Department of Mathematics Generic Syllabus
Boise State University Updated Fall 1998
Math 464
Mathematical Modeling
3 semester credits
Catalog Description
MATH 464 MATHEMATICAL MODELING (3-0-3)(F).
Introduction to mathematical
modeling through case studies. Deterministic and probabilistic models.
Optimization. Examples will be drawn from the physical, biological
and social sciences. PREREQ: MATH 361 or PERM/INST.
Prerequisites
M 361 is a post-calculus introduction to statistics and so carries
with it an additional level of mathematical maturity not inherent in
M 254 or statistics courses from some other departments on campus.
Naturally, the stronger the background the class has, the wider
variety of models they can tackle, and one is tempted to include other
prerequisites, particularly differential equations and linear algebra.
Still, a good calculus background together with some probability and
statistics is sufficient to allow investigation of some major types of
models, while keeping the class accessible to a reasonable number of
students.
Jurisdiction
Choice of text and topics is up to the individual instructor. A wide
number of approaches to this course have been made, with a
corresponding variety of texts.
Learning Objectives
As an applied mathematics course, the objectives of MATH 464 reflect
three of the Department's teaching goals: that students be able to
give examples of nontrivial applications of mathematics to various
(non-mathematical) fields, that students be able to use suitable
mathematical tools, and that students use mathematics as a language.
As a course designed primarily to give mathematics, secondary
education majors the knowledge use mathematical models in their future
teaching, MATH 464 does not stress the aesthetic side of mathematics or
the idea of mathematics as the study of patterns.
Upon completion of this course, students should be able to:
- Give examples of some simple models that were
significant in the development of a mathematical approach to various
disciplines.
- Give examples of mathematical models which are useful
in the secondary school curriculum.
- Solve problems involving optimization models, dynamic
models, and probabilistic models.
- Formulate a mathematical model given a clear
statement of the underlying scientific principles.
- Explain the sensitivity of a model to changes in data and
estimate the robustness of a model.
- Explain the use of modern technology in solving
real-world problems.
- Write up a solution to a problem in a way that makes
sense to both mathematical and non-mathematical readers.
Assessment of Learning Objectives
Students will be assessed by evaluating their ability to do problems
based on the learning objectives and their ability to do a substantial
modeling project. The problems may occur in several
contexts:
- Periodic problem sets for homework serve both as learning
and as assessment tools. Classroom activities may vary depending on
students' outcomes on homework assignments.
- If take-home exams are given, the questions are designed to evaluate a
student's ability to solve more complicated and time consuming
problems. Moreover, take-home problems give students the
opportunity to demonstrate their ability to use technology to solve
problems involving real data or otherwise not amenable to simple
analytic techniques.
- If in-class exams are given, the questions are designed to give students
the opportunity to demonstrate their ability to work simpler and
less time consuming problems which probably do not involve real
data.
The modeling project requires the students to choose a topic, find
data, formulate a model, analyze the model, and write up their
results. The successful completion of a project involves the exercise
of virtually all the abilities listed in the Learning Outcomes and
provides the opportunity to assess them.
Topics and Approximate Timeline
At present about 40% of the course is spent on single- and
multi-variable optimization models, if time spent getting students
adjusted to the computer software is included. The remaining 60% is
divided equally between dynamic models (including steady-state
analysis and eigenvalue methods) and probability models (including
Markov chains and Monte Carlo simulation).
Text
The current text is Mathematical Models in the Social &
Biological Sciences, F. Beltrami, Jones/Bartlett, 1993, with
Mathematical Modeling in the Secondary School Curriculum, N.C.T.M.,
1991, used as a secondary text and laboratory manual. Other texts
that have been used in recent years include A First Course in
Mathematical Modeling, F. Giordano and M. Weir, Brooks Cole, 1985,
Mathematical Modeling, M. Meerschaert, Academic Press, 1993,
Mathematical Models and Applications by Maki and Thompson and
An introduction to Mathematical Models in the Social and Life
Sciences, M. Olinick, Addison-Wesley, 1978.
Format, Student Activities, and Grades
Class meetings involve a combination of lecture, questions and
discussion, and sometimes small group activity; the instructor chooses
the appropriate mix. Group and individual projects are an important
part of the course, and quality of the write-ups is stressed. The
computer algebra system, Maple, is used for laboratory work and
projects. The instructor chooses the exact grading scheme, but a
typical distribution could be:
|
|
| Projects | 600
|
| Midterm Exam | 100
|
| Final Exam | 300
|
| Total | 1000
|
Letter grades are usually based on a standard scale in which 90% of
the total possible points guarantees an A , 80% a B, and 70% a C,
with the instructor having the discretion to lower these cut-offs.
File translated from TEX by TTH, version 1.56.