University of San Diego

What you'll study

The programme combines advanced coursework, comprehensive exams, original research and teaching experience. Early stages typically focus on core topics such as advanced real and functional analysis, partial differential equations, numerical analysis and scientific computing, together with electives in areas of application.

• Core coursework: real and complex analysis, functional analysis, numerical linear algebra, numerical methods for PDEs and mathematical modelling.
• Applied electives: computational fluid dynamics, mathematical biology and population modelling, inverse problems and data assimilation, optimisation and control, machine learning for scientific computing, stochastic processes and uncertainty quantification.
• Computational training: high-performance computing, software development for scientific applications, reproducible research practices and data management.
• Research thesis: students undertake an original research project under the supervision of a faculty advisor, culminating in a written dissertation and oral defence.
• Professional development: opportunities for presenting at conferences, publishing in peer-reviewed journals and participating in interdisciplinary research projects with other departments and external partners.

Programme structure normally includes a period of coursework and seminars, qualifying or candidacy examinations to assess readiness for independent research, followed by concentrated dissertation research. Many students also gain practical experience through collaborations, internships or research placements with local industry and laboratories.

Entry requirements

Successful applicants typically hold a relevant graduate degree (Master’s in mathematics, applied mathematics, or a closely related discipline) or a strong honours-level Bachelor’s degree with substantial preparation in advanced mathematics. Typical academic preparation includes coursework in real analysis, linear algebra, differential equations and numerical methods.

• Academic transcripts: evidence of strong performance in undergraduate and, where applicable, graduate coursework in mathematics and related areas.
• Letters of recommendation: usually three academic references that can speak to research potential and mathematical maturity.
• Statement of purpose: a clear description of research interests, relevant experience and reasons for pursuing doctoral study at the University of San Diego.
• Research samples: where available, a writing sample or examples of previous research/project work strengthen an application.
• English language proficiency: required for applicants whose first language is not English, in line with university policy.

Admissions are competitive and the department looks for demonstrated potential for independent research. Financial support in the form of teaching or research assistantships and fellowships may be available to admitted students; applicants are encouraged to review funding information and contact potential faculty advisors about research fit.

Career prospects

Graduates of a PhD in Applied Mathematics pursue a wide range of careers. Many move into academic roles as postdoctoral researchers and faculty, continuing research and teaching. Others take research scientist or quantitative positions in industry sectors such as data science and machine learning, computational finance, engineering simulation, biotechnology and pharmaceuticals, environmental modelling and energy.

• Research and development roles in technology companies, defence contractors and national or private research laboratories.
• Quantitative analyst, modeller or data scientist positions in finance, insurance and consulting.
• Technical leadership and applied research roles in engineering firms, software companies and start-ups focusing on simulation or algorithm development.
• Policy, operations research and analytics roles in government agencies and non-profit organisations.

The programme emphasises transferable skills — advanced modelling, programming, high-performance computing, and scientific communication — that are highly valued across these career paths.

Why study at University of San Diego

The University of San Diego offers a doctoral experience with close faculty mentorship, small cohorts and opportunities for interdisciplinary collaboration across science, engineering and data-focused units. The department emphasises applied, computation-intensive research and supports students with access to modern computing resources and collaborative project work.

• Faculty expertise: a range of supervisors working on applied analysis, numerical methods, computational modelling and data-driven applications.
• Location and partnerships: situated in a region with strong ties to industry and research organisations, offering potential for collaborations and internships with local companies and laboratories.
• Research culture: an environment that encourages presentation of results, publication and participation in regional and national research networks.
• Professional development: structured opportunities to gain teaching experience, grant-writing practice and career preparation for academic and non-academic paths.

Together, these factors make the University of San Diego a strong choice for students seeking a focused, applied mathematics PhD with practical and interdisciplinary research opportunities.