Objectives: To explore the role of mathematical models in explaining and predicting phenomena arising in the real world. To develop some skill in solving problems for applications in the life and physical sciences, business, or engineering. For a list of more specific objectives see "Some Modeling Course Objectives."

Intended for: Mathematics and science majors and students in other fields with knowledge of matrices and calculus.

Prerequisite: MATH 306 - Linear Algebra

Text: "Mathematical Modelling," Berry, J. and Houston, K.; Edward Arnold, London, 1995.

Topics/Weeks:

What is Mathematical Modelling (Chapter 1)/ 2-3 weeks
Modelling with Data, Using Mathematical Models, Modelling from Theory.

Modelling Population Growth (Chapter 2)/ 2-3 weeks
The Modelling Process - Understanding the Problem, Choosing Variables, Making Assumptions, Solving the Equations, Interpreting the Solution and Validating the Model, Criticising and Improving the Model..

Mathematical Modelling in Action (Chapter 3)/ 2-3 weeks
Selected Case Studies.

Developing Modeling Skills (Chapter 4)/5-8 weeks
Tutorial Problems and Projects, Modelling with Stella

Evaluatuion:
Homework Assignments.................25-30%
Projects & Presentations.................25-30%
Two Examinations...........................50-40%

NOTE: ONCE A STUDENT HAS RECEIVED CREDIT, INCLUDING TRANSFER CREDIT, FOR A COURSE, CREDIT MAY NOT BE RECEIVED FOR ANY COURSE WITH MATERIAL THAT IS EQUIVALENT TO IT OR IS A PREREQUISITE FOR IT.

DCC/lsa 8/97

Guidelines for Individual Exercise Assignments

Each time you are asked to work an assigned exercise, focus not only on solving the problem, but also on how you solve the problem. While you are working on the problem, keep notes on any difficulties you faced, false starts you made, and what led you to trying the approach you used. If you are able to solve the problem, clearly state your conclusion and explain why you think your approach works. If you feel you cannot solve the problem, describe in detail the process you used in attempting to find a solution. In either case, write a complete narrative telling the story of your attempt, successful or not, to solve the problem.  Pretend that you are writing the narrative for another student who is confused by the problem and would like to know how you solved it.

Guidelines for Electronic Journal Entries

At least once each week compose an e-mail message to your instructor consisting of a few lines reflecting on your experiences in this course. You may comment on any aspect of the course. For example, you might describe some "significant incident" that was particularly meaningful, surprising, or confusing to you. You might choose to indicate what you enjoyed the most, or liked the least.

Guidelines for the Modeling Portfolio

As you work through this course, develop a modeling portfolio. Design your portfolio to accomplish two purposes:

1) to provide samples of your, and your groups', best work in problem solving and mathematical communication, and
2) to indicate the range and quality of the mathematical and scientific techniques concepts you have acquired.

The contents of your portfolio should include the following - all listed in a table of contents:

1) some of the "best pieces" of your group work in this course including the solution, the work involved, and some commentary;
2) a print out of your electronic journal - including the instructor's responses;
3) a collection of some pieces of your individual work for this course; and
4) a letter to the instructor.

The criteria below will guide the assessment of your portfolio.

Problem Solving. How well does the student (group) understand the problem? How does the student (group) solve the problem? Why does the student (group) solve the problem in a particular way? What observations, connections, and generalizations does the student (group) make about the problem?

Communication. What terminology, notation, and symbols does the student (group) use to communicate his or her (its) thinking? What representations (graphs, charts, tables, diagrams, pictures, manipulatives) does the student (group) use? How clear is the student's (group's) communication of his or her (its) thinking and problem solving?

Guidelines for Interpreting Grades on Written Work

4, Excellent. Your response to the assignment is correct, complete and you have clearly communicated the process and techniques used to solve the problem. The paper is attractive and you have included appropriate diagrams, identified all variables introduced, and clearly stated, and verified, your conclusions.

3, Good. Your response is reasonably complete and your explination of the process and techniques used is fairly clear. Some aspect may not be as correct, clear, neat, or well organized as possible.

2, Satisfactory. Your response is not complete in some aspect, or has some errors, or lacks clarity or supporting evidence.

1, Needs Improvement. Your response is incomplete, unclear, or major errors exist.