Applied Mathematics (Ph.D.)

The IAM Ph.D. is a unique Applied Mathematics program designed to facilitate interdisciplinary research among graduate students and participating faculty. This interdisciplinary program gives students the opportunity to explore the frontier where the sciences meet cutting-edge mathematical analysis and high performance computing. Science topics include Fluid Dynamics, Plasma Physics, Space Physics, Geoscience, and Dynamical Systems.

Admission Requirement

Applicants to the Integrated Applied Mathematics Ph.D. program are expected to have a bachelor'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
Analytical Fluid Dynamics
and Viscous Flow
Magnetohydrodyamics of the Heliosphere
and Plasma Physics
Select a minimum of three technical electives:9
Asymptotic and Perturbation Methods
Waves in Fluids
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 numerical analysis and high-performance computing
  • Oral or written exam in specialization area

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


Students must present a seminar presentation of thesis proposal to dissertation committee.

Upon completion of research, students must present a seminar on the research.

Students must submit a dissertation that includes original research in integrated applied mathematics.