Differential equations is a central area of mathematics, and one of their recent and most exciting applications is in mathematical biology. ASU offers graduate studies in ordinary, partial, and functional differential equations and in related areas such as perturbation theory and dynamical systems. Applications in mathematical biology concern cellular and neural modeling, ecology, epidemics, genetics, physiology, and population dynamics.

PREREQUISITES

In addition to the general departmental prerequisites, Applied Complex Analysis, and proficiency in
MATLAB and a computer language are required. Advanced Linear Algebra is desirable.

COURSE WORK

The Ph.D. student takes 30 credit hours in the following six areas: intermediate and advanced Real Analysis, Numerical Analysis, Ordinary Differential Equations, Mathematical Biology, Partial Differential Equations, Probability and Statistics. In addition, 30 credit hours are taken in approved courses from the Department of Mathematics and courses from outside the Department that are related to mathematical modeling. The selection should ensure sufficient breadth and coherence in the student's program of study. Students who wish to place a greater emphasis on analysis would take further courses in differential equations, perturbation theory, dynamical systems, functional analysis, operator theory or topology, or would take further courses in computational mathematics. Students who emphasize modeling take further modeling courses from inside or outside the Department.

EXAMINATIONS

Two qualifying examinations are taken out of the following four: Real Analysis, Numerical Analysis, Differential Equations, Mathematical Statistics. The comprehensive examination, with the advisor's approval, may be chosen from the following seven areas: Mathematical Biology (physiological modeling, models in population dynamics), Ordinary Differential Equations, Partial Differential Equations, Applied Analysis (Functional Analysis, Topology, Fractal Geometry), Computational Mathematics, Probability and Statistics, outside field related to mathematical modeling.

FACULTY

For more information on specific aspects and content of this program, read this article in Science magazine's SCIENCE ONLINE, or contact one of the Differential Equations and Mathematical Biology faculty:

Baer, Steve (Bifurcation analysis, Numerical methods, Neurobiology)       
Castillo-Chavez, Carlos (Mathematical Biology)
Crook, Sharon ( Mathematical and computational neuroscience, Computational methods in genomics)
Kuang, Yang (Mathematical Biology and Medicine, Delay Differential Equations)
Kuiper, Hank (Partial Differential Equations, Numerical Analysis)
Smith, Hal (Differential Equations, Dynamical systems, Mathematical Biology)
Thieme, Horst (Differential Equations, Dynamical systems, Mathematical Biology)