2010

Team USA Wins World Puzzle Championship with Palmer Mebane '12 (2010-11-01)

Left-to-right, Palmer Mebane '12, Roger Barkan, Wei-Hwa Huang, Thomas Snyder.

Mathematics major Palmer Mebane's strong problem-solving skills helped Team USA to emerge victorious at the nineteenth World Puzzle Championship held in Paprotnia, Poland, October 26–29. Up from second last year, the team is now 12-6-1 (gold-silver-bronze) over the history of the World Puzzle Championships.

Team USA, consisting of Mebane, Thomas Snyder (two-time world Sudoku champion), and veteran competitors Roger Barkan and Wei-Hwa Huang, was in first place most of the first two days, but slipped to second place in the last round, allowing a slight time advantage to the Japanese team. On the final day, the Americans dominated the team relay round, and survived a “no-notes physical Skyscraper Sudoku puzzle” to win the team championship. Japan placed second, and Germany third.

Huang and Snyder both qualified for the eight-person individual playoffs, but were eliminated in the first round. Taro Arimatsu of Japan won first place, followed by Ulrich Voigt of Germany, Hideaki Jo of Japan, and Ko Okamoto of Japan. The Americans and Japanese each had three members who finished in the Top 10. Mebane, the rookie on the U.S. team, placed nineteenth—out of 105 competitors—in the individual round, a record-setting score for a first-timer. “They're all longtime veterans and I never expected to beat any of them,” said Mebane of his teammates. “Personally, I was proud of my performance, and my team certainly approved.”

“That Palmer performed so well during his first time at a world championship is a testament to his passion and talent for problem solving,” said HMC President Maria Klawe, who noted that Mebane was Mudd's top finisher in the 2009 Putnam Mathematical Competition and the recipient of a sophomore mathematics prize last year. “He's a very talented mathematician.”

Team USA had the top score during preliminary rounds one and two, which consisted of puzzle types in which Mebane excelled, thus allowing him to contribute to the team's strong performance.

During the team finals, there were four individual puzzles—whose order and types were known—and one team puzzle. After each individual puzzle was solved, that team member could go to the team desk and get a portion of the clues for the final Skyscraper Sudoku puzzle. Each remaining team member got additional clues so that the whole puzzle was available only when the whole team made it to the final table; the first team to solve the final puzzle were the winners of the round.

Mebane said, “The first puzzle turned out to be a major block for most teams, but our guy (Thomas Snyder) put it away quite quickly. Many minutes later, Japan's first solver got it, and not 30 seconds later our second (Wei-Hwa Huang) solved his. At this point we were a person ahead of all the teams. All four of the teams had someone cracking the second puzzle when our third guy (Roger Barkan) finished his, and that was when I started. I think Japan and Germany got to the third one while I was working, but that was it.”

Mebane's puzzle was called Akari, a puzzle with which he is very familiar, having constructed many of them on his puzzle blog. So he was quickly assigned to be the team member to do it. The puzzle contained some innovative logic but, undaunted, Mebane said he was able to “put it away very fast.”

Snyder, Huang, Barkan, and Mebane at work on a 45 × 19 Anaconda puzzle.

The Sudoku team puzzle was more challenging for Mebane, he admitted, but he said that he helped his team “by pointing out some obvious steps and by building the `skyscrapers' the solution had to be presented as.” With Sudoku veterans as teammates, Mebane wasn't feeling too much pressure. But there were some stressful times.

“The first tense moment was that we found a mistake about five minutes after I got to the table and had to clear the board,” Mebane said. “The second is that just before we got to the cleanup portion of the puzzle, we heard some commotion and I saw the audience looking at a team table that was not ours, so I thought we couldn't win anymore. The third was that we finished, asked to be checked, and were told we had messed up. It turned out to be a simple error in cleanup, though, so we got rid of some bad numbers we found, reinserted them and resubmitted to be declared correct and first place. This surprised all of us given the earlier commotion.

“I later learned that all four of our team members had finished our individual puzzles far faster than any other team did,” said Mebane. “The first and third puzzles were particular bottlenecks, but they apparently weren't a problem to either Thomas or Roger. So we were two solvers ahead of every team when we started solving the Sudoku, and there was no catching up to us (even though we broke the Sudoku and had to restart). It took Japan about 10 minutes more than us. Germany took about 20 minutes more.”

The goals of the World Puzzle Federation are to

• Provide the means for an international exchange of puzzle ideas
• Stimulate innovations in the field of puzzles
• Supervise the annual World Puzzle Championship (WPC) and other puzzle activities
• Foster friendship among puzzle enthusiasts world-wide

Original article by Judy Augsburger

NSF Grant Funds Su's Study of Geometric Combinatorics and Voting (2010-09-13)

Professor Francis Su levitates a geometric model.

Francis Su, professor of mathematics, was awarded a National Science Foundation (NSF) grant that continues the line of work begun in his prior NSF grant in which methods from combinatorics, topology and geometry are used to study problems in mathematical economics and the social sciences; in particular, problems related to voting and fair allocation.

The three-year grant of $205,668, is for his Research in Undergraduate Institutions (RUI) proposal in the Division of Mathematical Sciences, titled “Triangulations, Set Intersections, Fair Division, and Voting.”

Su's prior work introduced methods from combinatorial topology and discrete geometry to the study of fair division questions and voting problems. The current project will support the the development of the mathematics behinds these tools and the solution of several combinatorial questions that have been motivated by his prior work, including: (1) the study of triangulations of cubes and simplotopes, (2) the further development of combinatorial fixed point theorems and constructive solutions, and (3) the development of set intersection theorems and associated applications in social choice theory and fair division. This project will also support the active participation of undergraduates in this research.

Informally speaking, a “fair division” problem asks: how can we divide a set of goods among parties in such a way that each can be satisfied according to some notion of fairness. Social choice theory asks: how does a society make a group choice (e.g., in an election) in a way that best aggregates the preferences of all the individuals? Questions of fairness and social choice are of interest to political scientists, economists, and game theorists, and motivate interesting mathematical questions. The space of preferences and the preference sets of each person are often naturally geometric sets (e.g., convex, connected, polyhedral), and the desired solution is often at the intersection of such sets. This project aims to prove mathematical theorems (e.g., about set intersections and triangulations of polyhedra) that have direct bearing on important problems in the social sciences involving voting and fairness.

Su's work has been recognized by the Mathematical Association of America with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member (2004) and the Merten M. Hasse Prize for outstanding mathematical exposition (2001). In addition to his teaching and research activities, Su is the creator of the popular award-winning Math Fun Facts website. He is currently serving as first vice-president of the Mathematical Association of America.

Original article by Judy Augsburger, (909) 607-0713.

HMC Junior Palmer Mebane Places Third in U.S. Puzzle Championship, Wins Spot on U.S. National Team (2010-09-09)

Harvey Mudd College junior Palmer Mebane placed third in the 2010 U.S. Puzzle Championship, winning a spot on the U.S. national team and a chance to compete at the World Puzzle Championship in Warsaw, Poland in October. The U.S. Puzzle Championship is an annual competition in which puzzle takers from all over the world compete to solve up to twenty-three extremely challenging and varied logic puzzles in two and half hours, making as few errors as possible in the process.

“The U.S. team sent to the World Championship almost always wins first or second place in the team competition and has very low turnover of members,” Mebane said of the honor. “I think it's been the same four people for the last four years. So I was extremely happy to make it on.”

The U.S. Puzzle Championship typically consists of twenty to twenty-three language-neutral puzzles of various types, most of which are creative logic-based puzzles. Other puzzle types do appear, such as “spot the differences,” word searches, counting puzzles and criss-cross grids. None of the puzzles require knowledge of the English language. Each puzzle is given a point value according to how long it should take to solve and how difficult the puzzle is to solve. A correct answer gets that amount of points, an incorrect answer extracts a five-point penalty, and a blank answer neither gains nor loses points. The test is administered entirely online.

The top four U.S. contestants this year were Thomas Snyder, Roger Barkan, Palmer Mebane, and Zack Butler, with respective scores of 365, 235, 225, 205.

“Only a few of the rule sets used in the test are familiar and well-known, like Sudoku or KenKen, and these usually appear early in the test,” Mebane explained. “The last several puzzles, the hardest and most valuable, usually have completely new sets of rules, so success is not just doing thousands of Sudoku, for instance.”

Mebane attributes his winning score in part to his own passion for constructing puzzles. He creates his own challenging logic puzzles on his puzzle blog.

“Work on this blog was one of the many things I had done to help me get the result I did, as puzzle construction improves solving ability too,” Mebane said.

Original article by Judy Augsburger

2009 Mathematical Modeling Competition Results (2010-04-08)

The results of the 2010 International Mathematical Modeling Contest have just been announced. We are pleased that one of our HMC teams earned the designation of Finalist, given to only 12 out of the 2254 teams worldwide! The top two categories of Outstanding and Finalist are reserved for the top 1% of entries, so their score is quite an achievement!

Moreover, three HMC teams earned the designation Meritorious (top 20%), one earned Honorable Mention (top 44%), and one was a Successful Participant. These results are an incredible showing for HMC and a testament to the strength of our core curriculum and academic program.

The MCM/ICM is analogous to an applied Putnam exam, in the form of a grueling 96-hour competition. As Ben Fusaro, creator of the contest in 1983, puts it: “Most problems that come up in business, government, or industry are solved by teams, are likely to take many hours, and would not be restricted to using only pencil and paper. Moreover, the answer must be presented to an executive who wants a clear, understandable response.” Thus during the contest students work in teams of up to three students and have 96 consecutive hours to develop a mathematical model and write a formal paper describing their work. The team's papers are judged not only on their scientific and mathematical accuracy, but on their clarity of exposition, insight, and creativity.

This year's problems concerned

1. Explaining the sweet spot of a baseball bat;
2. Generating a geographical profile of serial criminals; and
3. Modeling the Great Pacific Ocean Garbage Patch

Here are the participating HMC teams:

Problem B—Finalist

• Richard Bowen '10
• Brett Cooper '10
• Bryce Lampe '10

Problem A–Meritorious

• Ryan Brewster '12
• Jackson Newhouse '12
• Richard Porczak '12

Problem B—Meritorious

• Kyle Luh '11
• Daniel Rozenfeld '11
• Dmitri Skjorshammer '11

Problem B—Meritorious

• Andrew Hilger '13
• John Peebles '13
• Jason Wyman '10

Problem B—Honorable Mention

• Julia Matsieva '11
• Jacob Scott '11

Problem A—Successful Participant

• Connor Ahlbach '13
• Matthew Johnson '13
• David Marangoni-Simonsen '13

Please join us in congratulating these Mudders on their excellent work.

For complete results, see http://www.comap.com/undergraduate/contests/mcm/contests/2010/results/.

For those of you who follow the contest each year, you will notice that Finalist is a new designation. The previous top designation of Outstanding, which once represented the top 1% of all entries, has been split into two categories, Outstanding and Finalist. These two categories collectively represent the top 1% of all entries.

Melvin Henriksen Memorial Conference Commemorates a Mathematician's Life Well-Lived (2010-04-05)

A picture of Mel at the blackboard with his mathematics, perhaps the place he felt most at home.

An honored guest at a mathematics conference in Iran? A passion for the sport of curling? A lover of dogs and small children? While many of us thought we knew Mel Henriksen, professor of mathematics emeritus at Harvey Mudd College, this softer side of Mel was revealed when his long and productive career was commemorated by the Claremont mathematics community, an assortment of prominent mathematicians, and members of Mel's family at a one-day conference on Saturday, March 27, 2010.

Mel passed away on October 14, 2009, at the age of 82, having spent a significant portion of his life at Harvey Mudd College where he served as a professor of mathematics from 1969 to 1997. After Mel retired, he remained an active member of the mathematics community in Claremont and beyond. Henriksen was best known for his work on the study of rings of continuous functions, which involves the interplay of algebra and topology.

Jezmynne Dene, the Claremont Science Librarian who perhaps knew Mel best in his last few years, compiled a set of “Mel memorabilia”, including copies of Mel's papers (he authored or co-authored over a hundred publications) and his single-variable calculus text. Mel's published papers spanned over half a century, starting in the early 1950s and continuing through this past year.

The opening speaker, W. Wistar Comfort (Wesleyan University), set the stage by recounting some of Mel's groundbreaking work in topology. Professor Comfort fondly noted that after a hiatus of communication of months or years, Mel was notorious for sending e-mails that consisted solely of mathematical questions, Mel's way of saying, “Hello”. He also noted that Mel was an expert at creating collaborations that tackled difficult and intricate questions. Sometimes these collaborations spanned multiple continents, with co-authors acquainted only via e-mail.

A Very Special Guest Speaker

Many of the participants commented that it was ironic that this conference would have been most enjoyed by Mel himself, and, through the wizardry of Judy Grabiner, Flora Sanborn Pitzer Professor of Mathematics at Pitzer College, Mel actually made an appearance and recounted his days as a mathematician. Judy, as a historian of mathematics, interviewed Mel in 2006 as part of an effort to create an oral history for the Archives of American Mathematics. Hearing Mel recount anecdotes from his long career brought back his passion for mathematics, his sense of humor, and his strong commitment and admiration of his collaborators and friends.

Former Students and the Erdős Connection

Three former students fondly recalled Mel's mentoring and guidance. Suzanne Larson (Loyola Marymount-Los Angeles; CGU '84) recounted tales including Mel's advice on how to pass a graduate oral exam. Frank Smith (Kent State University) gave examples of Mel's encyclopedic memory for papers and results. And Ted C.K. Chinburg (University of Pennsylvania; HMC '75) likened Mel's dexterity and inventiveness with mathematics to the virtuosity of a blues piano player.

Garth Dales (University of Leeds) described a seminal collaboration between Paul Erdős, Len Gillman and Mel. Paul Erdős was one of the most prolific mathematicians of all time and mathematicians measure their connectivity by their Erdős number—the number of “hops” via co-authorship of a published paper needed to get to Erdős. Mel, of course, has an Erdős number of 1 (a characteristic he shares with HMC President Maria Klawe). Professor Dales clued us in to the fact that Mel was involved in some of the conversations where the concept of the Erdős number was dreamed up.

Mathematical Reminiscences

Hank Krieger (HMC Professor of Mathematics Emeritus) described Mel's arrival at HMC in 1969, when he was appointed Chair of the Department of Mathematics (known affectionately as “Chairman Mel”). Mel promoted world-class research as a departmental value, a legacy reflected in our faculty's work today. He also recounted how Mel advised a Clinic project on “jury utilization” for the county of Los Angeles, a project that helped shape the development of their one-day or one-trial policy.

Sandy Grabiner, Joseph N. Fiske Professor of Mathematics at Pomona College, described Mel's early days in Claremont, how he was pivotal in the development of the Claremont colloquium, and how Mel was a “communitarian”, who was committed to nurturing his junior colleagues and developing a sense of mathematical community in the consortium.

Don Johnson (New Mexico State University) spoke about Mel's role in the mathematical community, and how he promoted collaboration and networking among topologists. One of Mel's passions later in life was reaching out to mathematicians in third world countries, helping them find resources and even visiting his collaborators in Iran where he was treated as an honored dignity.

Three of Mel's collaborators spoke to Mel's peripatetic nature, visiting collaborators and leaving a trail of topological results and anecdotes in his wake.

Grant Woods (University of Manitoba) spoke of Mel's time in Winnipeg, where he and his wife apparently became avid members of the local curling club.

David Kopperman's watercolor of Mel Henriksen

Ralph Kopperman (City College of New York) shed some light on Mel being, at heart, a New Yorker; he also brought a watercolor of Mel from his son David that captures a sense of Mel's enthusiasm.

Finally, Joanne Walters-Wayland (OCCTAL at Chapman College) spoke of Mel's last decade, and how Mel's generosity of spirit and continued enthusiasm lead to the development of OCCTAL, the Orange Center for Computation, Topology and Algebra.

Memorial Service

Mel's family was also well-represented, with his three children, Tom Henriksen, Richard Henriksen and Susan Beard and two of his grandchildren Woody Henriksen and Jessica Beard. The family hosted a more personal memorial the next day at Mel's home in Claremont.

The conference was organized by Professors Sandy Grabiner (Pomona), Asuman Aksoy (CMC), and Andrew Bernoff (HMC) and was made possible by the generosity of the HMC Mathematics Department and Harvey Mudd College. Pomona College's Barbara Beechler Colloquium Fund supported Garth Dales's travel.

A collection of mathematicians, friends, family, and colleagues who gathered to commemorate Mel Henriksen's career and legacy.

Math Club Discovers History of Math in Honnold-Mudd Library (2010-03-23)

Frontispiece from a Sixteenth-Century English Edition of Euclid's Elements, in Honnold/Mudd Library. (Note the muses of Arithmetic and Geometry in the lower left-hand corner!)

Prof. Ursula Whitcher, a Teaching and Research Postdoctoral Fellow, organized a Math Club field trip to the Honnold/Mudd Library's Special Collections department. Librarian Carrie Marsh identified multiple books of historic and mathematical interest for students and professors to pore over.

Club members and faculty advisors were encouraged to handle the books. Professor Francis Su exclaimed, “I'm touching a 1482 edition of Euclid's Elements in Latin! It's in the Claremont Colleges library and I didn't know it!” Other notable works included John Wilkins' seventeenth-century Mathematical Magick; John Wallis's Opera Mathematica (Wallis was an English mathematician who chose the infinity symbol); and an early textbook with a built-in paper wheel to model astronomical calculations.

Whitcher was intrigued by a fifteenth-century Italian book of useful arithmetic problems and formulas, including some classics: as she translated one problem, “A boat leaves Genoa, and five days later...”

HMC Has Strong Showing in 2009 William Lowell Putnam Mathematical Competition (2010-03-22)

The results of the nationwide 2009 William Lowell Putnam Mathematical Competition have just been announced, and HMC had another strong showing.

Forty-two HMC students spent Saturday, December 5, 2009, taking this very hard six-hour examination, which requires a unique blend of cleverness and problem-solving skills. Nationwide, 4036 students competed, and this year's median score was 2 out of a total of 120 points!

Our team of Jennifer Iglesias '12, Palmer Mebane '12, and Jackson Newhouse '12 placed twelfth in the Team category (out of 546 colleges and universities).

In the individual category, Palmer Mebane placed twelfth nationally and will receive $1000 for his stellar performance.

Special recognition also goes to Jenny Iglesias (rank 186.5) and Peter Fedak '13 (rank 202). Palmer, Jenny, and Peter will also be receiving RIF Prizes, which honor the top Mudd finishers in the Putnam each year.

In addition, the following students all made the Top 500 List:

• Olivia Beckwith '13
• Jeffrey Burkert '11
• Craig Burkhart '12
• Curtis Heberle '12
• Jackson Newhouse '12
• Kevin O'Neill '13
• Aaron Pribabdi '12
• Jacob Scott '11
• Donald (Lee) Wiyninger '11

We are proud of all 42 of our students—representing a cross-section of majors—who sacrificed their time, talent, and energies to represent HMC in this year's Putnam competition.

Mathematics Conference on Environmental Sustainability and Green Technology Addresses Both Everyday Questions and Cutting Edge Research (2010-02-17)

Prof. Rachel Levy presides over the opening panel discussion of the 2010 HMC Mathematics Conference on the Mathematics of Environmental Sustainability and Green Technology.

Prof. Rachel Levy organized this year's HMC Mathematics Conference on January 29–30, 2010. This year's topic was the mathematics of environmental sustainability and green technology, and over 100 participants took part, including many HMC students, faculty, alumni and trustees, as well as other representatives from the Claremont Colleges consortium, the local community, and academics from across the United States and Canada.

The conference opened Friday evening with a panel discussion focused on cutting edge developments in the field. Panelists and audience members discussed how to prepare for careers in sustainability, developments in green technologies, and crucial behaviors that support sustainability efforts. Panel participants included Jeffrey Byron of the California Energy Commission; Dan Davids, President of Plug In America; as well as local professors and sustainability advocates.

On Saturday, four speakers from the fields of physics, mathematics, environmental science, and engineering posed a variety of problems and challenges of interest to the mathematics community. The collection of talks included a discussion of plasmonics by Harry Atwater of Caltech; climate change and sea ice by Ken Golden from the University of Utah; wind power by Julie Lundquist of the University of Colorado at Boulder; and a variety of problems from industry by HMC alumnus and green technology consultant Ron Lloyd '80.

A poster session provided opportunities for participants, including undergraduates, graduates and postdocs to discuss their research with attendees.

Prof. Art Benjamin Featured on The Colbert Report (2010-01-27)

Professor Arthur Benjamin, Harvey Mudd College's resident Mathemagician, was a special guest on Comedy Central's The Colbert Report, airing on Wednesday, January 27; the whole show can be viewed on line, as can just Prof. Benjamin's segment.

Interviewed before the show, Benjamin hoped to perform his famous high-speed mental calculations, memorizations, and other astounding math stunts on the mock-news show hosted by Stephen Colbert. A dedicated professor of mathematics, Benjamin saw his appearance on the show as a chance to demonstrate the power and beauty of mathematics to a wide audience—potentially over one million viewers. He was the first mathematician to ever be interviewed on the program.

Said Benjamin, “I'll be interviewed for six minutes and I won't know what sorts of questions Colbert will ask me. I just plan to roll with the punches and have fun.”

Benjamin was recently featured in the “Education Life” section of the New York Times along with one of his challenging but entertaining math quizzes.

The online video of his talk at the TED (Technology, Entertainment, Design) conference has been viewed over one million times.

In 2006, Benjamin won the Beckenbach Book Prize from the Mathematical Association of America (MAA) for his book Proofs that Really Count: The Art of Combinatorial Proof. For that same book, in the category of outstanding academic title, Benjamin won the 2004 CHOICE award from the American Library Association.

Benjamin, who was co-editor of the magazine Math Horizons, was named “America's Best Math Whiz” in 2005 by Reader's Digest. In 2000, he received the MAA's Deborah and Franklin Tepper Haimo Award, which honors college or university teachers widely recognized as being exceedingly successful and whose teaching has influence beyond their own institutions.

He has written more than 70 research papers and authored four books. His most recent books are Secrets of Mental Math, published by Random House, and Biscuits of Number Theory, published by the MAA. In 2007 and 2009, he created DVD courses on The Joy of Mathematics and Discrete Mathematics for The Teaching Company as part of their Great Courses series.

The Colbert Report launched on October 17, 2005. Since its inception, the series has garnered a prestigious Peabody Award for Excellence in Broadcasting in 2008 and 15 Primetime Emmy nominations. Last fall, Colbert and his writing team won the show's first Emmy for Outstanding Writing for a Variety, Music or Comedy Program.

Original article by Judy Augsburger.

Mathemagics Featured in the New York Times (2010-01-04)

Recently, Arthur Benjamin, Harvey Mudd College's certified Mathemagician, was featured in the “Education Life” section of the New York Times.

Benjamin often takes to the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts, which is part of his drive to teach math and mental agility in interesting ways. The video of his talk at the TED (Technology, Entertainment, Design) conference has been viewed over 1,000,000 times.