University of Memphis

What you'll study

The PhD in Mathematics (Computational Mathematics) emphasises rigorous training in both theoretical and computational aspects of mathematical sciences. Course work typically covers advanced topics such as numerical analysis, scientific computing, numerical linear algebra, numerical solution of partial differential equations, optimisation, probability and stochastic modelling, and scientific machine learning.

• Core coursework: graduate real analysis, numerical analysis, and topics in applied mathematics to ensure a solid theoretical foundation.
• Advanced electives: spectral methods, finite element and finite difference methods, computational PDEs, high-performance computing, inverse problems, uncertainty quantification, and optimisation.
• Computational skills: programming for numerical computation (e.g. MATLAB, Python, C/C++), parallel computing concepts, and use of numerical libraries and HPC environments.
• Research training: seminars, reading courses and a taught research methods component that prepare students for original research leading to a doctoral dissertation.

Students progress through a combination of coursework, qualifying examinations or assessments, and an original research programme supervised by departmental faculty. The PhD culminates in a written dissertation and oral defence. Research areas represented in the department often include numerical methods for PDEs, scientific computation, computational inverse problems, applied optimisation, stochastic modelling and interdisciplinary computational projects with engineering, physics or data science.

Entry requirements

Applicants are normally expected to hold a relevant master's degree in mathematics, applied mathematics, computational science, or a closely related discipline demonstrating strong preparation in advanced mathematics. Exceptional applicants with a strong bachelor’s degree may also be considered. A competitive application typically includes:

• Official transcripts showing strong performance in advanced mathematics and related coursework.
• A statement of purpose describing research interests and relevant experience in computation or applied mathematics.
• Letters of recommendation from academic or professional referees familiar with the applicant's research potential.
• A CV detailing research projects, programming experience and relevant publications or presentations, if any.

Standardised test requirements, such as the GRE, are subject to departmental policy and may be optional or considered if submitted. Applicants whose first language is not English will need to demonstrate English proficiency in line with university regulations.

Career prospects

Graduates with a PhD in Computational Mathematics are prepared for a range of careers that demand deep analytical and computational expertise. Typical career paths include:

• Academic positions: postdoctoral research and faculty roles in mathematics, applied mathematics and computational science.
• Research scientist roles at national laboratories and research institutes working on modelling, simulation and algorithm development.
• Industry positions in sectors such as engineering firms, aerospace, telecommunications, finance and energy where numerical modelling and optimisation are core activities.
• Data science, machine learning and software development roles that require strong quantitative, statistical and computational skills.
• Consulting and technology development roles that apply advanced numerical methods to real-world problems.

Why study at University of Memphis

The Department of Mathematical Sciences at the University of Memphis offers a PhD environment with close faculty supervision, a balance of theoretical and applied research, and opportunities for interdisciplinary collaboration. Graduate students benefit from access to departmental seminars, collaborative projects with neighbouring engineering and science departments, and institutional computational resources suitable for large-scale numerical experiments.

The programme emphasises mentorship and prepares students for both academic and applied careers by combining rigorous coursework, hands-on computational training and original research. Students also find opportunities to engage with regional industry and research centres, contributing to projects that bridge theory and real-world application.