University of North Dakota

What you'll study

The programme blends advanced coursework, research seminars and a substantial original dissertation in computational mathematics. Core topics typically include numerical analysis, numerical linear algebra, scientific computing, numerical solutions of partial differential equations, optimisation and inverse problems, and computational statistics. Students also take supporting graduate courses drawn from real and functional analysis, applied partial differential equations, probability and stochastic processes, and applied algebra when relevant.

Training emphasises algorithm design, error analysis, stability and convergence, as well as practical implementation on modern architectures. Typical modules and components are:

• Advanced Numerical Analysis
• Numerical Linear Algebra and Matrix Computations
• Finite Element and Finite Difference Methods for PDEs
• Scientific Computing and High-Performance Computing
• Optimisation and Inverse Problems
• Computational Statistics and Data-Driven Methods
• Graduate Analysis (real and functional analysis)
• Research seminars and specialised electives in application areas (e.g. fluid dynamics, materials modelling, geophysics)

Programme structure normally consists of an initial phase of coursework and qualifying examinations, followed by focused research under the supervision of a faculty advisor, culminating in a written dissertation and oral defence. Students typically gain experience presenting work in seminars and conferences and often teach undergraduate mathematics courses as part of professional development.

Entry requirements

Applicants are expected to have a strong mathematical background. Typical requirements include:

• A master's degree in mathematics or a closely related discipline (strong applicants with an outstanding bachelor's degree and substantial preparation may be considered).
• Solid preparation in undergraduate and graduate-level analysis, linear algebra and differential equations; prior coursework in numerical analysis or scientific computing is highly desirable.
• Transcripts demonstrating strong academic performance; three letters of recommendation from academic or professional referees familiar with the applicant's quantitative abilities.
• A statement of purpose outlining research interests and potential faculty collaborators, and a curriculum vitae.
• Proof of English proficiency for applicants whose first language is not English (e.g. TOEFL or IELTS) as required by the university.

Additional materials such as sample publications, a writing sample or evidence of programming and HPC experience can strengthen an application. Applicants should consult the department for any programme-specific requirements and for information on financial support and assistantships.

Career prospects

Graduates with a PhD in Computational Mathematics pursue careers across academia, government research institutions, national laboratories and industry. Common roles include:

• University faculty and postdoctoral researcher positions in applied mathematics and computational science.
• Research scientist or applied mathematician roles at national laboratories and government agencies working on modelling, simulation and data analysis.
• Quantitative scientist, algorithm developer or data scientist positions in engineering, aerospace, energy, finance and technology companies.
• Software engineer or HPC specialist developing scalable numerical software and simulation codes.
• Consultancy roles addressing modelling, optimisation and uncertainty quantification challenges for industry clients.

The combination of deep mathematical training and hands-on computational skills makes graduates competitive for roles that require both theoretical insight and practical implementation on modern computing platforms.

Why study at University of North Dakota

The University of North Dakota's Department of Mathematics & Statistics offers a supportive environment for doctoral research in computational mathematics, with faculty expertise in numerical analysis, scientific computing and applied modelling. Students benefit from close faculty supervision, regular research seminars and opportunities for interdisciplinary collaboration across campus.

UND provides access to on-campus computing resources and encourages partnerships with engineering, aerospace and energy research units, offering applied projects relevant to aerospace, geophysics and energy systems. Doctoral students commonly receive financial support through research or teaching assistantships, which also provide valuable experience in instruction and grant-funded research.

Overall, the programme is geared towards students seeking rigorous mathematical training combined with practical skills in algorithm development and high-performance computation, preparing graduates for impactful careers in research and industry.