Also, since the introduction in 1999 of the Interdisciplinary Contest in Modeling (ICM)!R (which has separate funding and sponsorship from the MCM), the Journal has devoted a second of its four annual issues to Outstanding
papers from that contest.
A New Designation for Papers
It has become increasingly difficult to identify just a handful of Outstanding papers for each problem. After 14 Outstanding MCM teams in 2007, there have been 9 in each year since, despite more teams competing.
The judges have been overwhelmed by increasing numbers of Meritorious papers from which to select the truly Outstanding. As a result, this
year there is a new designation of Finalist teams, between Outstanding and Meritorious. It recognizes the less than 1% of papers that reached the final (seventh) round of judging but were not selected as Outstanding. Each Finalist paper displayed some modeling that distinguished it from the rest of the Meritorious papers. We think that the Finalist papers deserve special
The UMAP Journal 31 (2) (2010) 93–94. !c Copyright 2010 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.
94 The UMAP Journal 31.2 (2010)
recognition, and the mathematical professional societies are investigating ways to recognize the Finalist papers.
Just One Contest Issue Each Year
Taking up two of the four Journal issues each year, and sometimes twothirds
of the pages, the amount of material from the two contests has come to overbalance the other content of the Journal.
The Executive Publisher, Sol Garfunkel, and I have decided to return more of the Journal to its original purpose, as set out 30 years ago, to: acquaint readers with a wide variety of professional applications of the mathematical sciences, and provide a forumfor discussions of new directions in mathematical education. [Finney and Garfunkel 1980, 2–3]
Henceforth, we plan to devote just a single issue of the Journal each year to the two contests combined. That issue—this issue—will appear during the summer and contain
?reports on both contests, including the problem statements and names
of the Outstanding teams and their members;
?authors‘, judges‘, and practitioners‘ commentaries (as available) on the
problems and the Outstanding papers; and
?just one Outstanding paper from each problem.
Available separately from COMAP on a CD-ROM very soon after the contests (as in 2009 and again this year) will be:
?full original versions of all of the Outstanding papers, and ?full results for all teams.
Your Role
The ever-increasing engagement of students in the contests has been astonishing; the steps above help us to cope with this success.
There will now be more room in the Journal for material on mathematical modeling, applications of mathematics, and ideas and perspectives on mathematics education at the collegiate level—articles, UMAP Modules, Minimodules, ILAP Modules, guest editorials. We look forward to your contribution.
Reference
Finney, Ross L., and Solomon Garfunkel. 1980. UMAP and The UMAP Journal.
The UMAP Journal 0: 1–4. Results of the 2010 MCM 95
Modeling Forum
Results of the 2010
Mathematical Contest in Modeling
Frank R. Giordano, MCM Director
Naval Postgraduate School 1 University Circle
Monterey, CA 93943–5000
frgiorda@nps.edu
Introduction
A total of 2,254 teams of undergraduates from hundreds of institutions and departments in 14 countries, spent a weekend in February working on applied
mathematicsproblems inthe 26thMathematicalContest inModeling(MCM)!R . The 2010MCMbegan at 8:00 P.M. EST on Thursday, February 18, and ended at 8:00 P.M. EST on Monday, February 22. During that time, teams of up to three undergraduates researched, modeled, and submitted a solution to one of two open-ended modeling problems. Students registered, obtained contest materials, downloaded the problem and data, and entered completion data through COMAP‘s MCM Website. After a weekend of hard work, solution
papers were sent to COMAP on Monday. Two of the top papers appear in this issue of The UMAP Journal, together with commentaries.
In addition to this special issue of The UMAP Journal, COMAP has made available a special supplementary 2010 MCM-ICM CD-ROM containing the press releases for the two contests, the results, the problems, and original versions
of the Outstanding papers. Information about ordering the CD-ROM is at http://www.comap.com/product/cdrom/index.html or from (800) 772–6627.
Results and winning papers from the first 25 contests were published in special issues of Mathematical Modeling (1985–1987) and The UMAP Journal
(1985–2009). The 1994 volume of Tools for Teaching, commemorating the tenth
anniversary of the contest, contains the 20 problems used in the first 10 years of the contest and a winning paper for each year. That volume and the special
The UMAP Journal 31 (2) (2010) 95–104. !c Copyright 2010 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.
96 The UMAP Journal 31.2 (2010)
MCMissues of the Journal for the last few years are available fromCOMAP. The
1994volumeis also availableonCOMAP‘sspecial ModelingResourceCD-ROM. Also available is The MCM at 21 CD-ROM, which contains the 20 problems from the second 10 years of the contest, a winning paper from each year, and advice from advisors of Outstanding teams. These CD-ROMs can be ordered from COMAP at http://www.comap.com/product/cdrom/index.html . This year, the two MCM problems represented significant challenges:
?Problem A, ―The Sweet Spot,‖ asked teams to explain why the spot on a
baseball bat where maximum power is transferred to the ball is not at the end of the bat and to determine whether ―corking‖ a bat (hollowing it out and replacing the hardwood with cork) enhances the ―sweet spot‖ effect.
?Problem B, ―Criminology,‖ asked teams to develop geographical profiling
to aid police in finding serial criminals.
In addition to the MCM, COMAP also sponsors the Interdisciplinary Contest in Modeling (ICM)!R and the High School Mathematical Contest in Modeling (HiMCM)!R :
?The ICM runs concurrently with MCM and for the next several years will
offer a modeling problem involving an environmental topic. Results of this year‘s ICM are on the COMAP Website at http://www.comap.com/ undergraduate/contests. The contest report, an Outstanding paper, and commentaries appear in this issue.
?The HiMCM offers high school students a modeling opportunity similar to
the MCM. Further details about the HiMCM are at http://www.comap. com/highschool/contests .
2010 MCM Statistics
?2,254 teams participated ?15 high school teams (<1%) ?358 U.S. teams (21%)
?1,890 foreign teams (79%), from Australia, Canada, China, Finland,
Germany,
Indonesia, Ireland, Jamaica, Malaysia, Pakistan, Singapore, South Africa, United Kingdom
?9 OutstandingWinners (<0.5%) ?12 Finalists (0.5%)
?431 MeritoriousWinners (19%) ?542 Honorable Mentions (24%) ?1,245 Successful Participants (55%)
Results of the 2010 MCM 97
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 ballwhenhit. Whyisn‘t this spot at the end of the bat? Asimple 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 13murders and subjecting a number of other people to vicious attacks. Oneof the methods used to narrowthe 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.
98 The UMAP Journal 31.2 (2010)
The Results
The solution papers were coded at COMAP headquarters so that names and affiliations of the authors would be unknown to the judges. Each paper was then read preliminarily by two ―triage‖ judges at either Appalachian State