| Catalog Description: |
Discrete deterministic models. Applications of graph theory, linear programming, game theory, election theory, and finite difference equations. Computer simulation. Case studies in areas of student's choice. Prerequisite: COSC 181 and MATH 211. (Offered odd years, fall semester)
| Required Course Materials: |
Giordano, Weir, and Fox, A First Course in Mathematical Modeling, 3rd Edition, Brooks/Cole—Thomson Learning, 2003.
| Course Coordinator: |
Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics
| Course Audience: |
Mathematics majors whether planning on a career in industry or in teaching. Open to all students.
| Course Objectives: |
A course in mathematical modeling differs from a course in applied mathematics in one important way. Applied mathematics courses are typically taught as mathematics in search of an application. A mathematical modeling course is centered on real world situations in search of some appropriate mathematics. Thus the following objectives distinguish this course from other mathematics courses in the curriculum:
- To change the student's world view, so as to see the pervasiveness of mathematics in the natural sciences.
- To give teams of two or three students an opportunity to work together to solve real-world problems of the kind that professional applied mathematicians are paid to do.
- To discover the usefulness of discrete deterministic models in areas such as social choice, finance, and population growth.
- To learn powerful ideas of mathematics like "transform-solve-invert" and Polya-like strategies for attacking problems like looking for analogies and solving just a useful part of a problem.
- To learn to explain the mathematics that one has used to solve a problem both in formal writing and in oral presentation.
| Prerequisites: |
Mathematical modeling can be taught in elementary school, yet so as to have a collection of techniques on which to draw to solve harder problems, Calculus III is required. The ability to program a computer in a third-generation language like C, Pascal, Basic, Java, or JavaScript is required to do simulations and sometimes to exhaustively search for solutions.
| Topics: |
- Develop a mathematical representation of a problem or situation.
- Analyze the resulting mathematical structures.
- Research conclusions or decisions.
- Translate the results into the language of the original problem.
- Estimate how good the results are.
| Resources: |
Access to a computer and a variety of tools like tape measure, stopwatch, calculator, scissors, computer software such as spreadsheets or Derive, and other things that may become necessary as the course progresses.
| Pedagogy: |
A Piagetian approach is used in every class period. Lectures are minimal, and always after students have engaged the problems that the lectures discuss. Students are expected to use web and library resources to discover additional resources.
Models from the literature will be presented in class. Group models related to the models that are presented will be assigned (ten mini-models and two major ones). A final project will be done individually on an approved topic selected by the student. An oral report will be given by one group on each mini-model and each major model. Each student will present an oral report on his or her final project.
Revised: September 2007