Here is a partial list
1. Difference equations in population dynamics
2. Biological applications of ordinary differential equations
such as population dynamics, chemical kinetics, excitable systems
neural impulses, oscillations in chemical systems etc.)
3. Spatially distributed systems and pde models. convection ,diffusion and
attraction or repulsion, the spread of genes in a po;ulation, signal
propagation in axons, morphogenesis and pattern formation in biology.
Texts and references:
de-Vries et. al. A course in Mathematical Biology (Primary text)
Keshet - Mathematical Models in Biology (Primary text)
Keener - Sneyd Mathematical Physiology
Murray - Mathematical Biology
Taubes - Modelling Differential Equations in Biology
Grading: HW 65% Assigned problems.
May be done cooperatively. If you work together on a homework
set, you must tell me who was involved in the work.
Homework problems assigned thus far:
HW set #1. P8, problems 1,3 Due August 28,
set #2 p 48, problems 2, 5,6,7 Due September 6
HW set #3 p 51, problems 11, 13, 15b,18 Due September 15
HW set#4 p 91. problems 4,6,10,12,13,16,17 Due October 4,
HW set # 5. p116 problems 1, 5. Due October 30.
HW set # 6. p151 problems 5, 8 Due November 17.
Class project 35%. The class project
will be to give a 30 minute presentation to the class on the contents of
a paper of the student's choosing that must come from one of a given set of
mathematical biology journals
and must include a significant quantity of material from both mathematics
and from biology.
The student should be able to convince the audience that
he or she really understands both sides (mathematics and biology) of
The articles may come from any of the following journals. (I may add to this
list from time to time) (If you find a paper in another
journal, not listed here, I must preapprove the journal.)
1. Journal of Mathematical Biology
2. Bulletin of Mathematical Biology
of Theoretical Biology
4. Mathematical Biosciences
5. Theoretical Population biology
6. IMA Journal of
Mathematics Applied in Medicine and Biology
student must bring me not more than three articles for pre approval before
beginning the project. I must
see these papers no later than November 10, 2006.
Student Presentations for Math 690P, An Introduction to Mathematical
Biology. (In order of presentation)
1. Reaction-Diffusion Equations and Inverse functions
Jaemin Shin Presentation
2. Modeling Brain Energy Metabolism
Wen Zou Presentation
3. An Investigation of Population Interaction
Lindsay Kasuga Presentation