Rochester Institute of Technology

What you'll study

The PhD in Applied Mathematics emphasises rigorous mathematical theory, numerical analysis and computational methods applied to problems in engineering, physical sciences and data-driven domains. Students undertake advanced coursework in areas such as partial differential equations, numerical linear algebra, scientific computing, optimisation, stochastic processes, inverse problems and mathematical modelling.

Programme structure typically combines a period of advanced coursework, qualifying examinations, and an extended original research project leading to a dissertation. Coursework is tailored to each student’s research direction and often includes electives from adjacent departments (computer science, engineering, physics, imaging science, statistics).

Typical topics and modules you may encounter include:

• Advanced Partial Differential Equations – theory and methods for modelling continuum phenomena.
• Numerical Analysis and Scientific Computing – discretisation, error analysis and large-scale computation.
• Numerical Linear Algebra – iterative methods and preconditioning for large systems.
• Optimisation and Optimal Control – deterministic and stochastic optimisation techniques.
• Inverse Problems and Imaging – reconstruction methods, regularisation and applications to sensing and imaging.
• Probability, Stochastic Processes and Uncertainty Quantification – modelling and propagation of uncertainty in complex systems.
• Computational Methods for Data Science – algorithms for high-dimensional data, machine learning foundations and algorithmic efficiency.

Research training emphasises hands-on computational experiments, development of scalable algorithms, and close collaboration with faculty in interdisciplinary centres. Students are expected to present work at conferences, publish in peer-reviewed journals and contribute to team projects with industry or government partners.

Entry requirements

Applicants are normally expected to hold a relevant master's degree or an exceptional bachelor's degree in mathematics, applied mathematics, engineering, physics, computer science or a closely related field, with a strong record of quantitative coursework. A solid background in real and complex analysis, linear algebra, differential equations, numerical methods and programming is essential.

Typical application materials include:

• Academic transcripts demonstrating strong performance in quantitative subjects.
• A statement of research interests outlining proposed areas of study and potential faculty matches.
• Letters of recommendation from academic or professional referees who can speak to research potential.
• Evidence of prior research experience (thesis, publications or project work) where available.

International applicants may need to demonstrate English language proficiency according to university policy. Some applicants may be invited for interviews with potential supervisors. The programme evaluates applicants holistically; prior research experience and alignment with faculty expertise are important considerations.

Career prospects

Graduates of the PhD in Applied Mathematics pursue careers across academia, industry and government research. Common career paths include:

• Academic positions in mathematics, applied mathematics and computational science departments.
• Research scientist or senior developer roles in industrial research labs, technology companies and engineering firms.
• Quantitative roles in finance, data science and algorithm development, where advanced modelling and computational skills are required.
• Positions at national laboratories and government agencies working on simulation, modelling and high-performance computing projects.
• Leadership roles in interdisciplinary teams addressing imaging, materials modelling, climate modelling, biomedical computing and other applied domains.

Graduates are prepared to lead research projects, translate mathematical methods into software and tools, and collaborate across disciplinary boundaries to solve complex, data- and computation-driven problems.

Why study at Rochester Institute of Technology

Rochester Institute of Technology offers a strong applied and interdisciplinary culture that benefits PhD students in applied mathematics. The university is recognised for its emphasis on experiential learning and close ties between academic departments and applied research centres, enabling students to work on practical problems connected to imaging, computational science, engineering and data analytics.

PhD students have access to high-performance computing resources, specialised laboratories and collaborative research centres, and can draw on expertise across departments including computer science, physics and engineering. The institute’s location in the Rochester region provides proximity to a cluster of technology and imaging companies and national research organisations, facilitating collaborations and external partnerships.

Students benefit from mentorship by faculty actively engaged in applied and computational research, opportunities to teach and mentor undergraduates, and a research environment that values both theoretical advances and the development of robust computational tools for real-world applications.