Mathematical Biology
Mathematical Biology
Mathematics 439-839
Spring Semester 2007
David Logan, Willa Cather Professor of Mathematics
Textbook
L. Edelstein-Keshet, 2004. Mathematical Models in Biology, SIAM (Soc. Ind. Appl. Math.), Philadelphia (reprint).
References
There are many excellent texts on mathematical biology. Here is a short list:
- F. Brauer and C. Castillo-Chavez, 2001. Mathematical Models in Population Biology
and Epidemiology, Springer-Verlag.
- T. Case, 2000. An Illustrated Guide to Theoretical Ecology, Oxford University Press
- L. W. S. C. Gurney & R. M. Nisbet, 1998. Ecological Dynamics, Oxford University Press.
- M. Kot, 2001. Elements of Mathematical Ecology, Cambridge University Press.
- N. Britton, 2002. Essential Mathematical Biology , Springer-Verlag.
- L. Allen, 2007. Introduction to Mathematical Biology Pearson Prentice-Hall.
- E. Allman & J. Rhodes, 2004. Mathematical Models in Biology , Cambridge University Press.
Biology Topics in the Course
- Ecology and population biology
- Pharmacokinetics and compartmental analysis
- Life history theory and energy budgets
- Epidemiology and infectious diseases
- Age-Structured models (if time)
Prerequisites for Mathematical Biology
The prerequisite for the course is Calculus II (Math 107). However, because this is a 400-800 level course,
there is a certain amount of mathematical maturity, or sophistication, that is implied.
For example, students should be able to digest and then use key ideas in differential equations and
linear algebra to analyze biological systems. The text contains an excellent discussion of these two topics, and students
may be required to read some of the material on their own. Finally, 400-800 level mathematics courses are not formula-driven, or
"plug-and-chug", courses like algebra, calculus, differential equations, or linear algebra courses; they involve
critical thinking and the ability to understand and work with concepts, analyze mathematical problems, and write correct mathematics. There is no biology
prerequisite, except that students should have an interest in issues in the biological sciences.
Assessments
The final grade for the course will be based upon the following assessments:
assigned exercises (25%); two midterm exams (50%); final examination (25%).
The exams will have both a take-home and an in-class component. Computer laboratory exericises may be required.
Assigned Exercises from Textbook
Try to keep exercises in a separate, loose leaf, notebook so they can be easily removed and checked.
Suggested exercises from the text will be listed here, by chapter. These problems represent a minimal
assignment; clearly, the more exercises you do, the better you will understand the material. There will also be other
exercise sheets. I will let you know when and what exercises are due.
Chapter 1--- 1, 2cd, 3b(ii), 4, 6e, 7a, 8d, 9b, 10, 11, 16, 20abc (do for m=4 only).
Chapter 2---1abc, 2ad, 3, 4, 8, 10 (first rescale by letting P(t)=aN(t)), 14, 15, 16.
Chapter 3---3, 4, 5
Chapter 4---1, 3, 4, 5a-e, 15, 17, 18, 19, 20
Chapter 5---2
Chapter 6---1, 2ab, 3, 4, 6, 7a
MATLAB
As a part of the course, students will learn programming skills in MATLAB. I will give "templates" that you
can use in the computer laboratories. The MATLAB computer algebra system is on the
department's web site, and all students have an account. Student versions of MATLAB
can be purchased at the campus Computer Shop (501 Bldg) for about $100, if you want your own copy. Mathematica or
Maple will also suffice, but you are on your own if you choose one of these. Class time will be devoted to MATLAB.
pplane5.m (a Matlab program that numerically solves differential equations) can be downloaded
free from http://www.math.rice.edu/~polking/ .