Clarkson University

What you'll study

The PhD in Computational Mathematics combines advanced coursework with sustained original research. Early-stage study typically includes graduate-level modules in numerical analysis, scientific computing, numerical linear algebra, partial differential equations, optimization and probability/statistics for computation. Students also take classes in complementary areas such as high-performance computing, numerical methods for PDEs, inverse problems and data-driven methods including machine learning for scientific applications.

After completing required coursework and any qualifying examinations, students focus on an independent research programme under the supervision of a faculty advisor. Research topics commonly pursued by Clarkson faculty and students include:

• Numerical methods for time-dependent and nonlinear partial differential equations
• Scientific computing on parallel and GPU architectures
• Numerical linear algebra and fast solvers/preconditioners
• Computational inverse problems and data assimilation
• Optimization and control for large-scale systems
• Uncertainty quantification and stochastic simulation
• Machine learning methods for physical modelling and simulation

Programme milestones typically include passing a qualifying exam, presenting and defending a dissertation proposal, conducting original research, and submitting and defending a doctoral dissertation. Many students gain practical experience through teaching assistantships or research assistant positions on funded projects.

Entry requirements

Applicants are normally expected to hold a master’s degree (or equivalent) in mathematics, applied mathematics, computational science, or a closely related discipline. Exceptional candidates with a strong bachelor’s degree and substantial research or industry experience may also be considered. Typical expectations include:

• A strong academic record in undergraduate and graduate mathematics coursework (real analysis, linear algebra, numerical analysis, differential equations)
• Research experience or evidence of ability to conduct independent study, such as a thesis, publications, or substantial project work
• Letters of recommendation from academic or professional referees who can address research potential
• A statement of purpose outlining research interests and fit with Clarkson faculty expertise
• A curriculum vitae detailing relevant coursework, research, programming and computational skills

International applicants must meet English language proficiency requirements; specific score thresholds and acceptable tests are set by the university. Some applicants are asked to provide transcripts, GRE scores where relevant, or additional supporting materials at the admissions committee’s request.

Career prospects

Graduates of the computational mathematics PhD find roles in academia, national laboratories, research institutes and industry. Common career pathways include:

• University and college faculty positions in mathematics, applied mathematics or computational science
• Research scientist or applied mathematician roles at national laboratories and government research centres
• Quantitative and modelling positions in high-technology industries such as aerospace, energy, materials science and engineering firms
• Data science, machine learning and algorithm development roles in finance, healthcare and technology companies
• Software engineering and high-performance computing specialists focused on scientific applications

PhD training emphasises problem formulation, numerical algorithm development and high-performance implementation, preparing graduates to lead interdisciplinary teams and to translate mathematical research into practical computational tools.

Why study at Clarkson University

Clarkson emphasises applied, interdisciplinary research that connects mathematics with engineering, physical sciences and computational science. The Department of Mathematical Sciences works closely with departments such as engineering and computer science, offering students opportunities to collaborate on funded projects and to apply computational methods to real-world problems.

Students benefit from a focused research environment with relatively small doctoral cohorts, close faculty mentoring, and access to high-performance computing resources. Teaching and research assistantships are commonly available to support doctoral students, enabling both pedagogical experience and hands-on involvement in active research programmes. Clarkson’s location also fosters partnerships with regional industry and national research laboratories, providing pathways for internships and collaborative research placements.

Overall, the programme is well suited to mathematicians who want rigorous theoretical grounding combined with practical computational skills and applied research experience.