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Math 636 - Mathematical Modeling
Fall Semester, 2006
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© 2001, All Rights Reserved, SDSU & Joseph M. Mahaffy
San Diego State University -- This page last updated 06-Nov-08
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Math 636 - Projects
Because of the larger size of this class, I have decided to
make the Mathematical Modeling projects into team projects. The plan is to
have you form teams of 1-3 students working on a common project. We should be able to handle 10 teams for the entire class. By Tuesday, Nov. 14, I need to know who is on your team and what project you intend to work on. Create a sheet with the list of students on the team, the title or subject of the project, and an outline of your proposed ideas.
At the end of the term, you will need to write a one page summary about the
group dynamics with signatures of all team members. At the end of the semester,
we will schedule about 20-25 minutes for each group to present their project (depending on the size of the group).
(Note that the Final is scheduled for Tues. Dec. 12, 8-10 AM, so we should discuss
a time for presentations.)
Students are expected to write a group report on the project. The written
report that should be approximately 20-30 pages (including graphics). The written
part of the project should have:
- Background material on the literature and significance of the project.
- Development of the mathematical model or a survey of a collection of relevant
models.
- Discussion on the relevant mathematical theory that applies.
- Some original work on your own for either extending the model or performing
simulations.
- Discussion and conclusions to summarize your work.
The report will be due at the end of finals week.
Below are list of possible projects:
- Population Study - Extend
the work we did on competition models to cover all the populations in the
Crombie paper. Include model variations.
- Age-Structured Population Models - Examine the population studies of Crombie
and include the range of ages of the different insects.
- Circadian Rhythms - Study the PER and CLOCK protein interactions in fruit
flies to develop and analyze circadian rhythms.
- Genetic
Control Models - Examine the bacterial control systems of repression and
induction.
- Chemical Oscillator - Develop and analyze mathematical models for the Belousov-Zhabotinsky
reaction or the Briggs-Rauscher
reaction.
- Spring-Mass
Pendulum - Develop a more detailed study of the pendulum developed in
class, including a matching of the movie data.
- Double Pendulum - Create a mathematical model for the coupled pendulums
and analyze the model. (I have this apparatus in my office.)
- Magnetic Pendulum - Create a mathematical model for a pendulum that is perturbed
by magnetic fields and analyze the model.