Dartmouth College

What you'll study

The PhD in Mathematics with emphasis in Computational Mathematics combines foundational coursework in pure and applied mathematics with focused study in numerical analysis, scientific computing and algorithmic methods. Early years typically centre on core graduate courses such as real analysis, algebra and topology alongside specialised courses in numerical linear algebra, numerical solution of differential equations, approximation theory, and computational methods for partial differential equations. Students frequently take advanced electives in probability and stochastic processes, optimization, scientific machine learning, and high-performance computing; cross-registration with Computer Science, Engineering, or Data Science is common.

Programme milestones include passing qualifying examinations, completing a set of formal courses to satisfy departmental requirements, and advancing to candidacy after proposing an original research project. The doctoral dissertation requires sustained research under the supervision of a faculty advisor and is expected to make a substantive contribution to computational mathematics—examples include development of new numerical algorithms, analysis of algorithmic stability and convergence, multiscale modelling methods, or computational approaches for inverse problems and uncertainty quantification.

Teaching and professional development form part of the training: doctoral students typically serve as teaching fellows or instructors for undergraduate mathematics courses, and the department organises seminars and reading courses to support research development and communication skills.

Entry requirements

Successful applicants normally hold a strong undergraduate degree in mathematics or a closely related discipline; many have master's-level preparation or equivalent coursework in advanced mathematics. Typical preparation includes rigorous training in real analysis, linear algebra, differential equations and basic numerical methods. Evidence of prior research experience or significant computational project work is advantageous.

Applicants must submit academic transcripts, a statement of purpose outlining research interests (with emphasis on computational mathematics), a curriculum vitae, and letters of recommendation—usually three—from academics or professionals who can speak to the applicant's mathematical ability and research potential. International applicants whose first language is not English will need to demonstrate English proficiency in line with Dartmouth's graduate school requirements.

Career prospects

Graduates with a PhD in Computational Mathematics are prepared for careers in both academia and industry. Academic paths include postdoctoral research and faculty positions in mathematics, applied mathematics, and computational science departments. In industry, alumni work in areas such as quantitative finance, scientific and engineering software development, high-performance and cloud computing, data science, machine learning, and modelling for energy, climate and biomedical applications. Other common destinations include national laboratories, research institutes and tech companies where expertise in numerical methods, algorithm design and large-scale computation is valued.

Why study at Dartmouth College

Dartmouth's Mathematics Department provides a close-knit research environment with strong faculty mentorship and opportunities for interdisciplinary collaboration across Computer Science, Engineering, and data-science initiatives. The department emphasises personalised supervision and regular interaction between students and faculty, which is well suited to computational research projects that require sustained mentorship and access to diverse expertise.

Doctoral students benefit from Dartmouth's research computing resources and collaborations with campus centres and laboratories, enabling development and testing of high-performance algorithms and large-scale simulations. The college's supportive graduate community, combined with teaching experience and professional development offerings, prepares students for a wide range of research and career trajectories in computational mathematics.