Spring 2006--Math 375 : Mathematical Modeling
in Biology (Uhlenbeck)

Students: upper division majors in the college of natural science, especially biology, biochemistry and chemistry

Time: Tu-Th 11:00-12:15

Text: (note
change in text) Leah
Edelstein-Keshet, Mathematical Models in Biology, from SIAM
(Society for Industrial and Applied Mathematics) ($50 new in paperback)

Prerequisites: Calculus
and interest and knowledge in some area of science

Topics: The course covers basic material on the behavior of systems of difference equations and ordinary differential equations, especially linearization and limits. Applications are emphasized . Some material on side topics such as logarithms and exponentials, matrices and partial differential equations will be included.

Some of the aplications in the text (there are many others which you will find easy to find in the books on reserve):

- Cell-division
- Blood CO
_{2 }levels

- Population dynamics (insects, preditor-prey, competition, plant-herbivore, bacterial growth)
- logistics
equation and chaos

- Infectious diseases
- Glucose-insulin
kinetics

- Molecular
models

- Enzyme
kinetics (Michaelson-Menton equations)

- Nerve
Impulses (Hodgkin-Huxley equations)

Part of the
grade is based on class
presentations and projects (which may be done in groups). In class work
sheets will be used to practice the details of calculation.
Students
will learn to use simple software programs to graph functions and to
solve
differential equations. There will be a TA in addition to the
professor.

Frequently asked
questions:

$$I am a math major. Can I take the course? Yes, but you should be interested in science, or you will find it difficult and boring. If you have taken both linear algebra and differential equations, you will find the mathematical content pretty straightforward. I would not advise taking the course if you have had math 346 (applied linear algebra).

$$Can I get credit for math 375 and math 427K? Yes. There is a very small overlap of material, but it is not significant. If you took Math 427K from me in spring 2005, you covered some of the material in the second part of the course.

$$Can I use math 375 as a replacement for math 427K? Yes, at least if you are a math major. If you are not a math major, you need to consult with an advisor to your program.

$$Is the computer work very time consuming? The computer work is kept down to one assignment every other week. However it is important in science today to use computers, so we do this.

$$I am interested in **** (pharmacology, geology, conservation biology, water quality etc. etc.) Do we cover this in the course? Not necessarily, but you are expected to do a project, and you can do a project on whatever you are interested in. I have better references on some topics than others. Your science professor may help with other suggestions.

$$Will the course be taught again next spring (fall)? Professor Davis will teach the course next in the Spring of 2007.

$$Will
the course help me get into graduate school in my science?
As

far as we can tell, the students who took the course in past years did
well in their applications to graduate school.

$$I
plan to be a high school teacher. Will this course be useful? Yes,
the course would be very useful, but you have to know both math and
science.
It might turn out to be difficult.