MATH 405 Section # 59692 - SPRING 1998

MODELS IN BIOLOGY

Time:  1:25 - 2:15 Monday, Wednesday and Friday
Place:  Ayres Hall 320
Instructor:  Lou Gross, Professor of Ecology and Evolutionary Biology and Mathematics 
Office: 639 SERF. Office Hours: Monday and Wednesday 11-1 and by appointment. 
Phone: 974-4295 E-mail: gross@tiem.utk.edu

This course will provide an overview of mathematical modeling with emphasis on the 
biological sciences. The aim is to show how mathematical and analytical tools may be used 
to explore and explain a wide variety of biological phenomena that are not easily 
understood with verbal reasoning alone. We will begin by discussing the various purposes 
for which one might construct a mathematical model, and proceed with a description of the 
modeling process. This will be followed by an introduction to several mathematical areas 
which have been found to be extremely useful in biological modeling, in particular 
difference equations, stochastic distributions, and ordinary and partial differential 
equations. Applications of these mathematical techniques will be illustrated in a host of 
biological fields including molecular, cellular, physiological, ecological, genetical, 
and agricultural ones. The emphasis will be on deterministic models, though we will 
cover statistical approaches as time allows. The course will make use of a number of 
computer packages at various stages, including MATLAB, Maple, EcoBeaker, and Populus.
.PP
The course is oriented towards biological sciences students who may not have a strong 
mathematical background. Prerequisites are a year of calculus (e.g. Math 141-142, 
151-152, or the equivalent) as well as some exposure to biology at the 300-level. 
Math 405 is available for graduate credit, and one of the course objectives is to provide 
enough insight into biological modeling that participants without a strong math background 
will be able to read with understanding theoretical papers appearing in the current 
literature in their respective biological fields of study. Note: Math 405 does not satisfy 
math requirements for either undergraduate or graduate students majoring in mathematics, 
so students needing this should register for a Math Reading Course. 

The text for the course is: 

Models in Biology: Mathematics, Statistics and Computing

by D. Brown and P. Rothery. Course grading: The grade will be based on 3 components: 
(a) Participants will be expected to regularly work problems from the text. These may be 
worked on within a study group, as long as the instructor is notified, and each individual 
writes their own results; (b) Each participant will work on an individual project in an area 
of particular interest to themselves. A brief oral preliminary report on the project shall be 
presented to the class in the middle of the semster. Final results will be presented both 
orally to the class at the end of the term, as well as in a report written in a style appropriate 
to a technical journal. The report should be approximately 15-20 double-spaced pages in 
length, not counting references or figures; and (c) Each participant will take part in a class 
project, the topic for which will be chosen by the class. The weighting of these components 
of the grade are: (a) 30%, (b) 50%, (c) 20%.  

Course Outline:

For approximately the first week, lectures will give an overview of the modeling process 
and a review of biological areas in which mathematical models have been applied. The 
tentative schedule (which may be modified depending upon particular interests of the 
participants) will include the following sections from the text:

Introduction

Chapter 1

Chapter 2

Chapter 3

Chapter 8

Chapter 9

Chapter 10

Chapter 12

Chapter 13

Chapters 4, 5, and 6 as time allows