University of Michigan

What you'll study

The PhD emphasises rigorous coursework and original research. Early in the programme students take advanced courses in core areas such as real and functional analysis, numerical analysis and scientific computing, partial differential equations, optimisation, stochastic processes and probability, and mathematical aspects of data science. Typical taught modules include numerical linear algebra, finite element and spectral methods, inverse problems and parameter identification, dynamical systems, high-dimensional statistics and machine learning theory, and computational methods for PDEs.

Alongside formal classes, students participate in specialised seminars and reading courses tailored to their research interests. Program milestones commonly include preliminary/qualifying examinations that test breadth and depth, formation of a dissertation committee, submission and defence of a doctoral dissertation, and regular presentation of research at departmental seminars and conferences. Collaborative and interdisciplinary projects with units such as Engineering, Physics, Computer Science, and the Michigan Institute for Computational Discovery & Engineering (MICDE) are strongly encouraged.

Entry requirements

Successful applicants normally hold a bachelor’s or master’s degree in mathematics, applied mathematics, physics, engineering, computer science or a closely related quantitative discipline and demonstrate a strong foundation in advanced calculus, linear algebra, and differential equations. Evidence of mathematical maturity through coursework in real analysis, complex variables, numerical methods, probability or statistics is expected.

Typical application materials include official academic transcripts, a detailed CV, a statement of research interests, and at least three academic letters of recommendation. International applicants must meet the university’s English language requirements and provide any documentation required for admission. Admissions committees look for clear research potential, strong grades in relevant coursework, and evidence of independent work such as a master’s thesis, research project, or publications when available.

Career prospects

Graduates of the Applied Mathematics PhD secure positions across academia, industry and the public sector. Many pursue postdoctoral research and tenure-track academic careers in departments of mathematics, engineering and computational science. Others join national laboratories or research institutes working on modelling, simulation and large-scale computation.

In industry, graduates are in demand for roles in quantitative finance, data science and machine learning, scientific and engineering simulation, optimisation and control, software development for high-performance computing, and consulting. Increasingly, PhD mathematicians also take leadership roles in interdisciplinary R&D teams in biotech, energy, autonomous systems and advanced manufacturing.

Why study at University of Michigan

The University of Michigan offers a vibrant environment for applied mathematics with strengths in both theoretical foundations and large-scale computation. The department’s faculty cover a wide spectrum of applied math research, enabling students to work on problems ranging from rigorous analysis to algorithm design and high-performance implementations.

Students benefit from strong interdisciplinary connections across campus—notably with engineering, computer science and physical sciences—and access to research centres and computing infrastructure that support large-scale collaborative projects. The Ann Arbor community and the university’s industry partnerships provide additional opportunities for internships, collaboration and career placement. Funding support is typically available for graduate students through research assistantships, teaching appointments and fellowships, allowing them to focus on research training and professional development.