University of Northern Colorado

What you'll study

The programme integrates advanced training in both mathematics and statistics, allowing students to build a customised programme of study across core theoretical topics and applied areas. Typical elements include coursework, qualifying examinations, research rotations or directed reading, and a doctoral dissertation under faculty supervision.

• Core mathematical topics: real and complex analysis, abstract algebra, topology, differential equations and functional analysis.
• Core statistical topics: probability theory, mathematical statistics, regression and generalized linear models, Bayesian inference and asymptotic theory.
• Applied and computational areas: numerical analysis, scientific computing, stochastic processes, time series, multivariate analysis, computational statistics, and methods for big data.
• Specialised seminars and electives: subjects such as mathematical biology, financial mathematics, machine learning, spatial statistics, nonparametric methods and statistical computing are offered depending on faculty expertise and student interest.
• Research and dissertation: after completing coursework and any required qualifying exams, students focus on original research leading to a written dissertation and oral defence. Students are expected to present research at seminars and conferences during their studies.
• Teaching and professional development: doctoral students typically gain experience through teaching assistantships or lecturing, and through professional development workshops in pedagogy, grant writing and communication.

Entry requirements

Applicants are normally expected to hold a relevant master's degree in mathematics, statistics, or a closely related discipline. Exceptional candidates with a strong bachelor's degree and substantial research or applied experience may be considered.

• Academic preparation: solid background in advanced calculus, linear algebra, real analysis, and probability or mathematical statistics. Additional preparation in differential equations, abstract algebra or numerical methods is advantageous.
• Supporting documents: transcripts, a statement of purpose outlining research interests, and academic references from faculty who can speak to the applicant's research potential.
• Research fit: clear alignment with faculty research areas and the ability to identify potential supervisors strengthens an application.
• English language: international applicants whose first language is not English must meet the university's English-language proficiency requirements.
• Additional considerations: prior research experience, publications, programming skills and quantitative computing experience are viewed positively. Standardised test requirements vary; applicants should consult the programme for current guidance.

Career prospects

Graduates of the programme move into a wide range of careers that draw on deep quantitative, analytic and research skills.

• Academia: tenure-track faculty positions, postdoctoral research and university teaching roles.
• Industry and private sector: data science, machine learning engineering, quantitative analysis in finance, modelling and simulation roles in technology and engineering firms.
• Government and national labs: research scientist roles, statistical work in public health and policy, and applied modelling for defence or environmental agencies.
• Research and consulting: specialist consultant roles in analytics firms, biostatistics and pharmaceuticals, and consultancy on complex quantitative problems.
• Education and outreach: leadership roles in secondary or tertiary mathematics education, curriculum development and professional training.

Why study at University of Northern Colorado

The University of Northern Colorado offers a doctoral programme with a balance of rigorous theoretical training and applied research opportunities within a collegial, student-centred environment. Students benefit from close mentorship by faculty active in a range of research areas across pure mathematics, applied mathematics and statistics, and from opportunities to collaborate across departments and with regional research partners.

• Small cohort and personalised mentoring: the programme emphasises close working relationships with faculty, enabling tailored supervision and regular feedback on research progress.
• Research diversity: a variety of faculty interests means students can pursue pure theory, computational methods or applied statistical work, and often combine strands to suit interdisciplinary research questions.
• Teaching and funding opportunities: graduate assistantships and teaching roles provide professional development and financial support during study.
• Facilities and computing resources: access to departmental computing resources, statistical software and regional collaborative networks supports both theoretical and data-intensive research.
• Location advantages: proximity to a vibrant regional economy and to metropolitan research, industry and government hubs expands internship and employment possibilities while offering a supportive campus community.