Program Overview

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Overview

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 the mathematical modeling Ph.D. 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 are available from within the School of Mathematics and Statistics 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.

Qualifying Examinations

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.

Dissertation Research Advisor and Committee

A dissertation research advisor 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 advisor, the student, in consultation with the advisor, forms a dissertation committee consisting of at least four members, including the dissertation advisor.

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.

Dissertation Defense and Final Examination

The dissertation defense and final 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.

Residency

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.

Curriculum

Mathematical Modeling, Ph.D. degree, typical course sequence

• First Year
  • MATH-602: Numerical Analysis I
  • MATH-606: Graduate Seminar I
  • MATH-607: Graduate Seminar II
  • MATH-622: Mathematical Modeling I
  • MATH-722: Mathematical Modeling II
  • MATH Concentration Courses
  • MATH Elective
• Second Year
  • MATH-751: High-performance Computing For Mathematical Modeling
  • MATH-790: Research & Thesis
  • MATH Concentration Course
  • MATH Electives
• Third Year
  • MATH-790: Research & Thesis
• Fourth Year
  • MATH-790: Research & Thesis
• Fifth Year
  • MATH-790: Research & Thesis

Concentrations

Applied Inverse Problems

• MATH-625: Applied Inverse Problems
• MATH-633: Measure Theory of Elements and Functional Analysis
• MATH-741: Partial Differential Equations I

Biomedical Mathematics

• MATH-631: Dynamical Systems
• MATH-702: Numerical Analysis II
• MATH-761: Mathematical Biology

Discrete Mathematics

• CSCI-665: Foundations of Algorithms
• MATH-645: Graph Theory
• MATH-646: Combinatorics

Dynamical Systems and Fluid Dynamics

• MATH-631: Dynamical Systems
• MATH-741: Partial Differential Equations I
• MATH-831: Mathematical Fluid Dynamics

Geometry, Relativity and Gravitation

• ASTP-660: Introduction to Relativity and Gravitation
• ASTP-861: Advanced Relativity and Gravitation
• MATH-702: Numerical Analysis II

Admissions and Financial Aid

This program is available on-campus only.

• Offered: Fall
• Admit Term(s): Fall
• Application Deadline: January 15 priority deadline, rolling thereafter
• STEM Designated: Yes

Application Details

To be considered for admission to the Mathematical Modeling Ph.D. program, candidates must fulfill the following requirements:

• Learn tips to apply for a doctoral program and then complete a graduate application.
• Submit copies of official transcript(s) (in English) of all previously completed undergraduate and graduate course work, including any transfer credit earned.
• Hold a baccalaureate degree (or US equivalent) from an accredited university or college. A minimum cumulative GPA of 3.0 (or equivalent) is recommended.
• Satisfy prerequisite requirements and/or complete foundation courses prior to starting program coursework.
• Submit a current resume or curriculum vitae.
• Submit a statement of purpose for research which will allow the Admissions Committee to learn the most about you as a prospective researcher.
• Submit two letters of recommendation.
• Entrance exam requirements: None
• Submit English language test scores (TOEFL, IELTS, PTE Academic), if required.

Cost and Financial Aid

An RIT graduate degree is an investment with lifelong returns. Ph.D. students typically receive full tuition and an RIT Graduate Assistantship that will consist of a research assistantship (stipend) or a teaching assistantship (salary).