MATH 411 - Mathematical Modeling Instructor- Lou Gross INDIVIDUAL PROJECTS The purpose of this assignment is to allow each student to develop expertise in some area of mathematical modeling by analyzing in some detail a particular model or group of models. The essential elements of this project must be: (i) a literature review of appropriate background material related to the topic chosen; (ii) some type of analysis, which may be numerical, of the model or group of models; (iii) a carefully written report on your investigation; and (iv) an oral report to the class, of approximately 20 minutes, based upon your investigation. A brief 5 minute presentation by each participant on the area they have chosen will be given in class on Wednesday October 30 - the purpose is for the instructor and class to give feedback on your oral presentation as well as on the topic described (this brief report will not be graded, except that it is a required part of the coursework). Some details on each of these: (i) The literature review should consist of more than merely looking at one paper or book on the topic. You should make use of the library as well as distributed information systems (e.g. WWW). You need to sufficiently investigate the topic so as to have a basic understanding of the issues being addressed, why the models or groups of models are potentially useful, and what the purpose or purposes are for constructing the models. (ii) Your project should should not merely repeat verbatim what was in a published paper. You may wish to: compare the assumptions underlying several different models developed for the same underlying problem and compare the behavior of these models, investigate either analytically or numerically modified formulations of one or more models, and discuss how you would go about producing a new model and what the advantages would be of doing so. (iii) The report should be a minimum of 15-20 double-spaced pages in length, not counting references or figures. It should be written in standard technical writing format: including an abstract or summary, an introductory section that briefly describes the underlying problem, a literature review section that describes previous work in some detail, a methods and analysis section (which may have several subsections) which describes in detail what you have done to analyze the model, and a conclusions section that describes the results of your analysis. In your conclusions section, you should critique the models discussed and elaborate suggestions for future improvements of them, and/or ways to test them using data. (iv) The oral report should be carefully planned, and practiced beforehand. You may use visual aids (including overheads, 35 mm slides, and/or the computer) to aid in the presentation. You may wish to hand out materials during the presentation. It should include a clear, concise description of the underlying problem, a summary of what modeling approaches have been taken, then a careful description of what model you've investigated. The instructor is available to meet individually with each participant to discuss any of the above, including helping to understand any technical aspects of a particular model.