MCS 358 Mathematical Model Building

January Term 2008


Instructors:

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 321
Text: A Course in Mathematical Modeling by Douglas Mooney and Randall Swift
 
 

Course Description:

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.
 

Course Outline:

We will cover all six chapters in the text, with approximately 2 days per chapter.  The schedule is:
 


 

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

1/7

CD-Prob/stat

1/8

TL-Ch 1

1/9

TL-Ch 1

1/10

CD-Ch 2

1/11

Ch 1 presentations

Prelim Proj Mtgs

1/14

TL-Ch 3

 

1/15

TL-Ch 3

1/16

Ch 2 presentations

1/17

CD-Ch 4

1/18

CD-Ch 4

Research Proposal

1/21

Ch 3 Presentations

1/22

TL-Ch 5

1/23

TL-Ch 5

1/24

Ch 4 Presentations

1/25

CD Ch 6

Progress Report

1/28

CD-Ch 6

1/29

Work Day

1/30

Ch 5/6 Presentations

1/31

Work Day

2/1

Final Presentations

Final Project due


 

Assessment:

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:

Homework will be assigned occasionally and irregularly.  Homework will be posted on Moodle.  No late homework will be accepted.
 

Chapter Projects:

The end of each chapter contains several projects.  A group of 3 or 4 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 here.

 

Chapter

1

2

3

4

5

6

Colette

1.7

2.3A

3.2

4.7

 

 

Ying

1.3

2.3B

3.7

4.1

 

 

Sarah C

1.3

2.2B

3.1

4.6

 

 

John

1.2

2.2B

3.7

4.3

 

 

Kai

1.7

2.1

3.7

4.6

 

 

Matthew

1.8

2.4

3.3

4.6

 

 

Kyle

1.4/5

2.4

3.2

4.1

 

 

Helen

1.8

2.2B

3.5

4.3

 

 

Erik

1.3

2.1

3.6

4.5

 

 

Joshua

1.4/5

2.2A

3.6

4.5

 

 

Jenny

1.8

2.3B

3.3

4.2

 

 

Rachel

1.6

2.1

3.2

4.5

 

 

Sarah M

1.8

2.4

3.1

4.7

 

 

Allison

1.2

2.2A

3.1

4.7

 

 

Andrew

1.7

2.2A

3.6

4.6

 

 

Justin

1.6

2.4

3.6

4.3

 

 

Danielle

1.2

2.3B

3.3

4.2

 

 

Brett

1.6

2.3A

3.5

4.2

 

 

Jacquelynn

1.4/5

2.3A

3.5

4.1

 

 

 

2.2A:  But rather than using the lunar views suggested, your two views should include one view of the far side of the moon (away from the earth) and one of the near side.

 

2.2B:  But rather than using the lunar views suggested, your two views should include one from above one lunar pole, and one from above the other pole.

 

Final Project:

For this project, you will work in self-selected teams of three-four. 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.

Policies:

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.
 

Academic Honesty:

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 Links: