Brandeis University

What you'll study

The PhD programme centres on advanced coursework, qualifying examinations and an extended original research dissertation in areas of computational mathematics. Core study typically includes graduate-level real and complex analysis, algebra and topology as foundations, together with specialised courses in numerical analysis, scientific computing, numerical linear algebra, approximation theory, and the numerical solution of differential equations (ordinary and partial).

Students pursuing the computational track will encounter modules and topics such as:

• Numerical methods for linear and nonlinear systems
• Finite element and finite volume methods for PDEs
• Computational optimisation and variational methods
• Computational linear algebra and eigenvalue problems
• High-performance computing, parallel algorithms and GPU programming
• Uncertainty quantification, stochastic simulation and Monte Carlo methods
• Data-driven modelling, scientific machine learning and inverse problems
• Software engineering practices for scientific computing and reproducible research

Programme structure includes initial coursework and seminars, passing written and/or oral qualifying examinations, and completion of a doctoral research proposal followed by dissertation research under the supervision of a faculty advisor. Students regularly participate in department colloquia, workshops and cross-departmental seminars with computer science, physics, engineering and applied mathematics researchers.

Entry requirements

Applicants are normally expected to have a strong undergraduate degree in mathematics, applied mathematics, computer science, engineering or a closely related discipline; many successful candidates hold a relevant master's degree. Typical preparation includes undergraduate-level real analysis, linear algebra, differential equations and a background in numerical methods or scientific computing.

Required application materials usually comprise academic transcripts, a statement of purpose outlining research interests in computational mathematics, letters of recommendation (often from faculty who can comment on research potential), and a résumé or CV. Evidence of programming experience and prior research or project work in numerical computation, modelling or software development strengthens an application. Standardised test requirements (if any) and English language requirements follow university guidelines and should be checked on the Brandeis admissions pages.

Career prospects

Graduates with a PhD in Computational Mathematics are well placed for careers in academia as researchers and faculty, or in research positions at national laboratories and research institutes. Outside academia, common career paths include roles in quantitative finance, data science, machine learning research, scientific software development, computational engineering and industrial R&D.

PhD holders frequently take positions in technology companies that require large-scale simulation or algorithm development, in consulting firms solving optimisation and modelling problems, and in public-sector and healthcare organisations applying computational models. The combination of theoretical rigour and practical computational skills makes graduates attractive for interdisciplinary teams working on complex data-driven and simulation-based challenges.

Why study at Brandeis University

Brandeis offers a close-knit mathematics department with opportunities for close mentorship and early engagement in research. The university emphasises interdisciplinary collaboration, enabling computational mathematics students to work with faculty and researchers in computer science, physics, biology and engineering on applied projects.

Students benefit from access to university computing resources and regional research clusters, and from Brandeis's proximity to the broader Boston–Cambridge research ecosystem, which provides seminars, workshops and potential industry and national-laboratory collaborations. The department hosts regular colloquia and supports student participation in conferences and summer research programmes, fostering both theoretical depth and practical programming and software development experience essential for careers in computational science.