University of Iowa

What you'll study

The PhD programme combines advanced coursework, qualifying examinations, research seminars and an original dissertation. Core topics commonly studied include partial differential equations, numerical analysis and scientific computing, dynamical systems, optimisation, inverse problems, stochastic processes and mathematical modelling in the physical and life sciences. Students typically take a mix of required graduate-level courses and electives to support their research focus.

• Coursework and seminars: Advanced analysis, numerical linear algebra, finite element and finite difference methods, spectral methods, numerical PDEs, optimisation theory, stochastic differential equations, and specialised topics courses reflecting faculty expertise.
• Qualifying and preliminary exams: A written and/or oral qualifying examination assesses readiness to undertake research; a preliminary or candidacy exam establishes the dissertation topic and committee.
• Research and dissertation: Independent research under a faculty advisor leading to a doctoral dissertation. Research areas span theory, computation and application across disciplines.
• Teaching and professional development: Many students gain teaching experience as graduate instructors or teaching assistants and participate in departmental seminars, workshops and conference presentations.

Entry requirements

Applicants should hold a bachelor’s degree in mathematics or a closely related discipline; a master’s degree with substantial graduate coursework in mathematics is commonly expected or recommended. Successful candidates demonstrate strong preparation in advanced calculus/real analysis, linear algebra, differential equations and numerical methods.

• Academic record: A strong undergraduate and, if applicable, graduate transcript in mathematics or a related field.
• Supporting documents: Research statement or statement of purpose outlining interests and fit with the department, curriculum vitae, and letters of recommendation from instructors or supervisors who can speak to mathematical ability and research potential.
• English language proficiency: International applicants must meet the university’s English language requirements (e.g. recognised test scores) unless exempt by institutional policy.
• Additional considerations: Prior research experience, computing skills, and alignment with potential faculty advisors strengthen an application. Prospective students are encouraged to identify faculty whose research matches their interests.

Career prospects

Graduates of the PhD in Applied Mathematics pursue diverse careers. Many continue in academia as postdoctoral researchers and faculty members. Others take research scientist or data scientist roles in industry—such as finance, engineering, energy, technology and pharmaceuticals—or positions in government and national laboratories.

• Academic research and university teaching
• Postdoctoral appointments in mathematical sciences and interdisciplinary fields
• Industry roles in quantitative modelling, computational science, machine learning and data analytics
• Research positions in national labs, engineering firms, biotech and applied R&D groups
• Consulting and quantitative roles in finance, insurance and technology companies

Why study at University of Iowa

The University of Iowa offers a supportive research environment within a mathematics department that hosts experts in analysis, numerical methods, dynamical systems and interdisciplinary modelling. Students benefit from close mentorship, regular seminars and opportunities to collaborate with neighbouring departments such as engineering, physics, statistics and the life sciences.

Facilities and resources include access to campus computational resources and high-performance computing, as well as opportunities to engage with applied research centres and labs on campus. The programme emphasises both rigorous theoretical training and practical computational skills, preparing graduates for research and applied careers across sectors.