Idaho State University

What you'll study

The PhD programme combines advanced coursework, qualifying examinations and an independent research dissertation centred on computational mathematics. Core topics typically include numerical analysis, computational linear algebra, partial differential equations (PDEs) and finite element/finite difference methods, numerical optimisation, scientific computing, and parallel and high-performance computing. Elective or special-topic courses often cover stochastic modelling, inverse problems and data assimilation, computational geometry, machine learning for scientific computing, and advanced probability and statistics.

Programme structure generally comprises a sequence of graduate courses to build technical breadth, a written and/or oral qualifying examination to assess readiness for research, and a substantial original research project culminating in a dissertation. Students gain practical experience through computational projects, code development, collaboration with faculty on funded research, and opportunities to present at conferences.

Entry requirements

Applicants typically hold a master’s degree in mathematics, applied mathematics, computational science, or a closely related discipline, with a strong record in advanced coursework such as real analysis, linear algebra, and numerical methods. Exceptional applicants with a well-prepared bachelor’s degree and substantial research or computational experience may also be considered.

Required application materials normally include academic transcripts, a statement of research interests or purpose, a curriculum vitae, and letters of recommendation that address research potential. International applicants must demonstrate English proficiency as specified by the university (for example through recognised language tests) unless exempt. Admissions decisions also consider alignment with faculty research interests and availability of faculty to supervise the proposed project; a brief research proposal or identification of potential supervisors strengthens an application.

Funding is commonly available for doctoral students through teaching assistantships, research assistantships, and university fellowships; applicants are encouraged to indicate interest in assistantship support and to contact potential faculty advisors about openings.

Career prospects

Graduates of the PhD programme in Computational Mathematics pursue careers across academia, national and governmental laboratories, and industry. Typical roles include university faculty and postdoctoral researchers, research scientists at national labs, and applied research or quantitative roles in industries such as aerospace, energy, finance, engineering, data science, and software development. The programme’s emphasis on numerical algorithms, scientific computing and high-performance methods also prepares graduates for positions requiring expertise in large-scale simulation, algorithm implementation, and multidisciplinary collaboration.

Alumni commonly work on problems involving modelling and simulation of physical systems, optimisation and control, uncertainty quantification, and data-driven mathematical methods, bringing strong analytical and computational skills to teams in both research and product development contexts.

Why study at Idaho State University

Idaho State University offers a supportive, research-active environment with close faculty-student collaboration in mathematics and computational sciences. The department’s faculty have expertise across numerical analysis, PDE theory, optimisation and scientific computing, providing a range of supervision options for computational-research projects. Students benefit from access to university computing facilities and parallel computing resources, and there are opportunities to collaborate with nearby research institutions and national laboratories on applied computational problems.

The department emphasises hands-on computational training and teaching experience through assistantships, preparing graduates for both research and instructional careers. Additionally, the campus environment and regional research ecosystem make it practical to pursue interdisciplinary projects with engineering, physics, and computer science groups, enhancing employment and research opportunities after graduation.