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Training Materials
General Materials
- Kelly Cline's "Secrets of the Mathematical Contest in Modeling" (pdf) - In this excellent overview of the MCM/ICM Kelly Cline gives great strategies for achieving success during the COMAP weekend. This overview also includes descriptions of basic "roles" for the team members.
- A list of past MCM/ICM problems - Here Mark Parker has compiled a list that gives all COMAP MCM/ICM problems posed in the past.
- Dr. Dr. Ted Wendt (University of Wisconsin - La Crosse) has a webpage with several links to really good resources for COMAP teams. Be sure to check out the two COMAP contest guides written by winning teams. They give usable tips for all aspects of the contest, with especially good guidelines for working as a team and managing your time.
- Dr. Mark Parker's page with a brief description of the contest and MCM/ICM resources - Check out the resources on this page especially the keywords for library or web searches for both continuous and discrete problems.
- Official rules of the contest - These are the rules your team must follow.
Specific Materials
Mathematical Modeling of Infectious Diseases:
- "Epidemic Models for SARS and Measles" by Edward Rozema, in in The College Mathematics Journal, Vol. 38, No. 4, Sept. 2007, p 246 - 259. A nice introduction to infectious disease modeling. Only requires a Calc 2 background.
- Also here is a basic tutorial on the logistic growth mode with MATLAB code and/or an excel spreadsheet for helping you fit the model to data. The logistic growth model is a nonlinear differential equation. .... "This section will show how we can fit the data using either an Excel spreadsheet with ..."
Queuing Theory Resources:
- Our library has this textbook: Fundamentals of Queuing Theory by Gross and Harris (from George Mason University!) Call number: T57.9 .G76 1998
Sample Solutions from Previous LU Teams
2008
Problem A
This team earned a successful participant on this problem. Here is the problem statement: Consider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting, with particular attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.
Problem B
This team earned an honorable mention on this problem. Here is the problem statement: Develop an algorithm to construct Sudoku puzzles of varying difficulty. Develop metrics to define a difficulty level. The algorithm and metrics should be extensible to a varying number of difficulty levels. You should illustrate the algorithm with at least 4 difficulty levels. Your algorithm should guarantee a unique solution. Analyze the complexity of your algorithm. Your objective should be to minimize the complexity of the algorithm and meet the above requirements.
