Offered: Spring 1998
Instructors: James M. Ryan (Biology)
Kevin J. Mitchell (Mathematics)
Room: Napier 101 and Rosenberg 009
Time: T-TH: 9:00 to 10:45 AM
Readings: "The Pace of Life" by Bruce King
Mathematicial Models of Biological Systems by Mitchell, Ryan, and Kolmes
"Game Theory" by Kenneth Prestwich
The course supposes no particular background in either mathematics or biology beyond a normal high school education. We will develop the mathematical tools that we will need to use during the course. Biological material will be provided as we proceed through the various units. What we do suppose is that you will be interested and active participants in our learning endeavor!
In particular, we will use examples of biological systems to give an "exploded view" of the modeling processes: simplifying and idealizing the original system, translating the idealized system into mathematics, "solving" the resulting problem or system of equations, and translating "solutions" back to the biological world. We examine the appropriateness of particular kinds of mathematical techniques for certain types of problems and we discuss the possibilities and problems of generalizing the models we build. We emphasize the "translation processes" among the real biological world, an idealized biological world, and the mathematical world.
This is one of the many ponds at the Hanley Nature Preserve which is owned by the Colleges. It is about a 20 minute drive from campus. We will make three field trips here to collect data for the course.
There will be frequently assigned exercises. Some exercises will be done in
class in a group or with a partner, others will be assigned for you to
complete outside of class and to turn in as a written report. Some of the
exercises will involve using the computers in the Macintosh Lab in Rosenberg Hall.
We hope that this will make certain calculations and simulations easier and more
interesting. The course culminates in an individual, field-based project designed by the student and which requires a substantial (10 pages or more) written report in the form of a scientific paper and class presentation. A series of exercises and smaller projects throughout the term familiarize you with the particulars of writing a scientific paper (e.g., abstract, introduction, materials and methods, results, and discussion sections).
Final grades for the course will be based on: (a) class exercises, (b) individual exercises, (c) project proposal presentation, (d) field work, and (e) class participation. The term paper will count for approximately 33% of the final grade. As a general policy, no late materials will be accepted. Finally, attendance at all class meetings and field trips is required. Failure to attend more than two classes will adversely affect your grade in the course.
A note on field work. Three class periods will be spent doing field work at the Hanley Preserve. The tentative dates are: April 22nd, May 4th, and May 25th. Please mark them on your calendar. Because the Preserve is a 20 minute drive from campus, it will require meeting for class at 7:15 am on the mornings of the field trips. This will permit us to carry out our work and return for the next class period on campus.
Here students collect leaf-height data for a final project on biodiversity.
The course will be demanding, exciting, and unusual. We think that it
will be an interesting experience. Welcome aboard!
You can download his material in .pdf format
here.
Your computer must be equipped with
Adobe Acrobat Reader (tm) which you can obtain free
here.
(Left) Carrie Davis collects a plankton sample from a pond at the Hanley Presevre for a study on diversity by pond size and location. (Right) Christina Smith collects species-area data for a project comparing diversity in fields that have lain fallow for different lengths of time. (Hanley Presevre: 25 May 1999)
Kate Young collects and records plant species diversity data for a study of the effects of mowing and other factors on diversity in fields. (Hanley Presevre: 25 May 1999)
(Left) Amber Beutel collects data in a wooded area of the Hanley Preserve (25 May 1999) for a project on tree-species diversity in natural and disturbed environments. (Right) Dan Phillips collects data for a study on the species-area relationship under decomposing logs in deciduous forests (Hanley Preserve: 27 May 1997).
James M. Ryan Department of Biology Eaton Hall 210 Extension 3601 E-mail: ryan@hws.edu Office Hours: TWR 11:00--12:00 Kevin J. Mitchell Department of Mathematics and Computer Science Lansing Hall 305 Extension 3619 E-mail: mitchell@hws.edu Office Hours: MW 2:30--3:30, TT 12:30--1:30
Another of the ponds at the Hanley Nature Preserve.