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Table of Contents
Publisher’s Editorial
The Faffufnik–Chaim Yankel Effect
Solomon Garfunkel... 185
About This Issue
... 188Special Section on the MCM
Results of the 2009 Mathematical Contest in Modeling
Frank Giordano ... 189
Abstracts of the Outstanding Papers ... 207 A Simulation-Based Assessment of Traffic Circle Control
Christopher Chang, Zhou Fan, and Yi Sun ... 227 One Ring to Rule Them All: The Optimization of
Traffic Circles
Aaron Abromowitz, Andrea Levy, and Russell Melick ... 247 Three Steps to Make the Traffic Circle Go Round
Zeyuan Allen Zhu, Tianyi Mao, and Yichen Huang ... 261 Pseudo-Finite Jackson Networks and Simulation:
A Roundabout Approach to Traffic Control
Anna Lieb, Anil Damle, and Geoffrey Peterson ... 281 Judges Commentary: The Outstanding Traffic Circle
Papers
Kelly Black ... 305
Nevin Brackett-Rozinsky, Katelynn Wilton, and
Jason Altieri ... 313 Energy Implications of Cellular Proliferation
in the U.S.
Benjamin Coate, Zachary Kopplin, and Nate Landis ... 333 Modeling Telephony Energy Consumption
Amrish Deshmukh, Rudolf Nikolaus Stahl, and
Matthew Guay ... 353 America’s New Calling
Stephen R. Foster, J. Thomas Rogers, and Robert S. Potter .... 367 Wireless Networks: An Easy Cell
Jeff Bosco, Zachary Ulissi, and Bob Liu ... 385 Judges’ Commentary: The Outstanding Cellphone
Energy Papers
Marie Vanisko ... 403 Judges’ Commentary: The Fusaro Award for the
Cellphone Energy Problem
Marie Vanisko and Peter Anspach ...409
Publisher’s Editorial
The Faffufnik–Chaim Yankel Effect
Solomon A. Garfunkel
Executive Director COMAP, Inc.
175 Middlesex Turnpike, Suite 3B Bedford , MA 01730–1459
In the United States, as in many countries and more global entities, in order to receive funding for a major project, one has to submit a proposal. As anyone who has ever written one knows, writing a proposal is an unnatural act. Normally literate persons are reduced to using words such as “input”
as a verb, as well as “facilitating” and “orientating,” and talking about
“stakeholders” and “meta-cognition.” But large projects often require large budgets, and as painful as the process may be, we write the proposals and fill out the myriad forms required.
Most of the money that comes from federal sources in the United States for math education projects is given in grants from the National Science Foundation (NSF). NSF uses a peer-review process to determine which projects are funded. Panels of approximately six people are formed to review a set of proposals. The proposals in each panel are graded and compared with the grades from several other panels that are convened at the same time. The programs are ordered by grade, and funding proceeds on that basis. What actually happens is that on a first pass, a number of projects are graded highly enough to be assured of funding; a number are graded so low that they are immediately declined; and there is a group in the middle (said to be “on the bubble”) whose fate is decided some time later when the final yearly budget for these programs is negotiated. The criteria for reviewing proposals, as specifically cited in NSF guidelines, are
“intellectual merit” and “broader impacts.”
The Consortium for Mathematics and Its Applications (COMAP) has been submitting proposals and administering projects for over 29 years. In the “good old days,” if one had a good idea and a good staff of people to carry out that idea, then funding usually depended upon impressing one of
The UMAP Journal 30 (3) (2009) 185–188. c!Copyright 2009 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.
the program officers who worked at the Foundation. Outside reviews were mostly handled by mail and were considered advisory. The bottom line was that if the NSF program officer thought that a project should be funded, it was. Admittedly, this created something of an old-boy network. People and institutions with a good track record of success tended to continue to receive funding, while those who were not yet members of the club had a hard time joining. This has given way to the more overtly democratic process described above where the reviewers’ opinions rule.
It should also be said that if one goes back 20 years or so, most of the principal investigators (PIs) on mathematics education projects were Ph.D.
mathematicians who had, so to speak, “given their youth to the devil and were giving their old age to the Lord.” In other words, they had taken an interest in mathematics education later in their careers. And, to be honest, many other mathematics educators were persons who originally pursued careers as research mathematicians but were unable to complete their degrees. In any event, the PIs on these projects had extremely strong mathematics backgrounds.
In the United States at least, this has changed significantly. Mathematics education is now a well-established field unto itself and, in many cases, people highly successful in the field have relatively weak mathematical training. Increasingly, they are the principal investigators on new projects in mathematics education and they are the reviewers. They help decide what projects get funded and what projects don’t. And, increasingly, they are responsible for the Faffufnik–ChaimYankel Effect (FCE). What exactly is the FCE?
Years ago, a typical review of a COMAP proposal would read, “This is an excellent idea with an excellent staff with an excellent track record; we recommend this project for funding.” The FCE refers to more typical current reviews that read, “This is an excellent idea with an excellent staff with an excellent track record. However, we have to recommend against funding because they don’t make any reference to the seminal research papers of Faffufnik, nor do they plan to use the statistical protocols of Chaim Yankel.”
The reviewers may very well be students of Faffufnik and/or Chaim Yankel.
Of course, there are some sour grapes here. I am not a member of the Faffufnik and Chaim Yankel club. And now, as opposed to the good old days, it is the members of this club who get funded. But there is much more to be discussed. There appears to be an underlying assumption that mathematics education projects must proceed in the following way.
• First, they must be based upon research. Therefore, we heavily quote the results of prior research (see the papers of Faffufnik).
• Then, based upon that research, we make a new research hypothesis and test it with a small number of students. If at all possible, we make this experiment as close to a “gold standard” double-blind medical approach as possible.
• Then, using certain statistical protocols (see the work of Chaim Yankel), we conclude that there is some measurable effect and write a new pro- posal to test this effect on a larger population.
• This process is then iterated.
This is now a necessary condition for funding—independent of content and the strength of the ideas being considered.
The problem is that while this may very well help to make mathematics education research be seen as more of an established discipline, it is a cri- terion divorced from classroom practice. And we forget that we separate our efforts in education from the classroom at our peril. There has to be a way for good ideas that hold the promise of increasing student learning to be funded and for good people to work on them. Mathematics education is an art as well as a science, and it cannot be reduced to a set of research protocols and statistical tests and procedures. It is simply not possible to prove that an approach to teaching and learning will be effective before the fact.
Education, as a scientific discipline, is a young field with an active com- munity focused on R&D—research on learning coupled with the develop- ment of new and better curriculum materials. In truth, however, much of the work is better described as D&R—informed and thoughtful devel- opment followed by careful analysis of results. It is in the nature of the enterprise that we cannot discover what works before we create the what.
Curriculum development, in particular, is best related to an engineering paradigm. To test the efficacy of an approach, we must analyze needs, ex- amine existing programs, build an improved model program, and then test it—in the same way that we build scale models to design a better bridge or building. This kind of iterative D&R leads to new and more effective mate- rials and new pedagogical approaches that better incorporate the growing body of knowledge of cognitive science.
I wish to be clear. I recognize that Faffufnik has done important re- search. I recognize that Chaim Yankel’s protocols can help quantify our results. We must learn from the past, and theoretical frameworks are im- portant for future work. But we also must recognize that quoting Faffufnik and ChaimYankel is not a substitute for imagination, creativity, and the application of common sense. The problems of mathematics education are difficult and will require the work of many people over a long period of time. We cannot afford to lose sight of this, even as mathematics education becomes a more-established research discipline.
Acknowledgment
This editorial is adapted from the author’s talk at the International Com- mission on Mathematical Instruction (ICMI) meeting in Rome, Italy, 2008.
About the Author
Solomon Garfunkel, previously of Cornell University and the Univer- sity of Connecticut at Storrs, has dedicated the last 30 years to research and development efforts in mathematics education. He has served as project director for the Undergraduate Mathematics and Its Applications (UMAP) and the High School Mathematics and Its Applications (HiMAP) Projects funded by NSF, and directed three telecourse projects including Against All Odds: Inside Statistics, and In Simplest Terms: College Algebra, for the An- nenberg/CPB Project. He has been the Executive Director of COMAP, Inc.
since its inception in 1980. Dr. Garfunkel was the project director and host for the series, For All Practical Purposes: Introduction to Contemporary Math- ematics. He was the Co-Principal Investigator on the ARISE Project, and is currently the Co-Principal Investigator of the CourseMap, ResourceMap, and WorkMap projects. In 2003, Dr. Garfunkel was Chair of the National Academy of Sciences and Mathematical Sciences Education Board Com- mittee on the Preparation of High School Teachers.
About This Issue
Paul J. Campbell
Editor
This issue runs longer than a regular 92-page issue, to more than 200 pages. However, not all of the articles appear in the paper version. Some appear only on the Tools for Teaching 2009 CD-ROM (and athttp://www.
comap.com for COMAP members), which will reach members and sub- scribers later and will also contain the entire 2009 year of Journal issues.
All articles listed in the table of contents are regarded as published in the Journal. The abstract of each appears in the paper version. Pagination of the issue runs continuously, including in sequence articles that do not appear in the paper version. So if, say, p. 250 in the paper version is followed by p. 303, your copy is not necessarily defective! The articles on the intervening pages are on the CD-ROM.
We hope that you find this arrangement agreeable. It means that we do not have to procrusteanize the content to fit a fixed number of paper pages.
We might otherwise be forced to select only two or three Outstanding MCM papers to publish. Instead, we continue to bring you the full content.
Modeling Forum
Results of the 2009
Mathematical Contest in Modeling
Frank Giordano, MCM Director
Naval Postgraduate School 1 University Circle
Monterey, CA 93943-5000 [email protected]
Introduction
A total of 1,675 teams of undergraduates from hundreds of institutions and departments in 14 countries, spent the first weekend in February working on applied mathematics problems in the 25th Mathematical Contest in Modeling.
The 2009 Mathematical Contest in Modeling (MCM) began at 8:00 P.M. EST on Thursday, February 5 and ended at 8:00 P.M. EST on Monday, February 9.
During that time, teams of up to three undergraduates researched, modeled, and submitted a solution to one of two open-ended modeling problems. Stu- dents registered, obtained contest materials, downloaded the problem and data, and entered completion data through COMAP’s MCM Website. After a week- end of hard work, solution papers were sent to COMAP on Monday. The top papers appear in this issue ofThe UMAP Journal, together with commentaries.
In addition to this special issue of The UMAP Journal, this year—for the first time—COMAP has made available a special supplementary “2009 MCM- ICM CD-ROM” containing the press releases for the two contests, the results, the problems, and original versions of the Outstanding papers that appear here in edited form. Information about ordering the CD-ROM is at http:
//www.comap.com/product/?idx=1025or from (800) 772–6627.
Results and winning papers from the first 24 contests were published in special issues ofMathematical Modeling (1985–1987) and The UMAP Journal (1985–2008). The 1994 volume ofTools 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 30 (3) (2009) 189–206. c!Copyright 2009 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.
MCM issues of theJournal for the last few years are available from COMAP. The 1994 volume is also available on COMAP’s specialModeling Resource CD-ROM.
Also available isThe 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 athttp://www.comap.com/product/cdrom/index.html.
This year, the two MCM problems represented significant challenges. The author of Problem A, Daniel Solow of Case Western Reserve University, Cleve- land, OH, was also one of the final judges. His problem, “Designing a Traffic Circle,” asked teams to use a model to determine how best to control traffic flow in, around, and out of a circle, clearly stating the objective(s) and summarizing the conditions for use of various types of traffic-control methods. Problem B,
“Energy and the Cellphone,” was written by Joe Malkevitch of York College in Jamaica, NY. What is the long-term consequence of large-scale usage of cell- phones in terms of electricity use by the battery and the charger? Teams were asked to take into account the fact that cellphones last much less time (they get lost and break) than phones for landlines and to suggest an optimal way (in terms of an energy perspective) to provide phone service to a “Pseudo U.S.,”
a country of 300 million people with about the same economic status as the current U.S. but with no landlines or cellphones.
In addition to the MCM, COMAP also sponsors the Interdisciplinary Con- test in Modeling (ICM) and the High School Mathematical Contest in Model- ing (HiMCM). The ICM runs concurrently with MCM and for the next several years will offer a modeling problem involving an environmental topic. Re- sults of this year’s ICM are on the COMAP Website athttp://www.comap.
com/undergraduate/contests; results and Outstanding papers appeared in Vol. 30 (2009), No. 2. The HiMCM offers high school students a model- ing opportunity similar to the MCM. Further details about the HiMCM are at http://www.comap.com/highschool/contests.
2009 MCM Statistics
• 1,675 teams participated
• 7 high school teams (<1%)
• 350 U.S. teams (21%)
• 1,325 foreign teams (79%), from Australia, Canada, China, Finland, Ger- many, Hong Kong, Hungary, Indonesia, Ireland, Mexico, Singapore, South Africa, United Kingdom
• 9 Outstanding Winners (<1%)
• 294 Meritorious Winners (18%)
• 298 Honorable Mentions (18%)
• 1,074 Successful Participants (63%)
Problem A: Designing a Traffic Circle
Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road, which gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.
The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double- spaced pages that explains to a traffic engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.
Problem B: Energy and the Cellphone
This question involves the “energy” consequences of the cellphone revolu- tion. Cellphone usage is mushrooming, and many people are using cellphones and giving up their landline telephones. What is the consequence of this in terms of electricity use? Every cellphone comes with a battery and a recharger.
Requirement 1
Consider the current U.S., a country of about 300 million people. Estimate from available data the numberH of households, withmmembers each, that in the past were serviced by landlines. Now, suppose that all the landlines are replaced by cellphones; that is, each of themmembers of the household has a cellphone. Model the consequences of this change for electricity utilization in the current U.S., both during the transition and during the steady state. The analysis should take into account the need for charging the batteries of the cellphones, as well as the fact that cellphones do not last as long as landline phones (for example, the cellphones get lost and break).
Requirement 2
Consider a second “Pseudo U.S.”—a country of about 300 million people with about the same economic status as the current U.S. However, this emerging country has neither landlines nor cellphones. What is the optimal way of providing phone service to this country from an energy perspective? Of course, cellphones have many social consequences and uses that landline phones do not allow. A discussion of the broad and hidden consequences of having only landlines, only cellphones, or a mixture of the two is welcomed.
Requirement 3
Cellphones periodically need to be recharged. However, many people al- ways keep their recharger plugged in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the en- ergy costs of this wasteful practice for a Pseudo U.S. based on your answer to Requirement 2. Assume that the Pseudo U.S. supplies electricity from oil.
Interpret your results in terms of barrels of oil.
Requirement 4
Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device. Use accurate data to model the energy wasted by the current U.S. in terms of barrels of oil per day.
Requirement 5
Now consider population and economic growth over the next 50 years.
How might a typical Pseudo U.S. grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil.
Interpret your predictions in term of barrels of oil.
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 Uni- versity (Traffic Circle Problem) or at the National Security Agency (Cellphone Energy Problem). At the triage stage, the summary and overall organization are the basis for judging a paper. If the judges’ scores diverged for a paper, the judges conferred; if they still did not agree, a third judge evaluated the paper.
Additional Regional Judging sites were created at the U.S. Military Academy and at the Naval Postgraduate School to support the growing number of contest submissions.
Final judging took place at the Naval Postgraduate School, Monterey, CA.
The judges classified the papers as follows:
Honorable Successful
Outstanding Meritorious Mention Participation Total
Traffic Circle Problem 4 192 165 763 1124
Cellphone Energy Problem 5 102 133 311 551
9 294 298 1074 1675
The 9 papers that the judges designated as Outstanding appear in this spe- cial issue of The UMAP Journal, together with commentaries. We list those teams here and the Meritorious teams (and advisors) at the end of this report;
the list of all participating schools, advisors, and results is in theAppendix.
Outstanding Teams
Institution and Advisor Team Members
Traffic Circle Papers
“A Simulation-Based Assessment of Traffic Circle Control”
Harvard University Cambridge, MA Clifford H. Taubes
Christopher Chang Zhou Fan
Yi Sun
“One Ring to Rule Them All:
The Optimization of Traffic Circles”
Harvey Mudd College Claremont, CA
Susan E. Martonosi
Aaron Abromowitz Andrea Levyi Russell Melick
“Three Steps to Make the Traffic Circle Go Round”
Tsinghua University Beijing, China Jun Ye
Zeyuan Zhu Tianyi Mao Yichen Huang
“Pseudo-Finite Jackson Networks and Simulation: A Roundabout
Approach to Traffic Control”
University of Colorado Boulder, CO
Anne Dougherty
Anna Lieb Anil Damle
Geoffrey Peterson Cellphone Energy Papers
“Mobile to Mobil: The Primary Energy Costs for Cellular and Landline
Telephones”
Clarkson University Potsdam, NY
Joseph Skufca
Nevin Brackett-Rozinsky Katelynn Wilton
Jason Altieri
“Energy Implications of Cellular Proliferation in the U.S.”
College of Idaho Caldwell, IDA Michael P. Hitchman
Benjamin Coate Zachary Kopplin Nate Landis
“Modeling Telephony Energy Consumption”
Cornell University Ithaca, NY
Alexander Vladimirsky
Amrish Deshmukh Rudolf Nikolaus Stahl Matthew Guay
“America’s New Calling”
Southwestern University Georgetown, TX
Richard Denman
Stephen R. Foster J. Thomas Rogers Robert S. Potter
“Wireless Networks: An EasyCell”
University of Delaware Newark, DE
Louis Rossi
Jeff Bosco Zachary Ulissi Bob Liu
Awards and Contributions
Each participating MCM advisor and team member received a certificate signed by the Contest Director and the appropriate Head Judge.
INFORMS, the Institute for Operations Research and the Management Sciences, recognized the teams from the University of Colorado–Boulder (Traffic Circle Problem) and Cornell University (Cellphone Energy Problem) as INFORMS Outstanding teams and provided the following recognition:
• a letter of congratulations from the current president of INFORMS to each team member and to the faculty advisor;
• a check in the amount of $300 to each team member;
• a bronze plaque for display at the team’s institution, commemorating their achievement;
• individual certificates for team members and faculty advisor as a per- sonal commemoration of this achievement;
• a one-year student membership in INFORMS for each team member, which includes their choice of a professional journal plus the OR/MS Today periodical and the INFORMS society newsletter.
The Society for Industrial and Applied Mathematics (SIAM) designated one Outstanding team from each problem as a SIAM Winner. The teams were from Harvard University (Traffic Circle Problem) and Southwestern University (Cellphone Energy Problem). Each of the team members was awarded a $300 cash prize, and the teams received partial expenses to present their results in a special Minisymposium at the SIAM Annual Meet- ing in Denver, CO in July. Their schools were given a framed hand-lettered certificate in gold leaf.
The Mathematical Association of America (MAA) designated one Out- standing North American team from each problem as an MAA Winner. The teams were from Harvey Mudd College (Traffic Circle Problem) and Clark- son University (Cellphone Energy Problem). With partial travel support from the MAA, the teams presented their solution at a special session of the MAA Mathfest in Portland, OR in August. Each team member was pre- sented a certificate by an official of the MAA Committee on Undergraduate Student Activities and Chapters.
Ben Fusaro Award
One Meritorious or Outstanding paper was selected for each problem for the Ben Fusaro Award, named for the Founding Director of the MCM and awarded for the sixth time this year. It recognizes an especially creative approach; details concerning the award, its judging, and Ben Fusaro are in Vol. 25 (3) (2004): 195–196. The Ben Fusaro Award winners were the
University of Iowa (Traffic Circle Problem) and Lawrence Technological University (Cellphone Energy Problem).
Judging
Director
Frank R. Giordano, Naval Postgraduate School, Monterey, CA Associate Director
William P. Fox, Dept. of Defense Analysis, Naval Postgraduate School, Monterey, CA
Traffic Circle Problem Head Judge
Marvin S. Keener, Executive Vice-President, Oklahoma State University, Stillwater, OK
Associate Judges
William C. Bauldry, Chair, Dept. of Mathematical Sciences,
Appalachian State University, Boone, NC (Head Triage Judge) Kelly Black, Mathematics Dept., Union College, Schenectady, NY
Karen D. Bolinger, Mathematics Dept., Clarion University of Pennsylvania, Clarion, PA (SIAM Judge)
Patrick J. Driscoll, Dept. of Systems Engineering, U.S. Military Academy, West Point, NY
J. Douglas Faires, Youngstown State University, Youngstown, OH
Ben Fusaro, Dept. of Mathematics, Florida State University, Tallahassee, FL Jerry Griggs, Mathematics Dept., University of South Carolina, Columbia,
SC (Problem Author)
Steve Horton, Dept. of Mathematical Sciences, U.S. Military Academy, West Point, NY (MAA Judge)
Mario Juncosa, RAND Corporation, Santa Monica, CA (retired)
Michael Moody, Olin College of Engineering, Needham, MA (SIAM Judge) John L. Scharf, Mathematics Dept., Carroll College, Helena, MT
(Ben Fusaro Award Judge)
Dan Solow, Mathematics Dept., Case Western Reserve University, Cleveland, OH (INFORMS Judge)
Michael Tortorella, Dept. of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ
Richard Douglas West, Francis Marion University, Florence, SC Dan Zwillinger, Raytheon Company, Sudbury, MA
Cellphone Energy Problem Head Judge
Maynard Thompson, Mathematics Dept., University of Indiana, Bloomington, IN
Associate Judges
Peter Anspach, National Security Agency, Ft. Meade, MD (Head Triage Judge)
Jim Case (SIAM Judge)
Veena Mendiratta, Lucent Technologies, Naperville, IL
Peter Olsen, Johns Hopkins Applied Physics Laboratory, Baltimore, MD David H. Olwell, Naval Postgraduate School, Monterey, CA
(INFORMS Judge)
Kathleen M. Shannon, Dept. of Mathematics and Computer Science, Salisbury University, Salisbury, MD (SIAM Judge)
Marie Vanisko, Dept. of Mathematics, Carroll College, Helena, MT (Ben Fusaro Award Judge)
Regional Judging Session at U.S. Military Academy Head Judges
Patrick J. Driscoll, Dept. of Systems Engineering, and Steve Horton, Dept. of Mathematical Sciences,
United States Military Academy (USMA), West Point, NY Associate Judges
Tim Elkins, Dept. of Systems Engineering, USMA Michael Jaye, Dept. of Mathematical Sciences, USMA Darrall Henderson, Sphere Consulting, LLC
Steve Horton, Dept. of Mathematical Sciences, USMA Tom Meyer, Dept. of Mathematical Sciences, USMA Scott Nestler, Dept. of Mathematical Sciences, USMA Regional Judging Session at Naval Postgraduate School Head Judge
William P. Fox, Dept. of Defense Analysis, and Frank Giordano, Naval Postgraduate School (NPS), Monterey, CA
Associate Judges
Greg Mislik, Matt Boensel, and Pete Gustitis
—all from the Naval Postgraduate School, Monterey, CA Triage Session for Traffic Circle Problem
Head Triage Judge
William C. Bauldry, Chair, Dept. of Mathematical Sciences, Appalachian State University, Boone, NC
Associate Judges
Jeffry Hirst, Rick Klima, Mark Ginn, and Tracie McLemore Salinas
—all from Dept. of Mathematical Sciences, Appalachian State University, Boone, NC
Triage Session for Cellphone Energy Problem Head Triage Judges
Peter Anspach, National Security Agency (NSA), Ft. Meade, MD Jim Case
Associate Judges
Other judges from inside and outside NSA, who wish not to be named.
Sources of the Problems
The Traffic Circle Problem was contributed by Daniel Solow (Case West- ern Reserve University), who was also one of the final judges, and the Cellphone Energy Problem by Joe Malkevitch (York College of CUNY).
Acknowledgments
Major funding for the MCM is provided by the National Security Agency (NSA) and by COMAP. Additional support is provided by the Institute for Operations Research and the Management Sciences (INFORMS), the Soci- ety for Industrial and Applied Mathematics (SIAM), and the Mathematical Association of America (MAA). We are indebted to these organizations for providing judges and prizes.
We also thank for their involvement and support the MCM judges and MCM Board members for their valuable and unflagging efforts, as well as
• Two Sigma Investments. (This group of experienced, analytical, and technical financial professionals based in New York builds and operates sophisticated quantitative trading strategies for domestic and interna- tional markets. The firm is successfully managing several billion dollars using highly automated trading technologies. For more information about Two Sigma, please visithttp://www.twosigma.com.)
Cautions
To the reader of research journals:
Usually a published paper has been presented to an audience, shown to colleagues, rewritten, checked by referees, revised, and edited by a jour- nal editor. Each paper here is the result of undergraduates working on a problem over a weekend. Editing (and usually substantial cutting) has taken place; minor errors have been corrected, wording altered for clarity or economy, and style adjusted to that of The UMAP Journal. The student authors have proofed the results. Please peruse their efforts in that context.
To the potential MCM Advisor:
It might be overpowering to encounter such output from a weekend of work by a small team of undergraduates, but these solution papers are highly atypical. A team that prepares and participates will have an enrich- ing learning experience, independent of what any other team does.
COMAP’s Mathematical Contest in Modeling and Interdisciplinary Con- test in Modeling are the only international modeling contests in which students work in teams. Centering its educational philosophy on mathe- matical 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 better-prepared citi- zens.
Meritorious Teams
Designations of departments named Mathematics, Mathematical Sciences, Mathematics and Computer Science, or the like are omitted.
Traffic Circle Problem (192 teams)
Beihang University, Beijing, China (Peng Lin Ping)
Beihang University, Advanced Engineering, Beijing, China (Wei Feng) Beijing Institute of Technology, Beijing, China (Xue-Wen Li)
Beijing Institute of Technology, Beijing, China (Gui-Feng Yan) Beijing Institute of Technology, Beijing, China (Chun-guang Xiong) Beijing Institute of Technology, Beijing, China (Bing-Zhao Li) Beijing Jiaotong University, Beijing, China (Bingtuan Wang) Beijing Jiaotong University, Beijing, China (Peng Cao)
Beijing Language and Culture University, Computer Science, Beijing, China (Xiaoxia Zhao) Beijing Language and Culture University, Computer Science, Beijing, China (Ping Yang) Beijing Normal University, Beijing, China (Qing He)
Beijing Normal University, Beijing, China (Xianghui Shi)
Beijing University of Posts and Telecommunications, Computer Science and Technology, Beijing, China (Wenbo Zhang)
Beijing University of Posts and Telecommunications, Electronic Engineering, Beijing, China (Qing Zhou)
Beijing University of Posts and Telecommunications, Electronic Engineering, Beijing, China (Jianhua Yuan)
Bethel University, Arden Hills, MN (Nathan M. Gossett) (two teams) Bucknell University, Lewisburg, PA (Nathan, C. Ryan)
Carnegie Mellon University, Pittsburgh, PA (Dale J. Winter) Carroll College, Natural Sciences, Helena, MT (Anthony Szpilka)
Carroll College, Mathematics, Engineering, and Computer Science, Helena, MT (Jack Oberweiser)
Central China Normal University, Mathematics and Statistics Department, Wuhan, Hubei, China (Bo Li)
Central South University, Metallurgical Science and Engineering, Changsha, Hunan, China (Muzhou Hou)
Central South University, Mathematics and Applied Mathematics, Changsha, Hunan, China (Zheng Zhoushun)
Central University of Finance and Economics, Applied Mathematics, Beijing, China (Huiqing Huang)
Central Washington University, Ellensburg WA (James W. Bisgard)
Chengdu University of Technology, Information Management, Chengdu, Sichuan, China (YouHua Wei)
China University of Petroleum, Dongying, Shandong, China (Xinhai Liu)
China University of Petroleum–Beijing, Mathematics and Physics, Beijing, China (Ling Zhao) Chinese University of Hong Kong, Physics, Hong Kong, China (Ming Chung Chu)
City University of Hong Kong, Hong Kong, China (Jonathan J. Wylie) Clarion University, Clarion, PA (David M. Hipfel)
Clarkson University, Computer Science, Potsdam, NY (Kathleen R. Fowler) (two teams) Coe College, Cedar Rapids, IA (Jonathan White)
College of Charleston, Charleston, SC (William G. Mitchener) (two teams) Colorado College, Colorado Springs, CO (Amelia Taylor)
Cornell University, Ithaca, NY (Alexander Vladimirsky)
Dalian Maritime University, Dalian, Liaoning, China (Naxin Chen)
Dalian Maritime University, Dalian, Liaoning, China (Xiangpeng Kong) (two teams) Dalian University of Technology, Software, Dalian, Liaoning, China (Ning Ding) Dalian University of Technology, Software, Dalian, Liaoning, China (Tie Qiu)
Dalian University of Technology, Applied Mathematics, Dalian, Liaoning, China (Mingfeng He) Dalian University of Technology, Applied Mathematica, Dalian, Liaoning, China (Qiuhui Pan) Dalian University of Technology, Innovation Experiment, Dalian, Liaoning, China (Lin Feng) Davidson College, Davidson, NC (Tim Chartier)
East China Normal University, Statistics and Actuarial Science, Shanghai, China (Shujin Wu) Eastern Michigan University, Ypsilanti, MI (Andrew M. Ross)
Fudan University, Shanghai, China (Zhijie Cai)
Fujian Normal University, Fuzhou, Fujian, China (Qinghua Chen) Fujian Normal University, Fuzhou, Fujian, China (Changfeng Ma)
Guangdong University of Business Studies, Guangzhou, Guangdong, China (Zigui Xiang) Hangzhou Dianzi University, Information and Mathematical Science, Hangzhou, Zhejiang, China
(Hao Shen)
Harbin Engineering University, Science, Harbin, Heilongjiang, China (Zhenbin Gao) Harbin Engineering University, Science, Harbin, Heilongjiang, China (Dongqi Sun)
Harbin Institute of Technology, Harbin, Heilongjiang, China (Guofeng Fan) (two teams) Harbin Institute of Technology, Computer Science, Harbin, Heilongjiang, China (Zheng Kuang) Harbin Institute of Technology, Automatic Measurement and Control, Harbin, Heilongjiang, China
(Limin Zou)
Harbin Institute of Technology, Weihai, Shandong, China (Rongning Qu)
Harbin University of Science and Technology, Harbin, Heilongjiang, China (Fengqiu Liu) Harvard University, Engineering and Applied Sciences, Cambridge, MA
(Michael Brenner)
Harvey Mudd College, Claremont, CA (Rachel Levy) Harvey Mudd College, Claremont, CA (Francis Su)
Huazhong University of Science and Technology, Mathematics and Statistics, Wuhan, Hubei, China (Zhihong Lu)
Jiangsu University, Zhenjiang, Jiangsu, China (Yang Hong Lin) Jilin University, Changchun, Jilin, China (Yongkui Zou)
Lawrence Technological University, Southfield, MI (Ruth G. Favro) Lawrence University, Appleton, WI (Bruce H. Pourciau)
Linfield College, McMinnville, OR (Martha E. VanCleave) Luther College, Computer Science, Decorah, IA (Steve Hubbard) Macquarie University, North Ryde, NSW, Australia (Xuan Duong)
McGill University, Mathematics and Statistics, Montreal, QC, Canada (Bruce Shepherd) MIT, Cambridge, MA (Martin Zdenek Bazant)
Mount St. Mary’s University, Emmitsburg, MD (Brian Heinold)
Nanjing University, Computer Science and Technology, Nanjing, Jiangsu, China (Zhengxing Sun) Nanjing University, Nanjing, Jiangsu, China (Huang Wei Hua)
Nanjing University of Posts and Telecommunications, Mathematics and Physics, Nanjing, Jiangsu, China (Jun Ye)
National University of Defense Technology, Mathematics and System Science, Changsha, Hunan, China (Ziyang Mao)
National University of Defense Technology, Department of Mathematics and System Science, Changsha, Hunan, China (Mengda Wu)
National University of Singapore, Singapore (Hwee Huat Tan)
National University of Singapore, Statistics and Applied Probability, Singapore (Wei-Liem Loh) North Carolina School of Science and Mathematics, Durham, NC (Daniel J. Teague) (two teams) Northeastern University, Information Science and Engineering, Shenyang, Liaoning, China
(Dali Chen)
Northeastern University, System Science, Shenyang, Liaoning, China (Xuefeng Zhang) Northwest University, Xi’an, Shaanxi, China (Liantang Wang)
Oklahoma State University, Stillwater, OK (Benny Evans) Pacific Lutheran University, Tacoma, WA (Mei Zhu) Pacific University, Forest Grove, OR (Christine Guenther) Peking University, Computer Science, Beijing, China (Bo Peng) Peking University, Beijing, China (Shanjun Lin)
Peking University, Beijing, China (Shanjun Lin)
Peking University, Beijing, China (Xiang Ma) (two teams) Peking University, Beijing, China (Xufeng Liu)
Peking University, Probability and Statistics, Beijing, China (Minghua Deng)
People’s Liberation Army University of Science and Technology, Command Automation, Nanjing, Jiangsu, China (Jinren Shen)
Princeton University, Princeton, NJ (Ingrid Daubechies)
Quanzhou Normal University, Quanzhou, Fujiang, China (Xiyang Yang) Renmin University of China, Information, Beijing, China (Qingcai Zhang) Renmin University of China, Information, Beijing, China (Yong Lin) Rensselaer Polytechnic Institute, Troy, NY (Donald A. Drew) Xi’an Communication Institute, Xi’an, Shaanxi, China (Xinshe Qi) Seattle Pacific University, Seattle, WA (Wai Lau)
Shandong University, Jinan, Shandong, China (Hualin Huang) Shandong University, Jinan, Shandong, China (Tongchao Lu) Shandong University, Jinan, Shandong, China (Xiaoxia Rong)
Shandong University, Mathematics and System Sciences, Jinan, Shandong, China (Lu Lin) Shandong University, Computer Science, Jinan, Shandong, China (Jun Ma)
Shandong University, Jinan, Shandong, China (Jingtao Shi)
Shandong University, Computer Science and Technology, Jinan, Shandong, China (Xing Dong) Shandong University of Science and Technology, Information Science and Engineering, Qingdao,
Shandong, China (Xinzeng Wang) (two teams)
Shandong University, Jinan, Shandong, China (Tiande Zhang) Shanghai Jiaotong University, Shanghai, China (Baorui Song) Shanghai Jiaotong University, Shanghai, China (Ershun Pan) Shanghai University, Shanghai, China (Wei Huang)
Shanghai University of Finance and Economics, Shanghai, China (Yibo Zhu)
Shijianzhuang Railway Institute, Mechanical Engineering, Shijiazhuang, Hebei, China (Yongliang Wang)
Shippensburg University, Shippensburg, PA (Paul T. Taylor) Sichuan University, Chengdu, Sichuan, China (HuiLei Han)
Sichuan University, Chengdu, Sichuan, China (Yingyi Tan) (two teams) Sichuan University, Chengdu, Sichuan, China (Hai Niu)
Sichuan University, Chengdu, Sichuan, China (Jie Zhou) Siena Heights University, Adrian, MI (Jeffrey C. Kallenbach)
Simon Fraser University, Burnaby, BC. Canada (Nilima Nigam) (two teams) Slippery Rock University, Slippery Rock, PA (Richard J. Marchand) (two teams) South China Normal University, Guangzhou, Guangdong, China (Shaohui Zhang) South Fort Myers High School, Fort Myers, FL (Johnny Lee Jones)
Southeast University, Nanjing, Jiangsu, China (Enshui Chen) Southeast University, Nanjing, Jiangsu, China (Zhiqiang Zhang) Southeast University, Nanjing, Jiangsu, China (Xiang Yin) Southeast University, Nanjing, Jiangsu, China (Liyan Wang)
Southwestern University of Finance and Economics, International Business School, Chengdu, Sichuan, China (Dai Dai)
Southwestern University of Finance and Economics, Mathematical Economics, Chengdu, Sichuan, China ( Feng Xu)
Stanford University, Institute for Computational and Mathematical Engineering (iCME), Stanford, CA (Walter Murray)
Tsinghua University, Industrial Engineering, Beijing, China (Lei Zhao) Tsinghua University, Beijing, China (Heng Liang)
Tsinghua University, Beijing, China (Chunxiong Zheng) Tufts University, Medford, MA (Scott MacLachlan)
University of North Carolina–Chapel Hill, Chapel Hill, NC (Sarah A. Williams)
University of Electronic Science and Technology of China, Information and Computation Science, Chengdu, Sichuan, China (Qin Siyi) (two teams)
University of Adelaide, Adelaide, SA, Australia (Tony J. Roberts) University of Arizona, Tucson, AZ (Paul F. Dostert)
University of California–Merced, Merced, CA (Arnold D. Kim)
University of Colorado–Boulder, Applied Mathematics, Boulder, CO (Bengt Fornberg) University of Iowa, Iowa City, IA (Joe Eichholz)
University of Iowa, Iowa City, IA (Stephen Welch)
University of Michigan–Dearborn, Mathematics and Statistics, Dearborn, MI (Joan C. Remski) University of Minnesota–Duluth, Mathematics and Statistics, Duluth, MN (Bruce B. Peckham) University of Pittsburgh, Pittsburgh, PA (Jonathan Rubin)
University of Puget Sound, Tacoma, WA (Michael Z. Spivey) (two teams)
University of Science and Technology of China, Electronic Engineering and Information Science, Hefei, Anhui, China (Bo Pang)
University of Science and Technology of China, Hefei, Anhui, China (Yige Ding)
University of Science and Technology of China, Special Class for the Gifted Young, Hefei, Anhui, China (Yangyang Cheng)
University of Toronto at Scarborough, Scarborough, ON, Canada (Paul S. Selick) University of Washington, Seattle, WA (James Allen Morrow)
University of Washington, ACMS, Seattle, WA (Anne Greenbaum) (two teams) University of Western Ontario, London, ON, Canada (Allan B. MacIsaac) Virginia Tech, Blacksburg, VA (Henning S. Mortveit)
Wake Forest University, Winston Salem, NC (Jennifer B. Erway) Wesleyan College, Macon, GA (Joseph A. Iskra)
Western Carolina University, Cullowhee, NC (Erin K. McNelis) Western Washington University, Bellingham, WA (Tjalling Ypma) Western Washington University, Bellingham, WA (Saim Ural) Willamette University, Salem, OR (Cameron W. McLeman)
Wuhan University of Technology, Statistics, Wuhan, Hubei, China (Mao Shuhua) Xavier University, Cincinnati, OH (Bernd E. Rossa)
Xi’an Jiaotong University, Xi’an, Shaanxi, China (Huanqin Li) Xi’an Jiaotong University, Xi’an, Shaanxi, China (Lizhou Wang) Xi’an Jiaotong University, Xi’an, Shaanxi, China (Zhuosheng Zhang)
Xi’an Jiaotong–Liverpool University, Financial Mathematics, Suzhou, Jiangsu, China (Miaoxin Yao) Xi’an Jiaotong–Liverpool University, Computer Science, Suzhou, Jiangsu, China (Jingming Guo) Xidian University, Xi’an, Shaanxi, China (Yue Song)
Xidian University, Xi’an, China (Jimin Ye)
Xuzhou Institute of Architectural Technology, Foundation, Xuzhou, Jiangsu, China (Feng Xinyong) Youngstown State University, Mathematics and Statistics, Youngstown, OH (George T. Yates) Yunnan University, Electronic Engineering, Kunming, Yunnan, China (Haiyan Li)
Yunnan University, Communication Engineering, Kunming, Yunnan, China (Guanghui Cai) Zhejiang Gongshang University, Hangzhou, Zhejiang, China (Ding Zhengzhong)
Zhejiang University, Hangzhou, Zhejiang, China (Ling Lin)
Zhuhai College of Jinan University, Mathematical Modeling Innovative Practice Base, Zhuhai, Guangdong, China (Yuanbiao Zhang)
Zhuhai College of Jinan University, Mathematical Modeling Innovative Practice Base, Zhuhai, Guangdong, China (Advisor Team)
Cellphone Energy Problem (102 teams)
Academy of Armored Force Engineering, Mechanical Engineering, Beijing, China (Han De) Albion College, Albion, MI (Darren E. Mason)
Bandung Institut of Technology, Mathematics, Bandung, West Java, Indonesia (Nuning Nuraini) Beijing Institute of Technology, Beijing, China (Hongying Man)
Beijing Normal University, Beijing, China (Chun Yang) Beijing Normal University, Beijing, China (Su Xiao Le)
Beijing University of Posts and Telecommunications, Beijing, China (Xinchao Zhao)
Beijing University of Posts and Telecommunications, Computer Science and Technology, Beijing, China (Hongxiang Sun)
Beijing University of Posts and Telecommunications, Applied Mathematics, Beijing, China (Hongxiang Sun)
Beijing University of Posts and Telecommunications, Beijing, China (Tianping Shuai) Bemidji State University, Bemidji, MN (Colleen Livingston)
Carroll College, Mathematics, Engineering, and Computer Science, Helena, MT (Lahna VonEpps) China University of Petroleum–Beijing, Mathematics and Physics, Beijing, China (Xiaoguang Lu) Chongqing University, Information and Computational Science, Chongqing, Sichuan, China
(Jian Xiao)
Civil Aviation University of China, Air Traffic Control, Tianjin, Tianjin, China (Zhaoning Zhang) Clarkson University, Potsdam, NY (Joseph D. Skufca)
Dalian Maritime University, Dalian, Liaoning, China (Y. Zhang)
Dalian Neusoft Institute of Information, Information Technology and Business Administration, Dalian, Liaoning, China (Ping Song)
Dalian University, Dalian, Liaoning, China (Jiatai Gang) Dalian University of Technology, Dalian, China (Zhen Wang) Davidson College, Davidson, NC (Laurie Heyer)
Davidson College, Davidson, NC (Donna Molinek) Duke University, Durham, NC (David Kraines)
Eastern Mennonite University, Harrisonburg, VA (Leah Shao Boyer)
Electronic Engineering Institute, Electronic Engineering, Hefei, Anhui, China (Quancai Gan) Father Gabriel Richard High School, Ann Arbor, MI (William B. Dannemiller)
Grand View University, Des Moines, IA (Sergio Loch)
Hangzhou Dianzi University, Information and Mathematical Science, Hangzhou, Zhejiang, China (Zongmao Cheng)
Harbin Institute of Technology, Harbin, Heilongjiang, China (Xilian Wang) Harbin Institute of Technology, Harbin, Heilongjiang, China (Xiaofeng Shi)
Hebei Polytechnic University, College of Light Industry, Fundamental Teaching, Tangshan, Hebei, China (Shaohong Yan)
Hohai University, Nanjing, Jiangsu, China (Genhong Ding) (two teams) Hohai University, Nanjing, Jiangsu, China (Jifeng Chu)
Hong Kong University of Science and Technology, Kowloon, Hong Kong, China (Jimmy Chi-Hung Fung)
Huazhong University of Science and Technology, Mathematics and Statistics, Wuhan, Hubei, China (Nanzhong He)
Huazhong University of Science and Technology, Mathematics and Statistics, Wuhan, Hubei, China (Feng Pan)
Jacksonville University, Physics, Jacksonville, FL (W. Brian Lane) John Tyler Community College, Midlothian, VA (Peter R. Peterson)
Lanzhou University, Mathematics and Statistics, Lanzhou, Gansu, China (Yuewei Liu)
Lawrence Technological University, Southfield, MI (Ruth G. Favro)
Lawrence Technological University, Natural Sciences, Southfield, MI (Valentina Tobos) MIT, Cambridge, MA (Martin Zdenek Bazant)
Nanjing University, Nanjing, Jiangsu, China (Weihua Huang)
Nanjing University, Control and System Engineering, Nanjing, Jiangsu, China (Zhao Jiabao) Nanjing University of Science and Technology, Nanjing, Jiangsu, China (Chungen Xu) Nankai University, Tianjin, Tianjin, China (Kui Wang)
National University of Defense Technology, Mathematics and System Science, Changsha, Hunan, China (Ziyang Mao)
National University of Ireland Galway, Galway Ireland (Niall Madden) North China University of Technology, Beijing, China (Quan Zheng) Northwestern Polytechnical University, Xi’an, Shaanxi, China (Genjiu Xu) Oregon State University, Corvallis, OR (Nathan L. Gibson)
Oxford University, Merton College, Oxford, United Kingdom (Jeffrey H. Giansiracusa) Pacific University, Forest Grove, OR (Christine Guenther)
Pacific University, Forest Grove, OR (Michael Rowell) Peking University, Economics, Beijing, China (Jingyi Ye)
Peking University, Software Engineering, Beijing, China (Wei Zhang)
People’s Liberation Army University of Science and Technology, Meteorology, Nanjing, Jiangsu, China (Liu Shousheng)
PLA University of Science and Technology, Engineering Corps, Nanjing, Jiangsu, China (Hansheng Shi)
Regis University, Denver, CO (James A. Seibert)
Renmin University of China, Beijing, China (Yonghong Long) Rensselaer Polytechnic Institute, Troy, NY (Donald A. Drew) Seattle University, Seattle, WA (Jeffery C. DiFranco)
Shanghai Foreign Language School, Educational Research, Shanghai, China (Jia Wang) Shanghai University of Finance and Economics, Statistics, Shanghai, China (Ke Dai) Simpson College, Indianola, IA (Rick Spellerberg)
Southeast University, Nanjing, Jiangsu, China (Jinguan Lin)
Southern Connecticut State University, New Haven, CT (Ross B. Gingrich) Sun Yat Sen University, Physics, Guangzhou, China (Jian Liang Huang) Trinity University, San Antonio, TX (Peter Olofsson)
Union College, Schenectady, NY (Jue Wang)
United States Military Academy, West Point, NY (Jonathan Roginski) United States Military Academy, West Point, NY (Amanda Beecher) United States Military Academy, West Point, NY (Suzanne DeLong) United States Military Academy, West Point, NY (Randy Boucher) University of Arizona, Tucson, AZ (Paul F. Dostert)
University of Colorado Denver, Denver, CO (Gary A. Olson)
University of Electronic Science and Technology of China, Chengdu, Sichuan, China (Mingqi Li) University of Pittsburgh, Pittsburgh, PA (Jonathan Rubin)
University of North Carolina–Chapel Hill, Chapel Hill, NC (Amanda L. Traud) University of North Carolina–Chapel Hill, Chapel Hill, NC (Brian Pike) University of North Carolina–Chapel Hill, Chapel Hill, NC (Sarah A. Williams) University of Science and Technology of Bejiing, Beijing, China (Zhixin Hu)
University of Toronto at Scarborough, Scarborough, Ontario, ON, Canada (Paul S. Selick) University of Virginia, Charlottesville, VA (Tai Melcher)
University of Wisconsin–La Crosse, La Crosse, WI (Theodore Wendt)
