Math 636 - Mathematical Modeling
Fall Semester, 2006 

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San Diego State University -- This page last updated 06-Nov-08


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:

  1. Background material on the literature and significance of the project.
  2. Development of the mathematical model or a survey of a collection of relevant models.
  3. Discussion on the relevant mathematical theory that applies.
  4. Some original work on your own for either extending the model or performing simulations.
  5. Discussion and conclusions to summarize your work.

The report will be due at the end of finals week.

Below are list of possible projects:

  1. Population Study - Extend the work we did on competition models to cover all the populations in the Crombie paper. Include model variations.
  2. Age-Structured Population Models - Examine the population studies of Crombie and include the range of ages of the different insects.
  3. Circadian Rhythms - Study the PER and CLOCK protein interactions in fruit flies to develop and analyze circadian rhythms.
  4. Genetic Control Models - Examine the bacterial control systems of repression and induction.
  5. Chemical Oscillator - Develop and analyze mathematical models for the Belousov-Zhabotinsky reaction or the Briggs-Rauscher reaction.
  6. Spring-Mass Pendulum - Develop a more detailed study of the pendulum developed in class, including a matching of the movie data.
  7. Double Pendulum - Create a mathematical model for the coupled pendulums and analyze the model. (I have this apparatus in my office.)
  8. Magnetic Pendulum - Create a mathematical model for a pendulum that is perturbed by magnetic fields and analyze the model.