MATH 411 Section # 59188  - FALL 1996

MATHEMATICAL MODELING 

Time:  1:25 - 2:15 Monday, Wednesday and Friday

Place:  Ayres Hall 309B

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, Home Page http://www.math.utk.edu/~gross/,
Course Home Page http://www.math.utk.edu/~gross/411.html/ 

Course Text:

A Concrete Approach to Mathematical Modeling 

By Michael Mesterton-Gibbons, Wiley, 1995.

Course Goals:

1. Provide an introduction to the great diversity of applications of
mathematics to fields outside of math.

2. Provide experience in preparing and giving a cohesive oral
presentation on a mathematical topic.

3. Provide experience in researching the modern references in a
scientific/engineering field and evaluating this research.

4. Enhance students' technical writing experience.

5. Provide experience in working as a team to analyze and solve a
real-world problem requiring mathematical approaches.

6. Provide experience with a number of techniques which have been
found to be useful in a variety of application areas.

Course Structure:

Before proceeding with material in the text, I will give an
overview of the diverse fields in which modern mathematics is
employed, including the physical, biological and social sciences,
business and industry. This will be followed by a formal study of
the modeling process. We will then proceed through much of the text
at a rapid pace, emphasizing certain models and covering much of
the first nine chapters. This will include detailed examples of
mathematical models in a variety of fields. A few class meetings
will be held in workshop mode - the class will work together to
develop a math model for a particular situation. 

There will be a class project dealing with a real-world
application, that all students will be expected to participate in
as part of a team. The instructor will act as the team leader for
this project, with students assigned particular tasks based upon
their interests and expertise. Each student will be expected as
well to carry out an individual project, analyzing, developing
and/or modifying a model or set of models in an area of particular
interest to them. 

Students Responsibilities:

1. For the homework assignments: Hand in any written assignments on
time, written in a clear, concise form. These may be done using a
technical word-processor, or handwritten. 

2. For the class project: Carry out your part of the project
according to the workplan agreed upon by the class, but continuing
to consult with other class members as necessary for the whole team
to successfully complete the project. 

3. For the final project: 
(a) Pick a problem from one of the topics mentioned in class or
according to your particular interests, in consultation with the
instructor. 
(b) Research the literature in the chosen area to learn how the
problem chosen has been approached mathematically. Give a brief 5
minute presentation to the class at mid-semester on the math models
used on the problem. 
(c) Work on a particular model or group of models on the chosen
topic until you convince yourself that you understand what's been
done. 
(d) Demonstrate your understanding of the topic by 
   (i) Explaining the work in detail in a formal presentation to 
   the class near the end of the semester, utilizing audio-visual 
   devices and handouts as necessary. 
   (ii) Submitting a clearly written, well organized paper covering the
   problem. This should be written as a technical manuscript,
   including references to work done, an explanation of this work, and
   your evaluation of its quality and what areas remain to be
   investigated. The length of the paper should be about 15-20 double-spaced 
   pages, excluding references and figures.

Course Grading:

The course grade will be heavily based upon the individual projects
with the oral reports and the final written report together
counting for 60% of the course grade. The homework assignments and
class project will each account for 20% of the course grade. 

Note: This course satisfies a Capstone Experience requirement for the
Arts and Sciences B.S. degree and is designated as a writing
intensive course.