University of Delaware

What you'll study

This programme focuses on numerical and algorithmic techniques for solving mathematical problems that arise in science, engineering and data-driven applications. Core themes include numerical linear algebra, numerical solution of ordinary and partial differential equations, scientific computing, and numerical optimization. You will also study supporting subjects such as advanced calculus, real analysis, probability and statistics as needed to underpin computational work.

• Numerical Analysis and Error Analysis
• Numerical Linear Algebra and Iterative Methods
• Finite Difference and Finite Element Methods for PDEs
• Numerical Optimization and Variational Methods
• Scientific Computing and High-Performance Computing techniques
• Computational Methods in Applied Probability and Statistics
• Programming for Scientific Computing (often Python, MATLAB, C/C++)
• Electives from machine learning, computational fluid dynamics, dynamical systems or mathematical finance

Students may follow a thesis or non-thesis track. The thesis option emphasises original research under faculty supervision and is suitable for those aiming for doctoral study. The non-thesis option places more weight on coursework and may include a project or comprehensive exam. Many students combine coursework with supervised research projects or internships in applied settings.

Entry requirements

Applicants should hold a bachelor’s degree in mathematics or a closely related discipline (physics, engineering, computer science, or quantitative economics) with a strong foundation in calculus, linear algebra and differential equations. Prior exposure to proof-based courses and some programming experience is expected.

• Transcripts demonstrating relevant undergraduate preparation.
• A statement of purpose describing academic background, research or computational experience, and goals.
• Letters of recommendation from academic or professional referees familiar with your quantitative abilities.
• A curriculum vitae or résumé outlining relevant coursework, projects and programming skills.
• International applicants must meet university English language requirements (e.g. recognised English proficiency tests) and may need to supply credential evaluations.

Some applicants with gaps in prerequisites may be admitted conditionally and asked to complete specified undergraduate courses before or during the programme. The department reviews applications holistically; relevant research, internships or strong quantitative coursework strengthen an application.

Career prospects

Graduates from the computational mathematics programme are prepared for a mix of careers in industry, government and academia. Common roles include:

• Computational scientist or research scientist in national labs and research institutes
• Data scientist, machine learning engineer or quantitative analyst in finance and technology firms
• Numerical analyst or software developer for engineering, simulation and modelling companies
• Roles in scientific computing and high-performance computing teams
• Further study at the PhD level in applied mathematics, computational science or related fields

Graduates typically apply mathematical modelling and algorithm development skills to tasks such as simulation, uncertainty quantification, optimization and large-scale data analysis. The programme’s balance of theory and computation also supports transitions into software engineering and analytics roles.

Why study at University of Delaware

The University of Delaware’s Department of Mathematical Sciences offers close interaction with faculty who work on applied and computational problems, enabling students to engage in supervised research projects. The institution fosters interdisciplinary collaboration with engineering, physics, chemical engineering and data science groups, providing access to applied problems and co-supervised theses.

• Opportunities for hands-on computational work using modern scientific programming tools and access to university computing resources.
• Small cohort sizes and accessible faculty mentoring that support project-based learning and research.
• Connections with regional industry and research laboratories for internships and applied projects.

Overall, the programme is designed for students who want rigorous mathematical training combined with practical computational skills that are immediately applicable to research and industry problems.