Middle Tennessee State University (MTSU)

What you'll study

The programme combines advanced coursework, comprehensive examinations and an original research dissertation. Core coursework typically covers rigorous mathematical foundations and computational methods that underpin applied work, followed by specialised electives aligned with a student’s research interests.

• Core topics: advanced real and complex analysis, functional analysis, numerical analysis, partial differential equations (PDEs), and applied linear algebra.
• Computational and applied methods: scientific computing, numerical linear algebra, finite element/finite difference methods, numerical solution of PDEs, mathematical modelling, optimisation and computational statistics.
• Applied specialisms: dynamical systems and chaos, stochastic processes and SDEs, inverse problems, data-driven modelling, machine learning methods for scientific computing, and applications in fluid dynamics, materials, biology or finance depending on faculty expertise.
• Research training: research seminars, journal clubs, pedagogy and ethics in research, and dissertation research under the supervision of a faculty advisor.

Students progress from coursework to qualifying/comprehensive examinations that assess breadth and depth, then focus on an original research project culminating in a written dissertation and oral defence. Many students also gain teaching or research assistant experience as part of their training.

Entry requirements

Applicants are normally expected to hold a relevant master’s degree in mathematics, applied mathematics, or a closely related quantitative field, with strong preparation in advanced calculus, linear algebra, differential equations and introductory real analysis. Exceptional applicants with a strong bachelor’s degree and significant research or industry experience may be considered.

• Academic transcripts: evidence of strong performance in undergraduate and graduate coursework in mathematics or related areas.
• Letters of recommendation: typically two to three letters from academic or professional referees who can speak to research potential.
• Statement of research interests: a concise description of research background, interests and potential faculty mentors.
• Curriculum vitae: outlining academic background, publications, presentations and relevant work or research experience.
• English language proficiency: for international applicants, an accepted English language test score or approved equivalent is required if prior education was not in English.

Some specialisations or assistantship positions may require demonstration of programming experience (for example MATLAB, Python or C/C++) and numerical computation skills. Admissions decisions also consider fit with faculty research and availability of supervisory support and funding.

Career prospects

Graduates of an applied mathematics PhD pursue a wide range of careers where advanced quantitative and modelling skills are valued. Typical career paths include:

• Academic research and teaching: faculty positions in mathematics, applied mathematics, engineering departments and interdisciplinary programmes.
• Industry R&D: roles in engineering firms, aerospace, energy, telecommunications, pharmaceuticals and materials companies applying mathematical modelling and simulation to product development and process optimisation.
• Data science and quantitative analytics: positions in finance, insurance, technology companies and consulting where mathematical modelling, statistical methods and machine learning are applied to large-data problems.
• Government and national labs: research scientist or analyst positions in national laboratories, defence, environmental agencies and public-sector research organisations.
• Specialist technical roles: computational scientist, numerical analyst, systems modeller, and optimisation specialist in cross-disciplinary teams.

The programme’s emphasis on both theory and computation equips graduates to adapt to evolving technical challenges and lead interdisciplinary projects.

Why study at Middle Tennessee State University (MTSU)

MTSU’s Department of Mathematical Sciences provides a supportive environment for doctoral study with faculty engaged in a range of applied research areas, including numerical analysis, PDEs, dynamical systems, applied probability and computational modelling. Students benefit from close faculty mentoring, opportunities for collaborative projects across engineering and sciences, and access to university computing resources.

• Research-active faculty: a variety of supervisors with expertise in theoretical and computational aspects of applied mathematics, offering supervision across multiple application domains.
• Interdisciplinary collaboration: opportunities to work with engineering, physics, biology and computer science researchers on applied problems and grant-funded projects.
• Professional development: teaching assistantships and research assistantships help build communication, teaching and project management skills; students can also present at conferences and publish in peer-reviewed journals.
• Location and resources: based in Murfreesboro near a regional hub of industry and technology, with access to regional partnerships and computing infrastructure to support large-scale simulations and data analysis.

Overall, MTSU’s PhD in Applied Mathematics is structured to prepare graduates for research careers that bridge rigorous mathematics and real-world applications.