Ph.D.Emphasis in
Mathematical Ecology
Introduction
Below is a description of one curriculum leading to a PhD in Mathematics with
an emphasis in theoretical ecology. (Please note that other faculty in the Department of Mathematics may suggest
different courses and examinations, depending upon the student's interests and the faculty's own expertise,
research, and curricular philosophy). My own areas of interest include:
--Effects of global climate change and abiotic factos on food webs and predator-prey interactions
--Continuous, structured models involving partial differential equations, disease ecology, and predation
--Models involving stochastic processes
Students in theoretical ecology should expect to develop expertise in both
mathematics and in biology. This means students should take courses,
qualifying examinations, and Ph.D. comprehensive examinations in both applied
mathematics and mathematical ecology; the dissertation
will be in the area of theoretical biology.
Good, very elementary introductions are given in
- Vandermeer & Goldberg. Population Biology , Cambridge University Press.
- E. Allman & J. Rhodes. Mathematical Models in Biology , Cambridge University Press.
Students in the program should master most the topics discussed in the following reading list (there is
significant overlap):
- M. Kot. Mathematical Ecology , Cambridge University Press.
- N. Britton. Essential Mathematical Biology , Springer-Verlag.
- W. Gurney & R. Nisbet. Ecological Dynamics, Oxford University Press.
- P. Grindrod, Patterns and Waves , Oxford University Press.
- W. Murdoch & R. Nisbet, Consumer-Resource Dynamics , Princeton University Pres.s
- T. Case. An Illustrated Guide to Theoretical Ecology, Oxford University Press.
- M. Mangel. A Theoretical Biologist's Toolbox, Cambridge University Press.
- S. S. Otto & T. Day. Mathematical Modeling of Biological Systems, Princeton University Press.
- L. Allen, 2003. Introduction to Stochastic Processes with Applications to Biology,
Prentice-Hall.
- F. Brauer & C. Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology, Springer-Verlag.
- L. Edelstein-Keshet. Mathematical Models in Biology, SIAM.
- D. Logan & W. Wolesensky, 2009. Mathematical Methods in Biology, Wiley-Interscience.
Good undergraduate preparation
for the program includes Differential Equations (Math 221), Linear Algebra (Math 314), Partial Differential
Equations (Math 324), Probability and Statistics (Stat 380), Modern Algebra (Math 310), Elementary Analysis (Math 325), Complex Variables
(Math 423), and knowledge of Matlab. No courses in biology are required at this point.
The qualifying examinations in mathematics should be over the following sequences:
- Mathematics 825-826 Analysis (this exam is required)
- Mathematics 842-843 Applied Mathematics
The qualifying examination should be completed by the end of the second year.
The Ph.D. written comprehensive examination will be over the following:
- One area determined by the PhD Supervisory Committee with consultation with the student
- Mathematical Biology (the nature of the exam is decided with consultation with the PhD Supervisory Committee)
A student should complete the PhD comprehensive examination by the end of the third year.
The coursework for the PhD is determined by the student in consultation with the PhD Supervisory Committee.
A Suggested Curriculum for the first two years. Some courses are required*.
Note: Students should enroll for one credit hour each semester in the Math-Biology Seminar (Math 943).
YEAR 1
- Math 839-Bios 856 (Mathematical Biology)
- Math 825-826* (Mathematical Analysis)
- Math 842-843* (Applied Mathematics)
YEAR 2
- Ecology, Evolution, and Behavior (6 cr hr sequence from Biological Sciences)
- Math 847-942 Numerical Analysis.
- Mathematics 850-852*, Discrete Mathematics. LI>
OTHER SUGGESTED COURSES
- Math 887(Probability)
- Math 832-833 (Optimization)
- Math 921-922 (Real Analysis)
- Math 935-936 (Advanced Applied Mathematics)
- Math 816 (Linear Algebra)
- Math 937-941 (Partial Differential Equations)
- Math 927-938 (Asymptotics and Modeling)
- Math 932-933 (Ordinary Differential Equations)