MATHEMATICS 690-Fall, 2006 - Spring, 2007

Topics in Mathematical Biology

Carver 132

Instructor: Howard A. Levine , Department of Mathematics, 410 Carver

Office Hours: MWF  11-12

Phone 515-294-8145, e-mail:

Here is a partial list of topics:

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,

HW 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 paper.  

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

3.  Journal of Theoretical Biology

4.  Mathematical Biosciences

5. Theoretical Population biology

6. IMA Journal of Mathematics Applied in Medicine and Biology

The 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 and Function Wen Zou Presentation

     3. An Investigation of Population Interaction Dynamics  Lindsay Kasuga Presentation

     4.  Lumped processes for analyzing grouping in DNA sequences  Vladimir Sukhoy Presentation

    5.  Competitive Exclusion in a Vector-Host Model for the Dengue Fever Cory Howk Presentation