Syracuse University

What you'll study

The PhD in Mathematics with an emphasis on Computational Mathematics combines advanced coursework, qualifying examinations and an original research dissertation. Core topics typically include numerical analysis, scientific computing, numerical linear algebra, numerical methods for partial differential equations, optimisation, and uncertainty quantification. Students also study complementary areas such as high-performance computing, scientific programming, inverse problems, stochastic modelling and computational statistics depending on research interests.

• Year 1–2: advanced graduate coursework to build theoretical foundations and computational skills, usually including rigorous analysis and specialised numerical methods courses.
• Qualifying examinations: written and/or oral assessments to verify readiness to undertake independent research.
• Research rotations or preliminary research projects to identify a dissertation advisor and focus area.
• Dissertation: an original research contribution in computational mathematics, supervised by faculty and culminating in a written thesis and oral defence.
• Teaching and professional development: opportunities to gain experience as a teaching assistant and to develop communication, grant-writing and computational reproducibility skills.

Entry requirements

Successful applicants normally hold a strong undergraduate degree in mathematics, applied mathematics, computer science, engineering or a closely related discipline; many have a master’s-level qualification with coursework in advanced calculus, linear algebra, differential equations and numerical methods. The department looks for demonstrated mathematical maturity and experience with programming and numerical computation.

• Academic transcripts showing strong preparation in core mathematical subjects.
• Letters of recommendation that address research potential and quantitative ability.
• A statement of purpose outlining research interests and fit with faculty expertise, and a CV listing relevant computational or research experience.
• International applicants are required to demonstrate English proficiency through accepted tests or qualifications; research experience and prior publications are advantageous.

Career prospects

Graduates with a PhD in Computational Mathematics pursue careers across academia, industry and government. Common paths include tenured and research-track academic positions, postdoctoral appointments, research scientist roles at national laboratories, and applied research or quantitative roles in technology, finance, engineering and biotech firms.

• Academic researcher or faculty in mathematics, applied mathematics or computational science.
• Research scientist in national laboratories and government research centres, working on large-scale simulations and modelling.
• Quantitative scientist or algorithm developer in finance, tech and engineering companies, including roles in machine learning, optimisation and numerical simulation.
• Data scientist or computational modeller in industry and consulting, where strong algorithmic and HPC skills are valued.

Why study at Syracuse University

Syracuse University offers a collaborative environment with faculty working at the intersection of mathematics, computation and application domains. The department supports close faculty mentoring, access to university computational resources and opportunities for interdisciplinary collaboration with engineering, computer science and scientific disciplines. The programme emphasises both theoretical rigour and practical computational skills, preparing graduates to lead research projects and to translate mathematical methods into high-impact applications.

Doctoral students benefit from a research-active faculty, seminar series, and opportunities to present work at conferences. Financial support through teaching and research assistantships is typically available to qualified doctoral candidates, providing a pathway to focus on research and professional development.