Rice University

What you'll study

The PhD pathway in Computational Mathematics combines rigorous theoretical training with hands-on algorithm development and large-scale computation. Early coursework typically covers graduate analysis, numerical linear algebra, scientific computing, partial differential equations, numerical methods for PDEs, optimization, and probability or statistics as relevant to computational problems.

Advanced study is driven by research interests and may include topics such as spectral and finite element methods, multigrid and domain decomposition techniques, uncertainty quantification, inverse problems, computational geometry, high-performance and parallel computing, numerical optimization, computational algebra, and data-driven modelling. Students participate in seminars and journal clubs, and undertake teaching duties as part of their professional development.

The programme structure normally includes a period of core and elective coursework, qualifying examinations or assessments to demonstrate breadth and readiness for research, a proposal/qualifying oral in the chosen research area, and a dissertation based on original research under the supervision of a faculty advisor. Students are expected to engage in collaborative and interdisciplinary projects across departments and research centres.

Entry requirements

Successful applicants usually hold a strong bachelor’s degree in mathematics, applied mathematics, computer science, engineering or a closely related field; many have a master’s degree with substantial coursework or research experience in numerical analysis or computational science. Typical admissions criteria include evidence of strong mathematical preparation, programming and computational experience, and prior research or project work.

Application materials normally include academic transcripts, a statement of purpose outlining research interests, letters of recommendation from academic or professional referees, and a curriculum vitae. International applicants must demonstrate English proficiency through accepted tests or equivalent documentation when required by the university. Specific document requirements and any standardised-test policies are detailed on Rice University's graduate admissions pages.

Career prospects

Graduates with a PhD in Computational Mathematics move into a range of roles in academia, national laboratories, industry and the public sector. Common career paths include tenure-track positions in mathematics and computational science, research scientist or staff scientist roles in government and private research labs, and applied research or specialist positions in technology, energy, finance, biotechnology and engineering companies.

Other opportunities include data science and machine-learning roles that leverage advanced numerical methods, high-performance computing and algorithm development, as well as consulting and R&D management positions where deep quantitative and computational expertise is required. The programme also prepares graduates for interdisciplinary collaborations with computer science, engineering, physics and biomedical research.

Why study at Rice University

Rice offers a collaborative, research-intensive environment with close faculty-student interaction in a department known for strengths in both pure and applied mathematics. Computational mathematics students benefit from access to Rice’s high-performance computing resources and organised research centres, fostering interdisciplinary projects with engineering, computer science, bioinformatics and the broader Houston research community.

Doctoral students receive mentorship from faculty active in numerical analysis, scientific computing and applied mathematics, and can leverage institutional partnerships and local industry connections for internships and applied research. Funding is typically available through teaching or research assistantships, providing support while students focus on their research and professional development.