COMAP Training Materials

Below is a list of links I am compiling for your training.  I have divided them into three types: 

General Materials
Materials/Link Description
Kelly Cline's "Secrets of the Mathematical Contest in Modeling":  http://www.carroll.edu/~kcline/mcm.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: http://www.carroll.edu/~mparker/mcm/mcmproblems.htm Here Mark Parker has compiled a list that gives all COMAP MCM/ICM problems posed in the past.
Dr. Mark Parker's page with a brief desciption of the contest and MCM/ICM resources: http://www.carroll.edu/~mparker/mcm.html 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:  http://www.comap.com/undergraduate/contests/ These are the rules your team must follow.

 

 

Specific Materials
Materials/Link
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 ..."    http://www-rohan.sdsu.edu/~jmahaffy/courses/f01/math636/lectures/competition2/competition2.html

 

Queuing Theory Resources:

http://ite.pubs.informs.org/Vol2No3/Ashley/ - nice Excel spreadsheet tutorial for a simple easy to read introduction to basic queuing theory concepts including M/M/s queues (written by a business prof I believe)..should reference in paper if you use it.  Here is a pdf copy of the paper to reference http://mia.ece.uic.edu/~papers/etc/pdf00001.pdf 

Our library has this textbook:  Fundamentals of Queuing Theory by Gross and Harris (from George Mason University!)  Call number:  T57.9 .G76 1998  http://mason.gmu.edu/~dgross1/gross-harris/gh3.html  You can download the freely available QTS (Queuing Theory Software - based on above text - it is an Excel spreadsheet) at this link:  http://www.geocities.com/qtsplus/index.html  The software implements many basic queuing models.

"Gary shows you a simple implementation of the "Airline Check-In" queue that ... Our Airline Check-in desk / Blocking Queue model is approximated quite well"...the code is contained in a zip file - could be useful if you want to implement your own code:  http://dotnetjunkies.com/Article/D7E688B8-0BDD-4D44-9A0F-4CD26FB35F51.dcik
 
 

 

Sample Solutions from Previous LU Teams
Materials/Link Description
2008 Problem B Summary

2008 Problem B Paper

 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.
2008 Problem A Summary

2008 Problem A Paper

 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.