MATH 405 Section # 55456 and Math 411 Section #55469 - SPRING 1996
MODELS IN BIOLOGY
Time: 9:05 - 9:55 Monday, Wednesday and Friday
Place: Ayres Hall 324
Instructor: Lou Gross, Professor of Mathematics and Ecology
Office: 208 Ayres Hall. Office Hours: Monday and Wednesday 11-1 and by
appointment, or whenever door is open. Phone: 974-4295 E-mail:
gross@math.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, 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 course is oriented towards biological sciences students who may not
have a strong mathematical background as well as mathematics students
with little prior biological experience. 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 for biology students and at
least two years of mathematics for the mathematics students. 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
Math 411.
The text for the course is:
Mathematical Models in Biology
by Leah Edelstein-Keshet. 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. The 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:
Chapter 1, sections 1-7,9,10
Chapter 2, sections 1-10
Chapter 3, sections 1-4,6
Chapter 4, sections 1-11
Chapter 5, sections 1-10
Chapter 6, sections 1-5
Chapter 7, sections 1-3
Chapter 8, sections 1-5
Chapters 9 and 10 as time allows