Chapman University

What you'll study

The programme combines advanced coursework, qualifying examinations, and an original research dissertation. Early-stage coursework typically covers core areas such as real and complex analysis, algebra, topology, probability theory, statistical inference, and numerical analysis, with additional classes in applied and computational topics.

• Core theoretical modules: advanced real analysis, abstract algebra, topology and measure-theoretic probability to build a rigorous mathematical foundation.
• Statistical theory and methods: courses in mathematical statistics, linear models, multivariate analysis, and nonparametric methods emphasise both theory and practical implementation.
• Computational and applied topics: numerical linear algebra, scientific computing, optimisation, stochastic modelling, and machine learning provide tools for data-driven research.
• Electives and seminars: students choose advanced electives aligned with research interests (for example: PDEs, dynamical systems, time series, spatial statistics, Bayesian computation) and participate in reading groups and research seminars.
• Research components: after completing required coursework and passing qualifying exams, students undertake original research under a faculty advisor, culminating in a written dissertation and public defence.
• Teaching experience: structured opportunities to develop teaching skills through assistantships or supervised classroom teaching are a typical part of training.

Entry requirements

Successful applicants normally hold a strong undergraduate degree in mathematics, statistics, or a closely related field; many applicants also present a relevant master’s degree. Admissions consider the applicant’s mathematical preparation, letters of recommendation, statement of research interests, and evidence of ability to undertake independent research.

• A bachelor’s or master’s degree with substantial coursework in calculus, linear algebra, real analysis, probability and mathematical statistics is expected.
• Prior coursework or experience in proof-based mathematics is highly desirable.
• Applicants should provide academic transcripts, two to three academic references, and a statement describing research interests and preparation.
• Some applicants may submit evidence of programming or computational experience (for example in Python, R, MATLAB) depending on research focus.
• Standardised test requirements vary; applicants should check the department’s current guidance on tests such as the GRE or English language proficiency exams if applicable.

Career prospects

Graduates from doctoral programmes in mathematics and statistics move into a broad range of careers that value rigorous quantitative thinking and research skills. Career paths include academic positions (postdoctoral research and faculty appointments), research roles in industry and national laboratories, and applied analytical positions across several sectors.

• Academia: tenure-track and research appointments, postdoctoral fellowships in mathematics, statistics, applied mathematics and data science departments.
• Industry: roles in data science, machine learning, quantitative finance, software and technology companies, and advanced analytics teams where modelling and algorithm development are central.
• Government and national labs: research scientist and analyst positions in agencies and laboratories focusing on modelling, simulation, and statistical analysis.
• Consulting and applied roles: specialised quantitative consulting, biostatistics and epidemiology, actuarial work, and industrial R&D.

Why study at Chapman University

Chapman University offers a doctoral environment that emphasises close mentorship, small cohort sizes and opportunities for interdisciplinary collaboration. The university’s location in Southern California provides access to a vibrant regional technology and business ecosystem, which can be beneficial for applied research and industry connections.

• Faculty mentorship: students work directly with faculty on supervised research projects, benefiting from personalised guidance and accessible advisors.
• Interdisciplinary opportunities: collaborations across departments—such as computer science, engineering, economics and the life sciences—support applied and cross-cutting research topics.
• Computational resources: access to modern computing facilities and software tools supports computationally intensive research in statistics and applied mathematics.
• Professional development: teaching experience, seminar presentation opportunities and connections to regional employers help prepare graduates for both academic and non-academic careers.