Rice University

What you'll study

The PhD emphasises rigorous analysis together with computational practice. Early-stage study combines advanced coursework and qualifiers before students concentrate on independent research under a faculty advisor. Core subject areas include numerical analysis and scientific computing, partial differential equations, optimisation, dynamical systems, stochastic methods and inverse problems. Elective topics commonly taken by students include machine learning and data science, computational fluid dynamics, mathematical biology, probability and statistics, and high-performance computing.

• Coursework: Advanced numerical analysis, theory of PDEs, functional analysis, optimisation, probability and stochastic processes, numerical linear algebra.
• Qualifying/comprehensive examinations: A written and/or oral examination sequence that demonstrates readiness for research.
• Research and dissertation: Original research leading to a doctoral thesis; students typically publish in peer-reviewed journals and present at conferences.
• Teaching and professional development: Opportunities to gain teaching experience as graduate instructors or teaching assistants and training in scientific communication.

Entry requirements

Applicants are expected to have a strong undergraduate degree in mathematics, applied mathematics, or a closely related discipline; many successful applicants also hold a master’s degree. Required application materials typically include academic transcripts, a statement of purpose describing research interests, letters of recommendation from academic or professional referees, and a curriculum vitae. International applicants must demonstrate English language proficiency through an accepted test unless exempt.

Rice evaluates candidates on mathematical preparation, potential for research, and fit with faculty expertise. Some applicants will be invited to interview. Standardised tests are not universally required; applicants should check the department’s admissions guidance for current policies.

Career prospects

Graduates of the programme pursue careers in academia as postdoctoral researchers and faculty, and in research positions at national laboratories and industry R&D groups. Applied mathematicians from Rice are sought after in sectors that rely on modelling and computation, including technology and software companies, aerospace and defence, energy, finance, biotechnology and pharmaceuticals. Other common paths include data science and machine learning roles, quantitative engineering positions, and scientific computing and simulation development.

Why study at Rice University

Rice offers a collegial, research-intensive environment with a relatively small department that enables close mentoring by faculty. The university’s location in Houston provides access to wide interdisciplinary collaborations across engineering, computer science, bioengineering and the nearby medical and energy sectors. Students benefit from access to institutional computational resources and opportunities to work on applied problems in collaboration with local research centres and industry partners.

Faculty in the applied mathematics programme work on a diverse range of contemporary problems—from inverse problems and data assimilation to numerical methods for PDEs and computational biology—so students can tailor doctoral projects to theoretical or application-driven interests. Funding support through research assistantships and teaching assistantships is commonly available for admitted PhD students.