University of Delaware

What you'll study

The programme combines rigorous coursework in core mathematical theory with advanced training in numerical methods, scientific computing and modelling, followed by independent research leading to a doctoral dissertation. In the first years students typically complete courses in partial differential equations, advanced numerical analysis, optimisation, dynamical systems, probability and stochastic processes, and functional analysis or advanced linear algebra. Coursework often includes training in high-performance computing, scientific programming, and data-driven methods.

After the coursework phase students take qualifying examinations and begin research under the supervision of a faculty advisor. Research topics reflect the department's strengths and the interests of its faculty and may include computational fluid dynamics, numerical methods for PDEs, inverse problems and imaging, applied dynamical systems, mathematical biology, uncertainty quantification and stochastic modelling, optimisation and control, and data-science applications. Seminars and reading courses provide exposure to current research and opportunities for presenting work at internal and external venues.

Entry requirements

Applicants are normally expected to hold a strong undergraduate degree in mathematics, applied mathematics or a closely related discipline; many applicants also hold a master's degree. Typical preparation includes undergraduate courses in real analysis, linear algebra, differential equations, and multivariable calculus, together with some exposure to numerical methods and probability or statistics. Admissions committees look for evidence of mathematical maturity, such as advanced coursework, research experience, publications or strong independent projects.

Application materials usually include academic transcripts, a statement of purpose outlining research interests, three letters of recommendation, and a CV. International applicants must demonstrate English proficiency according to the university's requirements. GRE general or subject scores may be considered where provided, but requirements can vary; applicants should consult the department for current guidance. Admission decisions also take into account fit with potential faculty advisors and available funding through teaching or research assistantships.

Career prospects

Graduates of the PhD in Applied Mathematics pursue careers in academia, national laboratories and industry. Academic paths include postdoctoral research and tenure-track positions in mathematics, applied mathematics and engineering departments. In national and government laboratories, graduates work on large-scale simulation, computational modelling and algorithm development for scientific and defence applications.

Industry opportunities span finance and quantitative risk, data science and machine learning, computational sciences for engineering and manufacturing, biotechnology and pharmaceuticals, and software development for scientific computing. Employers value PhD graduates for their analytical problem-solving, modelling expertise and ability to design and implement computational solutions for complex, multidisciplinary problems.

Why study at University of Delaware

The University of Delaware's Department of Mathematical Sciences offers a supportive research environment with active faculty working across a broad range of applied mathematics areas. Students benefit from close interdisciplinary collaborations with engineering, physics, chemistry and biological sciences, enabling applied projects with practical impact.

Doctoral students have access to modern computing facilities and opportunities to work on externally funded research projects and collaborative centres. The department emphasises mentorship, seminar participation and professional development, and its location in the mid‑Atlantic provides proximity to regional research organisations and industry partners, facilitating internships and postdoctoral transitions.

Overall, the programme is well suited to students who seek deep theoretical training combined with practical computational and modelling experience, preparing them for research careers and leadership roles in quantitative fields.