The person or firm who contracts your services as a consultant is interested in knowing your solution to the problem and your recommendations with respect to implementing the solution. For most of the project assignements, you and your group will be acting as consultants for someone who has a problem. It will be your job to study the problem, and to make recommendations regarding its solution. A cover letter addressed to the person or firm who posed the problem should be the first page of your project report. In this cover letter you should clearly and simply (in one or two sentences) give the solution to the problem. Your report will then fill in the details about this solution.
Restate the problem in your own words. Develop the situation which gives a context to the problem you are studying. This may be a current news item or a fictional story. Identify your perspective with respect to the problem.
In one or two sentences, clearly state the problem you are studying, giving an indication of how you will determine if (when) it has been solved.
Identify the underlying assumptions. In order to turn a real life situation into a mathematical model, you will need to identify the major features of the problem, and indicate how these are addressed in your model. Identify the variables which are being taken into consideration by your model. Identify and discuss any interrelationships among these variables.
Present your mathematical work in this section of the report. The mathematical strategies which you will be learning to use in this course include formulating mathematical expressions, sketching qualitative graphs, fitting a curve to a set of data points, and carrying out a computer simulation experiment.
Apply your results to the original problem situation. How well does your solution address the problem? As the course progresses, you will learn strategies to specifically analyze how sensitive your solution is to your initial assumptions.
What did you learn about this problem as you developed this mathematical model? A good model will often lead to new insights about the problem itself. What are the implications of your model? What are the implications of your solution? How could you test your solution? What modifications might be necessary to implement and maintain this solution in the context of the original problem?
You may want to look at some of the winning papers from the Mathematical Modeling Contest which are published in the Fall issue of the UMAP Journal (available in our library) for some general examples of the style for your paper.
First impressions: Does your report give a good professional impression? Is it word-processed? Is it neat and attractive in appearance?
Clear and easy to read: Is your report written in standard English with good sentence structure? Has it been carefully proof-read and spell-checked?
Correct mathematical development of problem solution: Are you making appropriate use of mathematical techniques and strategies? Is your work correct? Have you checked to be sure that your results are reasonable and fit the original problem?
Evidence that you have given deep thought to the problem: In developing a model to study and solve the problem, have you made appropriate use of assigned reading in your text as well as sources beyond your text? Have you correctly documented all your sources? Have you synthesized these ideas and made them your own? Does your model demonstrate creative and constructive problem solving strategies appropriate to the given scenario?