MA495 - Special Topics in Mathematical Modeling
Class Syllabus - Fall 2006
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Course
Description:
This
course is an introduction to mathematical modeling. We will be
applying mathematics to solve open-ended real-world problems.
Modeling techniques (and the underlying mathematics) covered may
include:
- Discrete Modeling (difference
equations, dynamical system)
- Continuous Modeling
(differential equations)
- Empirical Modeling (fitting
curves to data, statistical analysis)
- Stochastic Models (probability
and statistical analysis, linear algebra and Markov chains, queuing
theory)
In
order to increase the likelihood of success in this course it is
recommended that the student attend class without fail, focus on
understanding the concepts (not just doing rote computations or trying
to memorize everything), read the textbook, religiously work the
homework, and seek help from the professor when needed. (3
Semester Hours)
Prerequisites:
Completion of MATH262 – Calculus II
or permission of instructor. It is also preferred that students
taking this course know how to program and/or are able to use software
packages such as Derive or Excel.
Professor:
Dr. M. Leigh Lunsford. For Dr. Lunsford's office location, phone
number, email address, schedule (including office hours), and other
general information, go to her homepage:
http://www.mathspace.com/Lunsford/
Meeting
Times and Location: MWF 8:00-8:50 a.m., Ruffner G56
Course Textbook, Textbook CD-ROM, &
Textbook Website: A
Course in Mathematical Modeling, Douglas D. Mooney and
Randall J. Swift, published by the
Mathematical Association of America, ISBN 0-88385-712-X.
Required
and Recommended Technology/Computer Configurations:
It is practically impossible to have too many good software tools at
your disposal! Since this is an applied mathematics class we will
definitely use software to solve problems and communicate our solutions.
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Our class will be in
the computer lab in the basement of Ruffner Hall. Thus it is not
necessary that you bring your laptop to class everyday. Software
packages installed on the lab machines and that we will use during class
include: Microsoft Excel, Derive, and occasionally, MATLAB.
You can find information on how to use some of these packages on the
Handy Documents page.
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On your laptop you will
want to make sure that you have the Data Analysis Add-In activated in
Excel (if it is not already on your machine then this should be on your
Excel or Microsoft Office installation CD or the Longwood IT
department). If you would like to purchase your own copy of
Derive, visit the
TI Derive website. If you would like to purchase your
own copy of MATLAB, you can purchase the MATLAB Student Version at the
Mathworks
web store for $99.00.
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It will be required for
you to turn in typed technical documents in this class. Thus you
should have the Microsoft Office Suite (or equivalent) installed on your
machine. In particular you should know how to use the equation
editor in Word. I use the MathType equation editor as a
supplement to the equation editor.
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A TI-83 Plus graphing calculator
(or equivalent) is recommended
for this course. If you do not use the TI-83 then you
will be responsible for knowing how to use your particular calculator.
You may not use a calculator with symbolic calculus capability.
Determination of
Course Grade:
30%
- Group Projects
20% - Individual Hand-In Homework Assignments
10% - In-Class Participation and Peer Evaluation
15% - Midterm Exam
5% - Mathematics Cultural Points (cults)
20% - Comprehensive Final Exam
Grades will be assigned on a ten point scale (90's
A; 80's B; 70's C; 60's D; 50's and below F).
To
understand the meaning of these letter grades please use the following
criteria which can be described in terms of the "real-world"
as follows:
A - You
have done an outstanding job! Not only will you receive a merit
raise (above the cost of living raise), but you will also receive a
substantial bonus.
B - You
have done a very good job! You will receive a merit raise (above
the cost of living raise).
C - You
have done a satisfactory job. You will receive the cost of
living raise but not a merit raise.
D - Your
work is below par. You may receive the cost of living
raise. Unless your performance improves you will most likely be
laid off during the next round of layoffs.
F - You
will probably be fired immediately.
Group Projects:
During the course of
the semester you will be assigned group projects. I will choose the groups
for each project. You will have an opportunity to
evaluate your peers in your group. Group project work is expected
to be exemplary. Not only does this include the mathematics in the
project but it also includes how well the group presents and explains
their approach to the project, their solution(s), and any conclusions
reached. Information about how to effectively write group projects
is given on the Handy Documents page. Towards the end of the
semester there will
Individual
Hand-In Homework Assignments: In addition to your
Group Projects, you will have individual hand-in homework assignments.
Hand-in homework should be neatly presented (preferably typed) with
clear explanations and answers. While I want you to discuss
mathematics with each other, you should not copy mathematics from each
other. Thus it is OK to discuss your homework assignments with
your classmates but it is not OK to completely give the solution to a
problem to another classmate nor is it OK to copy part or all of another
person's solution. Your solution should be presented in your own
words. If I even suspect that you have copied part or all of your
work from another individual in this class, both you and the person you
copied from will receive a zero on that assignment and be brought before
the LU judicial board. The LU honor system will be strictly
followed for these assignments. Information about how to
effectively write hand-in homework assignments is given on the Handy
Documents page.
Other
(non Hand-In) Homework:
I will also assign homework to help you practice what you are learning
but not hand-in to me. I strongly suggest you keep your homework
and notes organized in a class notebook.
In-Class
Participation and Peer Evaluation:
Ten percent of your grade will be determined by class participation and
peer evaluation. To earn an excellent class participation grade
you should come to class prepared (homework worked, assignments read,
questions ready), be engaged in class problem solving, show respect to
your classmates, and exhibit a thinking inquisitiveness. Your
peers will determine your peer evaluation grade via an evaluation form
they will fill out at the end of each project. Please
see the Handy Documents page for the Group Project Team Member
Evaluation Form.
Midterm
Exam: Around the 6th or 7th week of class we
will have a midterm exam. For more detailed information about test dates
see the Assignments page. Except in the case of an emergency, a make-up exam must be scheduled before
the scheduled exam date. If the exam has already been given and you have not
previously scheduled a make-up, then you will receive a zero on that
exam. Please see the make-up policy
below for additional information.
Mathematics Cultural
Points (cults): In order to
receive the full 5% credit for mathematics cultural points you must earn
at least 12 cults. To determine how to earn cults
please click here.
I will also put this information on the Handy Documents page. Final Exam:
The final exam for this course will be comprehensive. You cannot
miss the final - failure to take the final exam will automatically
result in an F grade for the course. Please see me as soon
as possible if you may have a conflict with the final exam date. Final Exam
Date: Wednesday, 13 December, 8:00-10:30 a.m. Extra
Credit: Extra
Credit will not be given -
period.
Honor System:
I expect
you (and your partners on the Group Projects) to conform to the
Longwood University Honor System as contained in the
Student
Handbook. All material handed in to me (homework, reports,
tests) must be pledged.
Attendance &
Excused Absences:
You are expected to attend every class. If you miss classes it will most likely be reflected in your grades (i.e. you will
perform poorly).
The following college attendance policy will be followed per the Class
Attendance section of the Academic Regulations chapter of the Longwood
University Undergraduate Catalog: Missing
10% of class meetings may result in a lowering of
one letter grade. Missing 25% of class meetings
for any reason will result in an automatic “F” for
the course.
Absences are
excused only for illness, college sponsored activities, and recognizable
emergencies. You must have the proper documentation for an excused
absence.
Student Health Services can provide documentation only for students
hospitalized locally or absent at the direction of Student Health
Services personnel.
You must also
assume full responsibility for all material covered during your absence,
including scheduling any make-up quizzes or exams. A grade of "0"
will be assigned for all work missed due to unexcused absences. Make-up
Policy:
Make-up assignments will be given only when the reason for missing the
assignment meets the criteria for an excused absence (see above).
Except in the case of emergencies, make-up assignments must be scheduled
and/or turned-in before the due date of the assignment being made-up
(i.e. you should plan ahead if you know you are going to miss class).
As a general rule, you can expect that make-up tests will more difficult
than regularly scheduled tests. If you have a recognizable
emergency, please contact me as soon as you can to discuss your make-up
options.
Office of Disability Services:
Any student who feels s/he may need an accommodation based on the impact
of a
physical, psychological, medical, or
learning disability
should contact me privately. If you have not already done so, please
contact the Office for Disability Services (103 Graham Building,
395-2391)
to register for services.
General Class Pace: Below is a tentative list of
the material we will cover and when we will cover it. For more
details please see the Class Pace and Assignments page.
|
Material Covered |
Week of Class |
| Chapter 0: Modeling Basics |
Week 0, 1 |
| Chapter 1: Discrete Dynamical
Systems |
Weeks 1 - 3 |
| Chapter 2: Discrete Stochasticity |
Weeks 3 - 5 |
| Chapter 3: Stages, States, and
Classes |
Weeks 5 -7 |
| Midterm Exam |
Around Week 7 |
| Chapter 4: Empirical Modeling |
Weeks 7 -10 |
| Chapter 5: Continuous Models |
Weeks 10 - 12 |
| Chapter 6: Continuous Stochasticity |
Weeks 12 - 14 |
|