be distributed to all members of the Dissertation Committee at least four weeks prior to the final examination. The final examination will consist of an oral presentation of the dissertation research that is open to the public. This public presentation must be scheduled and publicly advertised at least two weeks prior to the examination. After the presentation, questions will be fielded from the attending audience and a private questioning of the candidate by the dissertation committee will ensue. After the questioning, the Dissertation Committee will immediately deliberate and thereafter notify the candidate and the mathematical modeling graduate director of the result of the examination.
Mathematical modeling, Ph.D. degree, typical course sequence
To be considered for admission to the Ph.D. program in mathematical modeling, candidates must fulfill the following requirements:
- Submit official transcripts (in English) for all previously completed undergraduate and graduate coursework,
- Hold a baccalaureate degree from an accredited university,
- Have a minimum GPA of at least 3.0 in the primary field of study,
- Submit scores from the Graduate Record Exam (GRE),
- Submit two professional recommendations, and
- Complete a graduate application.
- International applicants whose native language is not English must submit scores from the Test of English as a Foreign Language (TOEFL). A minimum score of 600 (paper-based) or 100 (Internet-based) is required.
The following list contains the required foundation coursework.
- Calculus through Multivariable and Vector Calculus
- Differential Equations
- Linear Algebra
- Probability and Statistics
- One course in computer programming
- At least one of the following: Real Analysis, Numerical Analysis, or upper-level Discrete Mathematics.
Applicants without sufficient foundational coursework may be admitted conditionally and asked to take up to 9 credits of undergraduate courses. The program director and student will agree in writing on foundation courses the student will be required to take, and succeed in, prior to matriculating into the Ph.D. program in mathematical modeling.
Ph.D. to MS transfer
Students in the Ph.D. program have the option of transferring to and continuing their studies in a master's program administered by the School of Mathematical Sciences, with credit to be given for coursework already taken in the Ph.D. program.
All students in the program must spend at least two consecutive semesters (summer excluded) as resident full-time students to be eligible to receive the doctoral degree. If circumstances warrant, the residency requirement may be waived via petition to the graduate program coordinator, who will decide on the student’s petition in consultation with the adviser and graduate faculty. The request must be submitted at least nine months prior to the thesis defense.
University policy requires that doctoral programs be completed within seven years of the date of the student passing the qualifying exam. All candidates must maintain continuous enrollment during the research phase of the program. Such enrollment is not limited by the maximum number of research credits that apply to the degree.
Program taught in: