Tom
LoFaro
Carolyn Dobler
314
Olin Hall
306 Olin Hall
x7463
x7469
tlofaro@gustavus.edu
dobler@gustavus.edu
Class Meeting Times: M-F, 10:30-12:30 in Olin 318
Text:
A Course in Mathematical Modeling by Douglas Mooney and
Randall Swift
This course provides an introductory study of the formulation of mathematical models to represent, predict, and control real-world situations, especially in the social and biological sciences. The course will use ideas from calculus, linear algebra, differential equations, probability, and statistics to describe processes that change in time in some regular manner, which may be deterministic or stochastic.
A mathematical model is a mathematical representation of some physical process or system. Since real-world phenomena are often too complex to model exactly, there are always simplifications and assumptions that one must make in building a mathematical model. In this course we will look at the model-building process and how to critique and refine models.
There are two basic viewpoints in mathematical modeling:
deterministic and stochastic. Professor LoFaro will cover
deterministic models, while Professor Dobler will be responsible for
stochastic models and statistical analysis.
We will cover all six chapters in the text, with approximately 2 days per chapter. The schedule is:
|
MONDAY |
TUESDAY |
WEDNESDAY |
THURSDAY |
FRIDAY |
|
1/4 TL-Ch 1 |
1/5 TL-Ch 1 |
1/6 CD-Prob/stat |
1/7 CD-Ch 2 |
1/8 Ch 1 presentations Prelim Proj Mtgs |
|
1/11 TL-Ch 3
|
1/12 TL-Ch 3 |
1/13 Ch 2 presentations |
1/14 CD-Ch 4 |
1/15 CD-Ch 4 Research Proposal |
|
1/18 Ch 3 Presentations |
1/19 TL-Ch 5 |
1/20 TL-Ch 5 |
1/21 Ch 4 Presentations |
1/22 CD Ch 6 Progress Report |
|
1/25 CD-Ch 6 |
1/26 Work Day |
1/27 Ch 5/6 Presentations |
1/28 Work Day |
1/29 Final Presentations Final Project due |
Your final grade will be determined by occasional homework (10%), five chapter projects (12% each for a total of 60%), and final project (30%).
Homework will be assigned occasionally and irregularly. Homework will be posted on Moodle. No late homework will be accepted.
The end of each chapter contains several projects. Each group of 3 students will prepare a written or oral presentation. We will assign project groups and projects for each chapter. Guidelines for the grading of projects can be found on the Moodle page.
|
|
Chap. 1 |
Chap. 2 |
Chap. 3 |
Chap. 4 (fix) |
Chap. 5 |
Chap. 6 |
|
Stacy B. |
2 |
5 |
6 |
|
|
3 |
|
Andrew B. |
3 |
1 |
9 |
|
2 |
|
|
Eric. C |
6 |
3 |
3 |
|
9 |
|
|
John D. |
8 |
4 |
1 |
|
|
3 |
|
Robert K. |
3 |
3 |
6 |
|
2 |
|
|
Kelsey M. |
3 |
4 |
3 |
|
|
2 |
|
Andrew O. |
2 |
3 |
2 |
|
2 |
|
|
Sam R. |
8 |
4 |
9 |
|
9 |
|
|
Dan R. |
6 |
1 |
10 |
|
|
3 |
|
Kate S. |
8 |
1 |
10 |
|
|
2 |
|
Andrew T. |
6 |
5 |
1 |
|
|
2 |
|
Cory W. |
2 |
5 |
2 |
|
9 |
|
For this project, you will work in self-selected teams of
two-three. Your task is to select a topic of interest to you and
model it.
This will involve collecting real-world data and/or
building a mathematical model of the physical process associated with
this data. You will prepare a written report (about 5-10 pages)
and an oral presentation (20 minutes) on the last day of class.
For some helpful hints on writing your report click
here.
Attendance is required. Poor attendance may
cause your final grade to be lowered. We encourage you to work
together in discussing homework; however the work you turn in must
be your own.
As a community of scholars, the faculty and students of Gustavus
Adolphus College have formulated an academic honesty policy and honor
code system, which is printed in the Academic Bulletin and in the
Gustavus Guide. As a student at Gustavus Adolphus College I agree to
uphold the honor code. This means that I will abide by the academic
honesty policy, and abide by decisions of the joint student/faculty
Honor Board.
· Helpful hints on writing modeling papers.
· Applets for discrete dynamics.
· Internet Differential Equations Activities (IDEA)
· The Consortium for Mathematics and Its Applications (COMAP)