Emory University

What you'll study

Core study areas build a strong theoretical foundation while providing substantial training in computational methods and software used for large-scale problems.

• Foundational mathematics: real and complex analysis, functional analysis, algebra and topology as required for rigorous research.
• Numerical analysis and scientific computing: numerical linear algebra, error analysis, stability and convergence of numerical schemes.
• Partial differential equations and discretisation: finite difference, finite element and spectral methods for time-dependent and steady-state PDEs.
• Optimization and inverse problems: deterministic and stochastic optimisation, parameter estimation and regularisation techniques.
• Computational statistics and data-driven methods: numerical methods for large-scale inference, machine learning algorithms relevant to modelling and simulation.
• High-performance computing: parallel algorithms, performance modelling and implementation on modern architectures.
• Electives and applications: topics may include scientific visualization, computational geometry, dynamical systems, stochastic processes and domain-specific modelling (e.g. bio-mathematics or fluid dynamics).

Typically students take two to three years of coursework and seminars, participate in departmental seminars and special-topic workshops, and begin research projects in close collaboration with faculty. Students also gain teaching experience through graduate teaching assistantships.

Entry requirements

Successful applicants normally hold a strong undergraduate degree in mathematics or a closely related discipline; many incoming students also hold a master’s degree. Admissions decisions are based on the applicant’s academic record, letters of recommendation, research potential as described in the statement of purpose, and relevant coursework in analysis, linear algebra and differential equations. A curriculum vitae and examples of prior research (such as a thesis or publications) strengthen an application.

Standard documentation requirements include official transcripts and referees’ letters. Standardised tests may be requested on a case-by-case basis; international applicants must demonstrate English language proficiency according to university policy. Prospective students are encouraged to review department-specific guidance and contact potential advisors to discuss research fit prior to applying.

Career prospects

Graduates with a PhD in Computational Mathematics pursue a range of careers that exploit their skills in modelling, analysis and computation:

• Academic research and teaching: postdoctoral positions and faculty roles in mathematics, applied mathematics and computational science.
• National and government laboratories: research scientist roles addressing large-scale simulation, climate modelling, computational physics and defence-related problems.
• Industry R&D and technology: positions in simulation and modelling teams, algorithm development, machine learning infrastructure and scientific software engineering.
• Finance and quantitative analytics: quantitative modelling, risk analysis and algorithmic development for trading and asset management.
• Healthcare and biotechnology: computational modelling for systems biology, medical imaging and data-driven diagnostics.

Why study at Emory University

Emory offers a collaborative research environment with faculty working on both theoretical and computational problems. The university’s location in Atlanta provides proximity to other research institutions and industry partners, fostering interdisciplinary collaborations. Doctoral students benefit from departmental seminars, regular colloquia, access to university high-performance computing resources and opportunities to co-supervise or collaborate on applied projects across campus. The department supports graduate teaching and professional development that prepare students for diverse research careers.