University of Massachusetts Amherst

What you'll study

The programme combines rigorous graduate coursework in core mathematics with specialised training in numerical analysis, scientific computing and computational methods. Early years typically emphasise advanced topics such as real and complex analysis, algebra, and topology alongside computational subjects including numerical linear algebra, numerical methods for differential equations, scientific computing, and optimisation. Students select elective modules that may include high-performance computing, stochastic modelling and uncertainty quantification, computational statistics, inverse problems, and machine learning for scientific applications.

After completing required coursework, students complete qualifying examinations and progress to original research under the supervision of a faculty advisor. Research projects often involve the design and analysis of numerical algorithms, error and stability analysis, multi-scale modelling, structure-preserving methods, and computational frameworks for large-scale simulation and data assimilation. Collaboration with neighbouring departments (for example computer science, engineering and statistics) and use of departmental and campus computing resources are common components of student research.

Entry requirements

Applicants are normally expected to hold a strong undergraduate degree in mathematics or a closely related discipline; many incoming students also hold a master's degree. A solid grounding in advanced calculus, linear algebra, differential equations and basic numerical methods is expected. Admissions typically assess the applicant's academic transcripts, letters of recommendation, a research-orientated statement of purpose detailing interests in computational mathematics, and any evidence of programming or computational experience.

International applicants must demonstrate English language proficiency in line with university regulations. The department considers the overall profile of applicants; where background gaps exist, admitted students may be advised to take preparatory coursework in the first year. Specific departmental requirements and submission materials are published by the university graduate admissions office.

Career prospects

Graduates with a PhD in Computational Mathematics are prepared for a wide range of careers. Academic paths include postdoctoral research and faculty positions in mathematics, applied mathematics and computational science. Outside academia, alumni work in research divisions of technology and engineering firms, quantitative finance, data science and machine learning teams, and national or private research laboratories where advanced numerical modelling and algorithm development are required.

Typical roles include research scientist, numerical analyst, algorithm developer, quantitative modeller, computational engineer and data scientist. The analytical, modelling and software skills developed during the PhD are also valued in sectors such as energy, climate modelling, biomedical computing and high-performance computing infrastructure.

Why study at University of Massachusetts Amherst

UMass Amherst offers a large, research-active mathematics department with faculty working across numerical analysis, scientific computing, dynamical systems and applied mathematics, providing a broad intellectual environment for computational mathematics. The university encourages interdisciplinary collaboration and students frequently work with colleagues in computer science, statistics, engineering and other applied disciplines.

Students benefit from access to campus computing facilities and opportunities to engage in externally funded research projects. The department supports graduate training through seminars, reading groups and teaching experience, and provides mentoring for professional development aimed at academic and non-academic careers. The university's research culture and regional connections create pathways to collaborative projects and employment in both industry and research institutions.