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2012 Mathematical Contest in Modeling

Press Release—April 6, 2012

COMAP is pleased to announce the results of the 28th annual

Mathematical Contest in Modeling (MCM). This year, 3697 teams

representing institutions from seventeen countries participated in

the contest. Ten teams from the following institutions were

designated as OUTSTANDING WINNERS:

Bethel University,

Arden Hills, MN

Hong Kong Baptist University, Hong Kong

National University of Singapore, Singapore

Peking University, Beijing, China

Shanghai Foreign Language School,

Shanghai, China

University of Colorado, Boulder, CO (2)

University of Louisville, Louisville, KY

Western Washington University, Bellingham, WA

Zhejiang University, Hangzhou, China

This year’s contest ran from Thursday, February 9 to Monday,

February 13, 2011. During that time, teams of up to three

undergraduate or high school students researched, modeled, and

submitted a solution to one of two modeling problems. The 2012

MCM was primarily an online contest. Teams registered, obtained

contest materials, and downloaded the problem and data at the

prescribed time through COMAP’s MCM Website.

This year the two MCM problems represented significant challenges. The

author or Problem A is Lee Zia."How much do the leaves on a tree

weigh?'' How might one estimate the actual weight of the leaves (or for

that

matter any other parts of the tree)? How might one classify leaves?

Build a mathematical model to describe

and

classify leaves. Consider and

answer the

following:

Why do leaves have the various shapes that they

have?

Do the shapes

"minimize"

overlapping individual shadows that

are cast, so as to maximize exposure? Does

the

distribution of leaves

within the

"volume"

of the tree and its branches effect the

shape? I

s leaf

shape (general characteristics) related to tree profile/branching

structure?

How would you estimate the leaf mass of a tree? Is there a correlation

between the leaf mass and the

size

characteristics of the tree (height,

mass, volume defined by the

profile

)

In addition to your one page

summary sheet prepare a one page letter to an editor of a scientific

journal

outlining

your key

findings.

Problem B was written by Catherine Roberts, and required contestants

to analyze boat and camping trips down the Big Long River. Visitors to

the Big Long River (225 miles) can enjoy scenic views and exciting

white water rapids.

The

river is inaccessible to hikers, so the only

way to enjoy it is to take a river trip that requires several days of

camping. River trips all start at First Launch and exit the river at

Final Exit, 225 miles

downstream.

Passengers

take either oar- powered

rubber rafts, which travel on average 4 mph or motorized

boats,

which travel on average 8 mph. The trips range from 6 to 18 nights

of camping on the river, start

finish. The government agency

responsible for managing this river wants every trip to enjoy a

wilderness

experience, with minimal contact with other groups of

boats on the river. Currently,

trips

travel

down

the Big Long River

each year during a six month period (the rest of the year it is too

cold for river

trips).

There are

camp sites on the Big Long River,

distributed fairly uniformly

throughout

the river

corridor.

Given the

rise in popularity of river rafting, the park managers have been asked

to allow more trips

travel down the river. They want to determine

how they might schedule an optimal mix of trips,

varying

duration

(measured in nights on the river) and propulsion (motor or oar) that

will utilize

the

campsites in the best way possible.

other words,

how many more boat trips could be added to the Big Long River's

rafting season? The river managers have hired you to advise them on

ways in which

develop the best schedule and on ways in which to

determine the carrying capacity of the

river,

remembering that no

two sets of campers can occupy the same site at the same time.

addition to

your

one page summary sheet, prepare a one page memo

to the managers of the river describing your key

findings.

The ten Outstanding solution papers will be featured in The UMAP

Journal, along with commentary from the authors and other judges.

All 3697 of the competing teams are to be congratulated for their

excellent work and enthusiasm for mathematical modeling and

interdisciplinary problem solving.

2012 MCM Statistics

• 3697 teams participated

• 8 high school teams (1%)

• 341 US Teams (9%)

• 3356 Foreign Teams (91%) from Canada, China, Finland,

Germany, India, Indonesia, Ireland, Mexico, Malaysia,

Palestine, Singapore, South Africa, Spain, Turkey, United

Kingdom

• 10 Outstanding Winners (1%)

• 17 Finalist Winners (1%)

• 405 Meritorious Winners (9%)

• 1048 Honorable Mentions (28%)

• 2211 Successful Participants (60%)

• 6 Unsuccessful Participants (1%)

To obtain additional information about the MCM and to obtain a complete listing of all team designations, please visit the MCM Website at: www.mcmcontest.com, or

contact COMAP at: mcm@comap.com.

Major funding for the MCM is provided by COMAP. Additional support is provided by the Institute for Operations Research and the Management Sciences

(INFORMS) and Two Sigma Investments. COMAP's Mathematical Contest in Modeling and Interdisciplinary Contest in Modeling are unique among modeling

competitions in that they are the only international contests in which students work in teams to find a solution. Centering its educational philosophy on mathematical

modeling, COMAP uses mathematical tools to explore real-world problems. It serves the educational community as well as the world of work by preparing students to

become better informed—and prepared—citizens, consumers, and workers.

Contest Director

William Fox, Naval Postgraduate School, Monterey, CA

Executive Director

Solomon A. Garfunkel, COMAP, Inc., Bedford, MA

Founding Director

Ben Fusaro, Florida State University

Associate Director

Pat Driscoll, United States Military Academy, NY