Applied Mathematics Ph.D.

The IAM Program prepares students for research and teaching careers in the mathematical solution of critical problems in science and engineering. The emphasis of the IAM program is on the use of mathematics and computing to facilitate impactful interdisciplinary research. Accordingly, all students must achieve a high level of training through the required coursework. An IAM Ph.D. candidate is expected to achieve expertise in both applied and computational mathematics as well as one area of specialization including, but not limited to: Fluid Dynamics, Dynamical Systems, Plasma and Space Physics, Mathematical Geo- or Environmental Science, Materials and Solid Mechanics, or Biophysics.

Admission Requirements

Applicants to the IAM Ph.D. Program are expected to have a bachelor’s degree or master's degree in mathematics or an appropriate science or engineering field.


Please visit the Graduate School website for detailed instructions about applying to the program.

Required Courses
PHYS 931Mathematical Physics3
IAM 830Graduate Ordinary Differential Equations3
IAM 851Introduction to High-Performance Computing3
IAM 932Graduate Partial Differential Equations3
IAM 933Applied Functional Analysis3
IAM 961Numerical Analysis I: Numerical Linear Algebra3
IAM 962Numerical Partial Differential Equations3
Select a 2-course specialization sequence, for example, one of the following:6-7
Introduction to Nonlinear Dynamics and Chaos
and Spatiotemporal and Turbulent Dynamics
Magnetohydrodyamics of the Heliosphere
and Plasma Physics
Analytical Fluid Dynamics
and Viscous Flow
Select a minimum of three technical electives:9
Introduction to Artificial Intelligence
Asymptotic and Perturbation Methods
Waves in Fluids
Continuum Mechanics
Introduction to Space Plasma Physics
Introduction to Solid-State Physics
Electromagnetic Theory I
Advanced Solid-State Physics
and/or additional elective as approved by your adviser and program
Total Credits36-37

Candidacy Requirements

Students must pass a three part Ph.D. qualifying exam:

  • Comprehensive exam in mathematical methods
  • Comprehensive exam in scientific computing
  • Oral or written exam in a specialization area

Students must select a research adviser and have identified a research topic.


Students must submit a written thesis proposal and give a seminar presentation summarizing the proposal to a dissertation committee. 

Upon completion of research, a student must give a seminar summarizing the research objectives, methods, findings, and significance.

Students must submit a dissertation that includes original research in applied mathematics.  The dissertation must comply with all policies put forth by the Graduate School

  • Students are skilled at mathematical manipulations and analytic calculations broadly covering the field of applied mathematics. 
  • Students have developed sufficient mathematical background and understanding of key concepts to have a functional literacy in modern applied mathematics journals. 
  • Students can use numerical algorithms to approximate solutions to mathematical problems which are intractable by hand calculation and understand the impact of consistency, stability, and accuracy in the context of numerical computing. 
  • Students have made independent contributions to a significant mathematical research project and have clearly demonstrated the ability to conduct high-level, self-directed research in applied mathematics. 
  • Students are capable of disseminating the results of their research through written (e.g., journal) publications and oral presentations or seminars.