As indicated at the beginning of the semester, in lieu of a final exam, there will be a course project to be presented at the end of the semester, to count 25% towards the overall grade.
Dates:
The projects will be presented in a
poster session during the April final exam period, at the date and time
originally scheduled for the final exam. The poster session will be:
Thursday, April 17, 9:00am-12:00 noon, in room ASB 9896
in the Applied Science Building
I would like a project proposal including a (provisional) title and one-paragraph outline of your plans by Friday, March 17 (final deadline: Monday, March 20 by 5pm). Also please indicate the participants in the project; you may work by yourself or in pairs (groups of three or more are possible by special arrangement).
I would like every individual or group to
meet with me or contact me a few days before the due date (preferably by Monday
the 14th), with an update on your progress...
Some Guidelines:
The project can be on any aspect of dynamical systems you choose; the only criteria are that your topic have a clear connection to the course material, and that you find it interesting.
The goal of this project is for you to take some of the ideas we have encountered during the course and independently apply them to a problem you find interesting. Most importantly, you should learn something; this is your opportunity to explore a topic of your choice in more detail.
I would like you to do something - you could construct a physical or electronic device illustrating chaotic behaviour or a chemical experiment displaying oscillatory dynamics, write some computer programs and run numerical simulations to explore interesting dynamical systems or generate fractal images, or work through some problems and rigorously prove some fundamental results in dynamics. While a well-organized report on your reading of other people's work is important, the project should contain some of your own investigations.
Your project should be clearly and understandably presented as a poster (preferably no more than 10 pages) or, possibly, a demonstration; you should have your audience (mainly your classmates) in mind as you plan your presentation. Note: poster boards will be provided; you should bring your poster (usually in the form of about 10 pages of 8 1/2x11 paper; more than 12 won't fit) which will be affixed to the board.
Your project should be something you work on
for the next several weeks; don't leave everything until the last few days.
The intermediate deadlines are designed to facilitate your progress.
Some references, and ideas on getting started:
You could look at dynamical systems books in both the mathematics and physics collections in the library. Articles in Scientific American, New Scientist, Mathematical Intelligencer, or similar magazines may give you some ideas, as could a web search using some well-chosen keywords. There are by now several books on dynamical systems, chaos and complexity for a general readership, which you might wish to look at; a partial list of these (to give you some ideas...) is:
James Gleick, Chaos: Making a New Science, Penguin (1987).
Benoit Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman (1982).
Heinz-Otto Peitgen and Peter H. Richter, The Beauty of Fractals: Images of Complex Dynamical Systems, Springer-Verlag (1988).
Heinz-Otto Peitgen and Dietmar Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag (1992).
Michael F. Barnsley, Fractals Everywhere, Morgan Kaufmann (2nd ed. 1993).
Ilya Prigogine and Isabelle Stengers, Order Out of Chaos: Man's New Dialogue with Nature, Doubleday (1989).
David Ruelle, Chance and Chaos, Princeton University Press (1993).
Ian Stewart, Does God Play Dice? The Mathematics of Chaos, Blackwell (1989).
Mike Field and Martin Golubitsky, Symmetry in Chaos, Oxford University Press (1992).
Ian Stewart and Martin Golubitsky, Fearful Symmetry: Is God a Geometer? Blackwell (1992).
Florin Diacu and Philip Holmes, Celestial Encounters: The Origins of Chaos and Stability, Princeton University Press (1996).
Some possible project ideas:
The mathematics and computation of fractals
Further exploration of iterative maps: rigorous definitions and detailed proofs of chaos in one-dimensional maps, Sarkovskii's ordering and "period three implies chaos", universality; or numerical explorations of iterative maps, possibly in higher dimensions.
Biological oscillations, models of population dynamics and ecology, epidemiology or immunology, models of HIV/AIDS dynamics
Chemical or biochemical oscillations
Physical applications, such as models for lasers
Topics in classical mechanics
Celestial mechanics, planetary motion, ...
Pattern formation, such as convection in fluids or biological patterns
Chaos and cryptography; controlling chaos
Philosophical aspects: the implications of chaos for chance and determinism
Other topics related to dynamics,
bifurcation, chaos, complexity, ...
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