Michigan State University

What you'll study

The PhD programme emphasises a balance of theoretical mathematics and practical computational tools. Early study typically covers advanced coursework in numerical analysis, numerical linear algebra, scientific computing, partial differential equations, optimisation, and probability and stochastic processes. Students also take courses in algorithms, high-performance computing, and relevant applied areas such as computational fluid dynamics, inverse problems and data-driven methods.

After completing required coursework, students prepare for and pass qualifying examinations and then develop an original research programme under the supervision of a faculty advisor. Research topics in Computational Mathematics may include the development and analysis of numerical methods for PDEs, scalable solvers for large linear and nonlinear systems, uncertainty quantification, reduced-order modelling, data assimilation, and algorithmic aspects of machine learning and scientific data analysis.

Programme components commonly include:

• Graduate-level coursework in core and elective subjects
• Regular participation in departmental seminars, colloquia and computational research groups
• Teaching or research assistantship duties
• Qualifying/comprehensive examinations
• A supervised research dissertation and oral defence

Entry requirements

Applicants are expected to hold a strong undergraduate degree in mathematics or a closely related discipline; a master's degree in mathematics, applied mathematics, or a computational field is beneficial but not always required. Successful candidates typically demonstrate a solid background in real and complex analysis, linear algebra, differential equations and numerical methods, together with programming experience (for example in MATLAB, Python, C/C++ or Fortran).

Typical application materials include official academic transcripts, a curriculum vitae, a statement of research interests, and at least two or three letters of recommendation from academic referees who can assess the applicant's potential for doctoral research. Applicants whose first language is not English must meet the university's English proficiency requirements.

Admission is competitive and normally requires evidence of readiness for advanced independent research. Funding considerations, research fit with faculty, and availability of a supervisor influence admissions decisions.

Career prospects

Graduates with a PhD in Computational Mathematics are prepared for careers in university research and teaching, national and international research laboratories, and research-intensive positions in industry. Common career paths include:

• Academic positions in mathematics, applied mathematics or computational science departments
• Research scientist or computational scientist roles in national labs and research institutes
• Data scientist, quantitative analyst, or machine learning engineer in technology and finance sectors
• Research and development positions in engineering, energy, aerospace and biotechnology companies
• Software development roles focusing on scientific computing, high-performance computing and numerical libraries

The emphasis on rigorous analysis and large-scale computation also equips graduates to move into interdisciplinary teams addressing problems in climate modelling, materials simulation, imaging and medical data, and many other application domains.

Why study at Michigan State University

Michigan State University offers a strong research environment in computational and applied mathematics, with faculty whose research spans numerical analysis, scientific computing, optimisation and uncertainty quantification. Students benefit from collaborative opportunities across engineering, physics, computational biology and other departments, allowing access to real-world applications of computational methods.

The university provides significant computational infrastructure and support for high-performance research computing through its central facilities, enabling large-scale simulations and data-intensive projects. Graduate students receive mentorship through research groups and regular seminar series, and many are supported by teaching or research assistantships that provide professional development in teaching and project management.

Located in East Lansing and connected to a broad research community, Michigan State fosters an inclusive academic culture and offers the resources and collaborations that prospective computational mathematicians need to develop into independent researchers and professionals.