Mathematical Modeling of Social Phenomena

Dr. Courtney Brown

Assignment #5

This is your second chance to work with your own model. You can either modify and enhance the model that you developed for assignment #4b, or you can develop an entirely new model. You will be presenting this model to the class, so do your best to work through a theory and to get the graph algrebra to match your theory as closely as possible. You can also try (and present) a few versions of your model, without making a firm decision yet as to which one best characterizes your theory. Use graph algebra to specify your model, and derive an equation from your graph algebra. You will want to work with difference equations for this assignment, so be sure to use time operators. Think carefully about what kind of time operators you want to use, and where you want to place them. Remember that the model becomes more complicated as you add more time operators. For now, you should try to limit your specification to either first-order or second-order linear difference equations. You can have more than one equation if you want. In such a situation, you will need to think through your theory to explain why your system of equations should be interdependent, and how this interdependence will be specified.

Make a nice sketch of your graph algebra. If you have access to an illustrator program such as Adobe Illustrator or Macromedia Freehand, feel free to use it to make your graph algebra as professional as possible. But you can also do this using the graphing capabilities of Word or WordPerfect. If worse comes to worse, a good liquid-ink pen, a ruler, a typewriter, and a piece of paper will also work. Explain your theory and model with a few pages of text, and hand it all in. Bring overhead gels to class of your graph algebra and your equations so you can present these things to the class. You will have to explain your theory as well, so you might want to summarize it with some bullet points on a separate overhead gel.