Project Guidelnes and Suggestions

What is the term project?

Most important: for your term project you should study something that is interesting to you. Of course it should also involve numerical computational problems in a nontrivial and fundamental way -- but beyond that I'm very open about topic. The proposal report will give you experience giving a very short oral presentation; the final report will give you practice giving a longer presentation; and the written report will give you practice in preparing a documented scientific paper. All three of these skills are important in that world out there.

We'll devote a class meeting after the break to reports of your proposals, allotting 80/n minutes per student (see the master course schedule.) This is not much time, so you will have to put some effort in preparing a succinct and clear description of what you plan to do. Think of it in terms of one overhead.

We'll also schedule longer oral presentations at the end of reading period for your final report. And of course you must submit a written version that is coherently written and completely documented. Here's a tip: start taking notes immediately on your sources, if you haven't already. Write down a complete and accurate reference for every source you read, with notes on the content. This will save you immeasurable trouble when you come to the writeup, and ensure that you reference your sources properly.

I don't want to tie you down to a particular form of report, but typically I would expect it to include at least

• description of topic
• background and previous work
• statement of an open problem or question that you investigate
• method of attack, algorithms used, programs written
• computational results
• analysis of results and conclusions

For an estimate of scope, think of your project as the size of another assignment like the five in the course, but one of your own making. In fact, we may develop some of your term projects into new assignments for future COS 323 generations.

Choosing a topic

As I said above, choose something you're really interested in. If you have trouble choosing a topic, make an appointment to discuss it with me (ken@cs) or the grad TA (schneidr@cs), or talk to your friends, or ask other faculty, or browse current periodicals in the library, or take a walk in the woods.

Below are some suggestions for term projects. These are just suggestions, some very general. You are certainly not limited to these. On the contrary, the wider ranging the projects, the more interesting. I've provided some references, but a trip to the online catalog, search on the web, and a perusal of current periodials should provide you with lots of leads on most of these topics. Also, check other sites on the COS 323 links page. These point to a variety of university and research web pages that may stimulate your imagination or provide more information on given topics. If you get stuck with an idea you want to pursue and can't find any leads, be sure to see ken or the grad TA.

• cellular automata:
  • Lattice gasses

    These are discrete, binary, particle models for gasses, an alternative to differential equations for modeling fluid flow. Some good elementary material is in Gould and Tobochnik [GT96].

  • embedded computation To get started, see [SKW88, SS94, JSS97] and papers by Melanie Mitchell about evolving cellular automata.
  • anthropology
  • epidemics

• modeling prehistoric settlement behavior; if you're interested in learning more about this, see Dr. Peter Bogucki (Assistant Dean for Undergraduate Affairs, bogucki@pucc.princeton.edu), who studies the establishment of agricultural communities in north-central Europe

• n-Body simulation

• nonlinear pendulums

• weather simulations

• physical modeling of musical instruments

• solitons in optical fibers, water, plasmas

• option pricing

  In 1973, F. Black and M. Scholes derived a formula to price European call options on nondividend paying stocks. The formula has been generalized since then and is now used by professionals to price stock options, stock index options, currency options, and numerous other forms of options [Gib91].

• chaos in economic systems

• protein folding

• computation of equilibria in economic systems, game theory

• physical modeling of human motion

• physical modeling of paper marbling [Cha86]

  Paper marbling is a technique for making decorative paper, and has been widely used for book endpapers and edge decoration for centuries. Simply put, colors are floated on a water-based solution, disturbed to make patterns, and paper is laid on the surface to register the pattern [Cha86]. To my knowledge no one has tried to model the process physically, using differential equations or cellular automata, say. For some beautiful examples of real marbling, see Paola Kathuria's page of marbling. For more on shading and texturing in the computer graphics world, explore the RenderMan Repository.

  Prof. Patrick M. Hanrahan" writes:
  
  ``In terms of simulation, there have been a few related things. In 1986 Ken Perlin put together a nice procedure for generating noise, and he used it to simulate marble (the rock). Basically, he creates a 3D solid texture by putting a periodic function through a color table, and then perturbs the phase with the noise function. He has a nice marble vase in his paper. The reference is "The Image Synthesizer" by Perlin, in SIGGRAPH 1986.''

  
  

• ODE's and PDE's for modeling epidemics

• safe burning of plutonium, using Monte Carlo simulations of neutron transport