University of Alabama

What you'll study

The PhD in Applied Mathematics combines rigorous coursework, comprehensive examinations and an original research dissertation. Early in the programme you will take advanced core courses in areas such as real and functional analysis, partial differential equations, numerical analysis, and scientific computing. You will then select specialised electives related to your research focus — for example, mathematical modelling, fluid dynamics, optimisation, stochastic processes, computational methods for inverse problems, data assimilation, machine learning for scientific computing, or mathematical biology.

Research training emphasises the formulation and analysis of models, numerical algorithm development, and high-performance computing. Students work closely with a faculty advisor and research group and are expected to present at seminars and conferences. The degree requirements typically include qualifying or candidacy examinations, a written dissertation proposal, and the production and defence of a PhD dissertation based on original research.

Entry requirements

• Academic background: A master’s degree in mathematics, applied mathematics, or a closely related discipline is normally expected, although exceptionally well-prepared students with a strong bachelor’s degree may be considered. Applicants should have substantial coursework in advanced calculus/real analysis, linear algebra, differential equations, and numerical methods.
• Application documents: Transcripts, a statement of purpose outlining research interests, a curriculum vitae, and at least three academic or professional letters of recommendation are required.
• Quantitative preparation: Demonstrated ability in mathematical proof and computational work is important; familiarity with programming (e.g. Python, MATLAB, C/C++, or Fortran) and experience with numerical simulation or data analysis strengthen an application.
• English language: International applicants must meet the University’s English language requirements; acceptable test scores or approved waivers are considered per institutional policy.
• Additional assessment: Some applicants may be asked to submit writing samples, a research proposal, or to participate in an interview with potential advisors. Standardised test requirements (such as the GRE) are determined by the department and may vary; check the department admissions guidance for current expectations.

Career prospects

Graduates from a PhD in Applied Mathematics go on to a wide range of careers. Many pursue academic positions in mathematics or related departments, while others move into postdoctoral research to deepen specialised expertise. In industry, graduates are in demand for roles in R&D, quantitative modelling, data science, computational engineering, software development for scientific applications, and financial modelling.

Applied mathematicians are also employed by national laboratories and government agencies working on problems in climate modelling, defence, energy, and public health, and by private-sector firms developing optimisation and simulation tools. The programme’s emphasis on computation and interdisciplinary collaboration prepares graduates for positions that require both deep theoretical understanding and practical algorithmic implementation.

Why study at University of Alabama

• Research-active faculty: The Department of Mathematics at the University of Alabama includes faculty working across a range of applied mathematics areas, offering opportunities to join projects in numerical analysis, PDEs, fluid mechanics, mathematical biology, and data-driven modelling.
• Interdisciplinary collaboration: There are strong links with other units on campus — including engineering, computer science, physics and biomedical research — enabling interdisciplinary projects and co-supervision opportunities.
• Computational resources: Graduate students have access to campus computing facilities and software resources needed for large-scale numerical experiments and data analysis.
• Funding and training support: The department typically offers funded opportunities such as teaching and research assistantships, which provide tuition support and professional development in teaching and research.
• Graduate community and professional development: Regular seminars, workshops and student-led activities create a collaborative environment; students receive mentoring in presenting research, publishing, and preparing for academic and non-academic careers.