Math 538 - Projects:

Depending on the class size, the projects will be tackled in teams. The plan is to choose teams of 2 or 3 students (depending on the class size) working in a common project. Students must form teams and choose a project no later than 5 weeks before the project presentations (final's week).

At the end of the semester (precise date to be announced) each team will present a 20-25 minutes slide or power point presentation that will be judged by the rest of the class, the instructor and other faculty members that will attend the presentations.

The teams must also submit a formal project (very much in the style of a journal publication). The report should not exceed 20 pages (including all graphic material) and should include sections like:

• Title, authors, affiliations.
• Abstract.
• Introduction: 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 and performing simulations.
• Discussion and conclusions to summarize your work.
• References.

• The report should be written having in mind your peers as the audience.
• Use formal English (check spelling/grammar, complete phrases, no colloquialisms, no contractions, etc.).
• Make sure to indicate which portions correspond to new/novel work (i.e., what is your contribution).
• If in any portion you are reproducing results already in the literature indicate so (failing to indicate so is a flagrant violation of scientific etiquete).
• Format properly your figures/tables (include labels, choose font sizes that make labels readable).
• Include figure/table captions (a good caption is self-contained, explain what is that is plotted, has all info to be reproducible [i.e., value of parameters]), include a short explanation of the results that can be drawn from figure).
• Number and refer to equations properly (equations are part of text and they must read like a normal phrase, inc. having their own punctuation) (you might want not to number equations that you do not refer to in the text).
• What is the difference between its and it's? (the latter should no be used, no contractions!).

Here is a list of old project topics that students had worked in the past just to give you a flavor of the possibilities. You should propose a project on your own. Possibly something related to your MS thesis or other research projects that you are working on (provided they fit within the scope of the course). Please consult with the instructor for suitability of your project as soon as possible.

• Lyapunov Exponents in chains of coupled maps.
• Period doubling of the leaky tap.
• Homoclinic/heteroclinic tangles.
• Population dynamics models.
• Fractal dimension, Lyapunov dimension.
• The 3-body problem.
• Chaotic tumbling of a leaf.
• Chaos in Hyperion's orbit.
• ....