University of Kansas

What you'll study

The PhD programme combines advanced coursework, qualifying examinations and an original research dissertation. Core study areas include numerical analysis, scientific computing, computational partial differential equations, numerical linear algebra, optimisation, uncertainty quantification and high-performance computing. Students also encounter complementary topics such as advanced real and complex analysis, probability and stochastic processes, and computational aspects of algebra when needed for specific research projects.

Typical elements of the programme:

• Coursework: Advanced graduate modules in numerical analysis, computational methods for PDEs, numerical linear algebra, optimisation and probabilistic numerics.
• Qualifying exams: Written and/or oral exams to assess readiness for independent research and to confirm breadth in pure and applied mathematical foundations.
• Research seminars: Regular departmental seminars and specialised reading groups in computational mathematics and neighbouring disciplines.
• Teaching or research assistantships: Many students gain experience teaching undergraduate courses or supporting faculty research, which also provide professional development and financial support.
• Dissertation: An extended, original research project under the supervision of a faculty advisor that contributes new methods, analysis or applications in computational mathematics.

Entry requirements

Successful applicants typically hold a strong undergraduate degree in mathematics, applied mathematics, or a closely related discipline; many applicants also hold a master’s degree. Essential preparation includes coursework in real analysis, linear algebra and numerical analysis, together with programming experience in languages commonly used for scientific computing (for example Python, C/C++ or MATLAB).

Typical application materials include academic transcripts, a statement of research interests, letters of recommendation and a CV. Evidence of mathematical maturity (such as advanced coursework or research experience) is important. Prospective students whose first language is not English will need to meet the university's English language proficiency requirements.

Funding is commonly available through departmental teaching or research assistantships and fellowships; applicants are encouraged to indicate their interest in funding on the application and to contact potential faculty advisors whose research matches their interests.

Career prospects

Graduates of the programme pursue careers across academia, industry and government. Common pathways include tenure-track positions in mathematics or applied mathematics departments, postdoctoral research in computational sciences, and research roles at national laboratories. Industry opportunities include quantitative roles in finance, data science and machine learning, software engineering for scientific computing, and algorithm development for engineering, energy, or biomedical applications.

The PhD training emphasises both rigorous analysis and practical computational skills, equipping graduates to lead interdisciplinary teams, develop scalable algorithms, and contribute to high-performance computing projects.

Why study at University of Kansas

The University of Kansas offers a collaborative environment with faculty working across traditional boundaries between pure and applied mathematics, computer science and engineering. Students benefit from access to departmental seminars, specialised research groups and opportunities to collaborate on interdisciplinary projects.

Graduate students have access to institutional computing resources and research infrastructure needed for large-scale numerical experiments, as well as a supportive graduate community and mentoring from faculty active in computational mathematics. The department emphasises professional development, teaching experience and preparation for diverse careers that combine mathematical rigour with computational practice.