M375 Mathematical Biology Fall 2002

Minor Project Description

For your minor project, you form a group and initiate some  background research research into a topic in either mathematics or biology.  The material should be presented orally to the class.  The idea is to  find some initial material which you would like to develop more seriously, and give an initial presentation.

The general rule of the presentation is that your group  is expected to talk  for 10-15 minutes plus five minutes for every member of the group.  You are advised (but not required) to prepare overheads,  as this is a standard method of giving material.   Power point is OK, too -- there are projectors available, and even without them we're such a small group that we can huddle around a laptop.  You may essential elect to chose any sort of topic for your project.  I would suggest roughly three types of projects:

1)  Groups which start  from actual scientific data:

Here the suggestion is to need to present the information, the experiment, the data, or whatever it is that you have.  Students who work in a lab can use their experiments, it is possible to choose one of the articles in the text or in a journal  with the goal of  later developing mathematical ideas which connect with the article, and it is possible simply to get information from the library,  a professor, or the web.  You may use biology, chemistry, geology, or conservation questions.  Dr. Uhlenbeck even had a graduate student study voting behavior!

In the second  major  project , which is a written report,   these ideas are to be written down and some mathematics introduced, whether it is successful or not in answering the questions!

In the past, students have talked about the lab work they did, (two  students in chemistry), obtained basic information about drug absorption (A student in pharmacy) , taken material from the web (a group of three  math students  learning about control of fire ants), obtained a journal paper  from a professor with the ultimate goal of understanding the details (one student with a paper on  AIDS) and obtained information from public sources (a math student  working on critical water management in her home town).

2)  Groups starting from mathematics:

It is certainly possible to select a topic in  mathematics, (chaos  in the logistic equations, the  history and behavior of  classical differential equations like the  behavior in the Lorenz  or another attractor,  the Poincare Bendixson theorem about periodic orbits  of differential equations in the plane) or even something like the numerical algorithms which are used on the computer to solve equations)  The initial presentation is only to describe the  basic idea to the class. There is no requirement to hand in written paper.

In the second  major project, the goal would be to  make the mathematical description more complete and possibly to apply to some biological or other scientific model.

3)  Groups wishing to do a more traditional modeling project:

There are a number of texts in Professor Uhlenbeck's office which have chapters on all sorts of things, from shock waves in traffic flow,  models of enzyme reactions,,   epidemic modeling,  and so forth.  This is the typical project she has had students from math 427K (mostly engineers) do for a long time.  There are LOT of examples in her office that you can look at. (Just see her secretary, Toria Esile)

4)  Topics which are a mixture:

Especially if you have a group with varied backgrounds, you might mix and match the above. I assume you are more creative than I am at this.

5) Something else:

Well, past submissions have included movies , videos, web sites and physical models.  I do not accept computer discs (the past experience has been that they never work without  a couple of hours of input from our  math department  systems manager. If you get an idea about this, talk to Dr. Zhou first!)  These are all  probably more  work.

Incidentally, there are poster sessions in the college , and you might like to keep in mind that your project could be developed into a nice poster  presentation  for some future poster session.

It is not necessary to continue the minor project into the major if something  more intriguing comes along.  In particular, several groups might join efforts after  they hear the presentations.