University of North Carolina at Chapel Hill

What you'll study

This programme concentrates on numerical methods, algorithm design and computational techniques for solving mathematical models arising in the sciences and engineering. Typical topics include numerical linear algebra, numerical solution of ordinary and partial differential equations, scientific computing, optimisation, approximation theory, and stochastic methods for computation. Coursework emphasises both theoretical foundations and practical implementation using modern programming environments and high-performance computing.

• Core areas: Numerical Analysis, Scientific Computing, Computational Linear Algebra, Numerical PDEs.
• Common elective topics: Optimisation and Control, Finite Element Methods, Numerical Probability and Stochastic Simulation, Data Assimilation, Machine Learning for Scientific Computing, High‑Performance Computing and Parallel Algorithms.
• Programming and tools: Proficiency typically developed with languages and tools such as Python, MATLAB, C/C++, and parallel computing frameworks (MPI/OpenMP), together with software for numerical libraries and visualization.
• Structure and dissertation: The department commonly offers both coursework-only and research options; students may complete a capstone project or a supervised thesis under a faculty advisor. Programme credit requirements follow departmental regulations and are designed to prepare students for research or professional practice.
• Research and seminars: Students can engage with faculty research groups and attend regular departmental seminars and workshops in areas such as scientific computing, applied analysis and computational statistics.

Entry requirements

Applicants should hold a bachelor’s degree in mathematics, applied mathematics, engineering, physics, computer science or a related quantitative discipline, with a strong foundation in calculus, linear algebra and differential equations. Prior exposure to numerical methods and programming is expected.

• Academic transcripts: A record of strong performance in relevant undergraduate courses.
• References: Two or three academic or professional references who can speak to quantitative preparation and research or project potential.
• Supporting documents: A statement of purpose outlining academic background, computational experience and research or career goals, and a CV/resume.
• English language: International applicants must demonstrate English proficiency through accepted tests unless exempted under university policy.
• Other considerations: Demonstrated programming experience and any prior research, internships or project work in computational mathematics, scientific computing or related fields strengthen an application. Some applicants with strong quantitative preparation may be invited to discuss their background with faculty.

Career prospects

Graduates of the computational mathematics master's develop skills that are in demand across academia, government and industry. Typical career paths include:

• Computational scientist or numerical analyst in research labs and industry
• Data scientist, quantitative analyst or machine learning engineer in finance, tech and consulting
• Software engineer specialising in scientific and high-performance computing
• Research assistant or PhD candidate in applied mathematics, computational science or related fields
• Roles in engineering companies and government agencies that require simulation, modelling and optimisation expertise

The programme’s combination of theoretical training and practical coding experience prepares graduates to both implement scalable algorithms and to collaborate across interdisciplinary teams.

Why study at University of North Carolina at Chapel Hill

UNC Chapel Hill’s Department of Mathematics has active research groups in numerical analysis, scientific computing and applied mathematics, providing access to faculty with expertise in computational methods and applications. The university’s research infrastructure—including collaborations with centres such as the Renaissance Computing Institute (RENCI) and links to neighbouring institutions and industry in the Research Triangle—offers opportunities for interdisciplinary projects and access to advanced computing resources.

• Interdisciplinary collaboration: Opportunities to work with departments such as computer science, statistics, engineering and the biological and physical sciences on computational problems.
• Research-led teaching: Courses and projects often reflect current research trends and practical challenges, with options for thesis work under active investigators.
• Professional development: Seminars, workshops and connections to regional employers support transition into research roles or industry careers.

Overall, the programme is well suited to students seeking rigorous mathematical training combined with hands-on computational experience and pathways into research or applied roles in industry and government.