[ugrads] [Mathclub-members] Mathematical Contest in Modeling in Feb 10-14 2011

Zhihe Liu zliu34 at iit.edu
Thu Jan 27 20:19:12 CST 2011


Dear all,

Thanks for Prof. Ellis. He pointed out the mistake that I made. By saying
"less than 3", I actually meant no more than 3. Sorry about the ambiguous I
made. Also, there are people asking to see the sample problems. You can
click previous contest<http://www.comap.com/undergraduate/contests/mcm/previous-contests.php>at
their website
***http://www.comap.com/undergraduate/contests/mcm/*

People who want to compete in this contest must submit a final paper of your
solution. Especially, for ICM teams, you'll need one summary sheet and a 10
page report.

If you want to solve something practical, than problem C may be interesting
to you. Please see the attachment for details of Problem C.

Thanks,

Zhihe Liu


Here is problem of last year.

*2010 MCM Problems
*
*PROBLEM A: **The Sweet Spot**
 *

Explain the “sweet spot” on a baseball bat.



Every hitter knows that there is a spot on the fat part of a baseball bat
where maximum power is transferred to the ball when hit. Why isn’t this spot
at the end of the bat? A simple explanation based on torque might seem to
identify the end of the bat as the sweet spot, but this is known to be
empirically incorrect. Develop a model that helps explain this empirical
finding.



Some players believe that “corking” a bat (hollowing out a cylinder in the
head of the bat and filling it with cork or rubber, then replacing a wood
cap) enhances the “sweet spot” effect. Augment your model to confirm or deny
this effect. Does this explain why Major League Baseball prohibits
“corking”?



Does the material out of which the bat is constructed matter? That is, does
this model predict different behavior for wood (usually ash) or metal
(usually aluminum) bats? Is this why Major League Baseball prohibits metal
bats?



*PROBLEM B: **Criminology
*

In 1981 Peter Sutcliffe was convicted of thirteen murders and subjecting a
number of other people to vicious attacks. One of the methods used to narrow
the search for Mr. Sutcliffe was to find a “center of mass” of the locations
of the attacks. In the end, the suspect happened to live in the same town
predicted by this technique. Since that time, a number of more sophisticated
techniques have been developed to determine the “geographical profile” of a
suspected serial criminal based on the locations of the crimes.

Your team has been asked by a local police agency to develop a method to aid
in their investigations of serial criminals. The approach that you develop
should make use of at least two different schemes to generate a geographical
profile. You should develop a technique to combine the results of the
different schemes and generate a useful prediction for law enforcement
officers. The prediction should provide some kind of estimate or guidance
about possible locations of the next crime based on the time and locations
of the past crime scenes. If you make use of any other evidence in your
estimate, you must provide specific details about how you incorporate the
extra information. Your method should also provide some kind of estimate
about how reliable the estimate will be in a given situation, including
appropriate warnings.

In addition to the required one-page summary, your report should include an
additional two-page executive summary. The executive summary should provide
a broad overview of the potential issues. It should provide an overview of
your approach and describe situations when it is an appropriate tool and
situations in which it is not an appropriate tool. The executive summary
will be read by a chief of police and should include technical details
appropriate to the intended audience.


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