Colorado State University

What you'll study

The PhD programme combines advanced coursework, qualifying examinations and original research. Core study areas include real and complex analysis, functional analysis, numerical linear algebra, numerical methods for ordinary and partial differential equations, scientific computing, optimisation, and probability and statistics for computation. Students take seminars and readings in specialised topics such as finite element and spectral methods, computational inverse problems, uncertainty quantification, high-performance computing, model reduction, and data-driven numerical methods.

Typical progression includes a period of structured coursework to build breadth and depth, written and/or oral qualifying examinations to demonstrate readiness for research, selection of an adviser and research committee, and focused dissertation research. Students participate in departmental seminars, research groups, and interdisciplinary projects with engineering, physics, statistics and computer science faculty. Teaching assistantships are commonly part of the training experience.

Entry requirements

Applicants are expected to have a strong undergraduate or master's degree in mathematics, applied mathematics, or a closely related discipline. Essential preparation includes rigorous coursework in real analysis, linear algebra, differential equations and introductory numerical analysis; familiarity with programming and scientific computing is highly recommended. Admission typically requires academic transcripts, a statement of research interests, letters of recommendation, and a CV.

The department assesses candidates on academic record, preparedness for advanced mathematical research, and fit with available faculty supervision. International applicants must provide proof of English language proficiency where required. Some applicants enter with a master’s degree, while others proceed directly from a bachelor’s; prospective students should consult the department for specific documentation and any test requirements.

Career prospects

Graduates from the computational mathematics track pursue careers in academic research and teaching, national and government laboratories, and industry. Common roles include university faculty, postdoctoral researcher, research scientist or applied mathematician in areas such as computational engineering, climate modelling, energy systems, materials science, and computational biology. Graduates also work in high-performance computing, quantitative finance, data science and software development for technical computing, where expertise in numerical algorithms and large-scale computation is in demand.

Why study at Colorado State University

Colorado State University offers a collaborative research environment with faculty active in numerical analysis, scientific computing and interdisciplinary computational science. Students benefit from access to campus high-performance computing resources, departmental seminars, and opportunities to work with researchers in engineering, physics, statistics and computer science. The department emphasises mentorship and close adviser-student interaction, and Colorado’s regional network of industry and federal research centres provides avenues for applied collaboration and internships.

Located in Fort Collins, the university combines a strong research profile with an engaged academic community, making it a solid choice for students seeking rigorous training in computational mathematics and preparation for research-driven careers.