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. Through extensive study and 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 the solution of 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 course work and research. The curriculum consists of three required core courses, three required concentration foundation courses, a course in scientific computing and high-performance computing (HPC), three elective courses focused on the student’s chosen research concentration, and a doctoral dissertation. Elective courses for the mathematical modeling program are available from within the School of Mathematical Sciences as well as from other graduate programs at RIT, which can provide application-specific courses of interest for particular research projects. A minimum of 30 credits hours of course work is required. In addition to courses, at least 30 credit hours of research, including the Graduate Research Seminar, and an interdisciplinary internship outside of RIT are required.
Students develop a plan of study in consultation with an application domain advisory committee. This committee consists 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 ensures that all students have a roadmap for completing their degree based on their background and research interests. The plan of study may be revised as needed.
All students must pass two qualifying examinations to determine whether they have sufficient knowledge of modeling principles, mathematics, and computational methods to conduct doctoral research. Students must pass the examinations in order to continue in the Ph.D. program.
The first exam is based on the Numerical Analysis I and the Mathematical Modeling courses. The second exam is based on the student's concentration foundation courses and additional material deemed appropriate by the committee and consists of a short research project.
Dissertation research adviser and committee
A dissertation research adviser is selected from the program faculty based on the student's research interests, faculty research interest, and discussions with the program director. Once a student has chosen a dissertation adviser, the student, in consultation with the adviser, forms a dissertation committee consisting of four members, including the dissertation adviser. The committee includes, in addition to the dissertation adviser, one other member of the mathematical modeling program faculty and an external chair appointed by the dean of graduate education. The external chair must be a tenured member of the RIT faculty who is not a current member of the mathematical modeling program faculty. The fourth committee member must not be a member of the RIT faculty and may be a professional affiliated with industry or with another institution; the program director must approve this committee member.
The main duties of the dissertation committee are adminstering both the candidacy exam and final dissertation defense. In addition, the dissertation committee assists students in planning and conducting their dissertation research and provides guidance during the writing of the dissertation.
Admission to candidacy
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. 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 specific doctoral-level research project. 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. This examination must be completed at least one year before the student can graduate.
Final examination of the dissertation
The final dissertation examination may be scheduled after the dissertation has been written and distributed to the dissertation committee and the committee has consented 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 consists of an oral presentation of the dissertation research, which is open to the public. This public presentation must be scheduled and publicly advertised at least four 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 immediately deliberates and thereafter notifies the candidate and the mathematical modeling graduate director of the result of the examination.
Mathematical modeling, Ph.D. degree, typical course sequence
|Course||Sem. Cr. Hrs.|
|MATH-602||Numerical Analysis I||3|
|MATH-622, 722||Mathematical Modeling I, II||6|
|Concentration Foundation I, II, III||9|
|MATH-606, 607||Graduate Seminar||2|
|Scientific Computing /HPC Course||3|
|Research and Thesis||9|
|Research and Thesis||7|
|Research and Thesis||6|
|Research and Thesis||6|
|Total Semester Credit Hours||60|
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 course work,
- 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 at least two letters of academic and/or professional recommendation,
- Submit a personal statement addressing educational objectives and research interests, 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.
Mathematical Modeling encompasses a wide variety of scientific disciplines, and candidates from diverse backgrounds are encouraged to apply. If applicants have not taken expected foundational course work, the program director may require the student to take, and succeed in, foundational courses prior to matriculating into the Ph.D. program in mathematical modeling.
Typical expected foundation course work includes calculus through multivariable and vector calculus, differential equations, linear algebra, probability and statistics, one course in computer programming, and at least one course in: real analysis, numerical analysis, or upper-level discrete mathematics.
Financial aid, scholarships, and assistantships
Graduate assistantships and tuition remission scholarships are available to qualified students. Applicants seeking financial assistance must submit all application documents to the Office of Graduate Enrollment Services by January 15 for the following academic year. Students whose native language is not English are advised to obtain as high a TOEFL or IELTS score as possible if they wish to apply for a teaching or research assistantship. These candidates also are encouraged to take the Test of Spoken English in order to be considered for financial assistance.
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.
Maximum time limitations
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.