A Firsthand Look at the Novel Ph.D. Program in Mathematical Modeling at Rochester Institute of Technology

The innovative Ph.D. program in mathematical modeling at Rochester Institute of Technology (RIT) accepted its initial cohort of students in 2017. RIT's Ph.D. program is the first in the U.S. to offer a specific degree in "Mathematical Modeling," rather than applied mathematics or another variation with a modeling track. Since its onset, the program—which seeks to fill a niche in the workforce for applied mathematicians and computational scientists—has grown steadily, exposing students to a wide variety of classes, research areas, and hands-on experiences. Applications doubled in the last year alone, likely because increasingly more students are encountering mathematical modeling at the undergraduate level.

SIAM News recently sat down with Nathan Cahill, who has served as the director of RIT’s Ph.D. program in mathematical modeling since 2019. Nathan detailed the program’s origins, explained the structure and organization of relevant coursework and research projects, discussed internship and career opportunities, and shared his vision for the program’s continued evolution in the coming years.

SIAM News: Why did RIT decide to establish a Ph.D. program in mathematical modeling?

Nathan Cahill: We owe a large part of our program’s history to Sophia Maggelakis, current dean of RIT’s College of Science and former head of the School of Mathematical Sciences. She started her career as a mathematics faculty member and recognized a huge need in the workplace for the type of skills that are associated with a mathematical modeling education. Sophia realized that RIT could fill a gap by creating a program that specifically trains students to collaborate with experts in different fields and use mathematics to solve complicated, real-world problems. She broadened our Department of Mathematics and Statistics to a School of Mathematical Sciences, and brought in faculty who did not necessarily have traditional mathematics backgrounds but could involve students in research that applies math modeling to various settings. For instance, my Ph.D. is in engineering science.

In the early 2010s, we began mapping out a prospective Ph.D. program in mathematical modeling. It took a few years to put together a solid proposal and figure out how it would fit within RIT and the broader context of companies and government agencies that hire mathematicians. We finally got approval from the state of New York in 2016 and welcomed our first class of students in 2017.

SN: Was it difficult to assemble a cohesive proposal since faculty backgrounds are so diverse?

NC: We have a very heterogeneous group of faculty members in terms of research application areas, but we all draw on fundamental aspects of bringing mathematics to bear in real-world situations. We all tackle real-world problems in some capacity and work with experts who have domain-specific expertise that we don’t necessarily possess. We think about how we can translate their problems into the language of mathematics; generate ideas based on mathematical tools; and propose mathematical methods to predict, analyze, and/or provide insights. Once we understood that we all have this common foundation, we saw the foundation as something that we can teach graduate students.

SN: How has the program grown since its origin?

NC: We started with about five students in 2017 and admitted five or six students for the first few years, but we’ll probably admit eight or nine this fall. We tell students that it typically takes five years to get through the program; we’re at that five-year point right now and our first two graduates have defended their dissertations. 28 Ph.D. students are currently enrolled across all levels, and 16 of them are women. We have a strong contingent of female faculty and want to build an accessible environment that promotes women in the pipeline of the workforce.

SN: What is the program’s structure?

NC: The first year is entirely coursework. All students take one semester of numerical analysis and a two-semester sequence in mathematical modeling. We also require a one-credit graduate seminar course in both the fall and spring that teaches general research methods and exposes participants to different research areas. In addition, a high-performance computing course introduces students to distributed and parallel computing for various types of problems.

Candidates also choose a concentration in their first year, each of which has several core courses. Possible concentrations include biomedical mathematics, applied inverse problems and optimization, dynamical systems and fluid dynamics, and discrete mathematics, among other topics. Beyond these courses, students must enroll in three electives of their choosing; they can even take graduate courses in other departments.

During their second year, students must take at least three research credits, identify a faculty mentor, and carry out a research project. At the end of that year, an examination of this project determines whether they are ready to begin dissertation research. From then on, it’s basically all dissertation research.

SN: What makes RIT’s math modeling Ph.D. different from a Ph.D. in applied mathematics?

NC: There is of course some overlap, but the thing that sets us apart is that we want our students to learn the process of modeling itself and understand how to talk to experts in specific domain areas. We train students to work collaboratively across disciplines, tease out the problems that domain experts are trying to solve, and establish these problems in mathematical settings. So while our focus does involve applied mathematics, it’s broader in the sense of learning how to set up and build models in the first place.

There is also one component that is fairly unique, especially within mathematics programs: we require all students to complete an interdisciplinary internship. We keep things pretty flexible; our minimum requirement is a paid, full-time position that is outside of the university and at least a term long — either a full semester or eight-10 weeks during the summer. We’ve had students work in pharmaceutical companies, research wings of hospitals, and consulting companies. Some have done great work in national labs or government organizations, including Los Alamos National Laboratory (LANL), Oak Ridge National Laboratory, and the Air Force Research Laboratory. We even allow students to conduct research in the labs of potential experimental collaborators at other universities. It’s been a great experience for them, and many have received offers for further internships.

SN: What sort of qualifications do you look for in prospective students?

NC: Applicants don’t have to be applied math majors to find success in our program. Instead, our admissions committee looks for a specific interest in mathematical modeling and strong evidence of success in undergraduate coursework that is related to linear algebra, probability, differential equations, and the like. We also see whether prospective students have demonstrated that they’re not afraid to get their hands dirty and do some coding. A lot of our applicants have strong research experience, either with faculty members or through the National Science Foundation’s Research Experiences for Undergraduates program, and that’s great. However, we recognize that some students don’t have the opportunity to spend a summer doing research.

As we grow, we hope to attract undergraduates who realize that their passion is not just doing mathematics, but specifically finding ways to apply mathematics to complicated, real-world problems.

SN: What types of careers do students envision for themselves after graduation?

NC: A number of students have found real interest in the government sector, and some have gone to the national labs. Two students recently received fellowships through the Oak Ridge Institute for Science and Education. Both are working with the U.S. Food and Drug Administration to validate and analyze COVID-19 models and data.

A lot of students are interested in biomedical applications and could work for companies that are devoted to health care and/or pharmaceuticals. And a number are trying to discern whether they want to follow an academic path after realizing that many research opportunities do exist in academia.

SN: Can you share a few examples of student success stories?

NC: Nicole Rosato, our first graduate, currently works at Rochester Gas and Electric. The title of her job is “data engineer,” but she does a great deal of data science. She develops models to analyze and predict outage events — causes of outages, when and where they’re going to occur, potential impacts, and possible fixes to prevent them from happening in the first place.

I’d also like to highlight Jenna McDanold, who came to our program as more of a nontraditional student. She is an artist who specializes in woodburning, and she wanted to learn how to apply mathematical modeling to wildfire spread. During her second year, Jenna reached out to a group at LANL under Rodman Linn, one of the world’s leading wildfire experts. She completed an internship there and they liked her so much that they asked her to stay. Now she’s a research assistant at LANL, which is supporting her as she finishes her Ph.D.

SN: What do you envision for the program’s future?

NC: RIT faculty members Kara Maki and David Ross recently founded the Industrial Math Modeling Center (IMMC) within the College of Science at RIT, which started with connections that they had with local companies. Kara and David envision the IMMC as a place where organizations can connect with mathematical modeling students as prospective interns or employees. We hope that the IMMC will be integrally associated with our Ph.D. program; as more companies feed us industrial problems in the next five to 10 years, we will connect students and faculty members to these projects so that they lead to internships and turn into dissertation topics.

SN: What do you hope that students will take away from this program?

NC: We want students to feel comfortable entering a new environment or application area—a company, government lab, research setting in academia, or even a hospital system—where they don’t necessarily have much background knowledge. If they can talk with experts in that area, understand the relevant problems, and use mathematical modeling to propose techniques to solve these problems, then we’ll have done our job. We’re trying to help students build these foundational skills because new and complicated issues always arise in the world. 10 years from now, there will be problems that we can’t even envision — problems that people with strong analytical skills and mathematical backgrounds will be able to tackle. If we produce graduates who are capable of entering new settings and communicating with experts in those fields, then our program will have been wildly successful.