Creative Streak: WilliamsCollege Math DepartmentWins National AMS AwardAllyn Jackson

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SMALL at 4th of July Parade, 2012.

It was 1988, and Colin Adams was in his third yearon the faculty at Williams College. He donned agaudy green suit plus cowboy boots, mustered aTexas accent, and gave a lecture in his department.In the lecture, “Real Estate in Hyperbolic Space:Investment Opportunities for the Next Millennium”,he played an unprincipled salesman called MelSlugbate, who was hawking hyperbolic plots tothose chary about investing in traditional realestate. It was the first time Adams had ever puton a costume to give a lecture. He was a littlenervous. “I was a junior faculty member,” herecalled. “I thought, ‘This is the end of my careerright here’.” As it turned out, his department wasvery supportive of this unconventional way ofintroducing ideas about hyperbolic space. Sincethen, Mel Slugbate has made many appearancesin mathematics departments and at meetings,and Adams has developed a thriving sideline inmathematical humor. The now-classic “Great π -eDebate”, which he performs with his Williamscolleague Thomas Garrity, is available on DVD.

One big reason Adams’s risky venture work-ed is the open and creative atmosphere of the

Allyn Jackson is senior writer and deputy editor of the No-tices. Her email address is axj@ams.org.

DOI: http://dx.doi.org/10.1090/noti1126

Department of Mathematics and Statistics atWilliams College. The department hires extraor-dinarily talented people and gives them a greatdeal of freedom in deciding how best to meettheir dual responsibilities in teaching and research.This diverse group of dynamic individuals worktogether on an enormous variety of programs andactivities, and they do so in a harmonious way,keeping their focus trained on the big picture:Communicating, doing, and enjoying mathematics.For their wide-ranging accomplishments and forbeing an inspiration to mathematics departmentsaround the nation, Williams College is receivingthe 2014 AMS Award for an Exemplary Program orAchievement in a Mathematics Department.

Serving All Students WellWithin the mathematical community, the mostfamous math major from Williams College is nodoubt Curtis McMullen, who earned his bachelor’sdegree in 1980 and was awarded the Fields Medal in1998. But outside the mathematical community, thebest-known Williams math major might be BethanyMcLean, who finished a double-major degree inmath and English in 1992. In 1995, she got a jobas a fact-checker at Fortune and eventually startedwriting stories for the magazine. On March 5, 2001,Fortune published her bombshell story, “Is EnronOverpriced?”, the first report in a major magazinethat raised questions about Enron’s accounting.People at Enron tried to dissuade McLean fromdigging into the details, telling her she didn’t reallyunderstand the numbers. “But she had understoodvery hard mathematics problems, so she believedshe could understand the Enron numbers,” saidCesar Silva, who has been at Williams since 1984.As a math major, McLean had also learned tenacity,which helped her to pursue the Enron story ata time when others believed the company to beabove reproach. Today McLean is a visiting scholarat New York University, writes for Vanity Fair andReuters, and often appears on television newsprograms (see sidebar on page 522).

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Around the time McMullen got his degree,Williams had perhaps half a dozen senior majors.By McLean’s time, the number had risen to betweentwenty and thirty. “When we hit forty majors ayear, we thought, okay, it’s stabilizing,” recalledSusan Loepp, who joined the department in 1996.This year, the department has sixty-seven seniormajors, about twelve percent of the senior class(nationally, about one percent of seniors are mathmajors). The department continues to serve wellthose like McMullen, who are bound for graduateschool in mathematics, while also reaching out tostudents like McLean, who have other aspirations.For both kinds of students, the department triesto spark and stoke a love of mathematics.

The department did not set out to increase thenumber of math majors. Rather, its goal has beento increase student learning and enjoyment ofmathematics. One turning point for the departmentcame about twenty years ago, when it changedits calculus sequence. At the time, the coursecrammed single- and multi-variable calculus intoa single year. Students had “quite a time withit,” recalled Frank Morgan, who has been inthe department since 1988. Freshmen coming tocampus would hear from other students, “Don’ttake calculus.” The department made the coursemore approachable by rearranging the material torun over three semesters. The course’s reputationchanged overnight, and now freshmen hear, “Youhave to take calculus.”

And they do: Eighty-four percent of Williamsstudents take a course in mathematics or statistics,and about sixty percent complete multivariablecalculus. Only a few of these students intend tomajor in mathematics, but after taking a coupleof introductory courses, they are hooked. Thedepartment’s statistics courses are also highlypopular: Sixty percent of the graduating classhas taken a statistics course, compared to fifteenpercent a decade ago. “We like having a lot ofstudents,” Loepp commented. “It adds an energyto the department.”

Once the students are hooked on mathematics,the department keeps them hooked by deliveringoutstanding teaching and offering a wide variety ofactivities that build a sense of community. Williamshas a long tradition of excellent mathematicsteaching. These days, in order to be hired atWilliams, Morgan said, one’s application must havea document containing a statement like, “This isthe best teacher I have ever known.” Many Williamsmathematicians have won teaching awards at thelocal or national level, and teaching quality asmeasured in student surveys has risen over theyears. When faculty come up for tenure, the qualityof their teaching is compared to that of the tenured

SMALL 2013.

faculty, creating a climate in which continualimprovement is the norm.

Using what Adams calls an “n-pronged ap-proach”, where n is a fairly large integer, thedepartment has created a range of student activ-ities. There are weekly problem-solving dinners,monthly dinners for students and faculty, andan ice cream social in which new students getinformal course advising from older students,all the while enjoying ice cream sundaes. Thereis a weekly math puzzle night, and a monthly“Math Conundrum”: A mathematics problem withan unusual twist is posted on the departmentalwebpage, and students can win prizes for solvingit. Faculty member Steven Miller runs a “MathRiddles” website that gets 4,000 hits a month.Students have the opportunity to attend confer-ences, including the Joint Mathematics Meetingsand the Hudson River Undergraduate MathematicsConference, of which the Williams department isone of the founders. The many activities contributeto students’ enjoyment of mathematics and makethe department a friendly, sociable place to be.Students often comment on the high level ofactivity in the department.

Another major activity in the department is theseries of colloquia given by senior math majors.The colloquium talk is a requirement for thedegree. Each math major works intensively witha faculty member to choose and study a topicand to prepare the lecture. Faculty routinely listento two or more practice runs of the talk beforethe student is ready. Students often identify thecolloquium lecture as one of their most valuableeducational experiences. With so many mathmajors, scheduling all the colloquia is a logisticalchallenge, and the department has sometimes hadto resort to running talks in parallel sessions. Thecolloquia are well attended, often with friends andfamily in the audience, and they create a buzz oncampus. “Everyone has a friend who gives a mathcolloquium,” Morgan said.

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A group of Williams math majors, mostlyseniors, in 2010.

SMALL Program, Large ImpactOne day during his first summer at Williams, Mor-gan attended a science lunch talk and encountereda hundred undergraduates who were working onresearch projects. “I thought, What a marvelousthing,” he recalled. “I knew then that mathematicshad to be a part of it.” People understood howundergraduates could contribute to research in alab science—but to mathematics research? Thiswas 1988, and today’s proliferation of ResearchExperiences for Undergraduates (REU) programs inmathematics had not yet occurred, so there werenot many exemplars to follow. But Adams and Silvahad done a couple of research projects with mathe-matics students, and they had a sense of what waspossible. That same summer Silva, Morgan, Adams,William Lenhart, and David B. Levine submitteda proposal to the National Science Foundation tostart an undergraduate research program namedSMALL, an acronym of their last names.

Now more than twenty-five years old, SMALLis one of the best known and most successfulREUs. It runs for nine weeks over the summerand brings in about thirty students, some ofthem from Williams, some from other schoolsaround the nation, and even some from abroad.Each SMALL faculty member assembles a group ofundergraduate students, chooses a problem forthem to work on, and provides guidance and adviceas the students collaborate. Many of the groupshave published in standard research journals. Thestudents have done research in a wide variety oftopics, including knot theory, minimal surfaces,number theory, symmetry groups, combinatorics,graph theory, computational geometry, dynamicsand ergodic theory, neural networks, Bayesianstatistics, and commutative algebra.

How do the SMALL faculty come up withappropriate problems for the students? Partly itis a matter of experience, and partly it is a matterof keeping one’s antennae up, Adams noted. Forexample, when listening to lectures or talking

to people at meetings, “you look for problemswhere you don’t need a lot of background to makeprogress, or that can be broken down into casesor boiled down to a simpler situation,” Adamsexplained. When one is thinking like this, “it justtakes off.”

Because SMALL is a well-established programwith an excellent reputation, it gets very strongapplicants. “It’s so much fun for us to work withthese students at an early point in their careers,”Adams said. Today sixty SMALL alumni are in theprocess of getting their Ph.D.’s in mathematics,and many others have finished their degrees andhold faculty, postdoctoral, and visiting positionsin a variety of institutions. Two of the best-known SMALL alumni are Michael Hutchings of theUniversity of California, Berkeley, and Jeff Brock ofBrown University. Several SMALL participants havereceived distinctions such as the Schafer Prize ofthe Association for Women in Mathematics andthe Morgan Prize for Outstanding Research by anUndergraduate, which is sponsored jointly by theAMS, the Mathematical Association of America, andthe Society for Industrial and Applied Mathematics(Morgan’s mother endowed the latter prize, whichis named after her and his late father).

Susan Loepp served as principal investigator onthe NSF grant for SMALL from 2009 to 2013 anddirected the program for three of those years. Forher SMALL groups, she used to choose the studentswith the strongest records. “Now, I take those Ithink will work the hardest,” she said. She and theother SMALL faculty have also made a concertedeffort in recent years to recruit more studentsfrom underrepresented minorities, in particular byforging ties with programs like the Math Allianceand its Field of Dreams conference. Before 2009,SMALL usually had one or two students fromunderrepresented groups every few years. Today,it is unusual for SMALL to have a year withoutseveral such students. About one-third of SMALLparticipants have been women. “I try to be reallysupportive of underrepresented students here andelsewhere,” said Loepp. “We need to encouragethem and let them know they’re good even if theythink they’re not.”

Hiring Outstanding PeopleLoepp grew up in the Midwest and had neverheard of Williams until she was on the job marketafter getting her Ph.D. Many people recommendedshe apply to Williams, so she did. “I came outand saw all the fantastic things the departmentwas doing,” she said. The department clearlyvalued both teaching and research—and excelledin both. “The faculty were writing books, advisingundergraduates, teaching innovative classes,” shesaid. “No one in the department, after getting

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tenure, was slacking off. Some did even more. Thatwas the kind of energetic department I wanted tobe in.” Not wanting to be a “trailblazer”, as sheput it, Loepp was glad that the department alreadyhad two women. Today five of the department’sfifteen faculty are women.

One of the main reasons for the success of theWilliams department is its approach to hiring. “Wesay, let’s hire the best person in terms of teachingand research and not worry about area,” Adamsexplained. “So our pool is maybe eight times aslarge as at other places. That has served us well.”One exception is statistics, where the departmentmade targeted hires in the belief that statistics isone of the most important needs for the college.In 1992, the department hired Richard De Veaux,who had been at Princeton University. “That wasa huge hire,” Adams remarked. “He is someonewho organizes things and moves them forward.”The department now has four statisticians, two ofthem women, and enough faculty to support itsnew statistics major, established last year.

The department hires serious researchers andexpects them to produce. In decisions about hiringand promotion, research and teaching qualityare weighted close to equally. The research mustconsist of published articles in good journals; littlecredit is given for writing a textbook. (The facultyhas nevertheless written a range of textbooks,some of which have been used widely in otherinstitutions and have led to successful teachinginnovations.) Faculty in the department are indeedvery active in research. Since 2000, they havebeen awarded a total of twelve National ScienceFoundation research grants and have publishedon average a total of nineteen journal articles peryear. A weekly department-wide faculty seminarprovides a venue to discuss current research, andthis seminar has sometimes led to collaborations.The Williams mathematicians and statisticiansare in demand as speakers outside the college,delivering each year nearly 200 talks at conferencesand other institutions.

Research in the department is closely tied toteaching. “At Williams, we get really strong, smartstudents,” Adams said. “To be a successful teacherhere you have to be involved in research andexcited about it. The students expect that.” Thedepartment offers a range of advanced coursesin areas such as hyperbolic three-manifolds, tran-scendental number theory, analytic number theory,Riemannian geometry, ergodic theory, algebraicgeometry, and Fuchsian groups. These courses aresimilar in level to graduate courses. “I couldn’tteach such courses without doing research in thearea,” Adams said. Math majors have the optionof writing a senior thesis, and faculty need to be

SMALL 20th anniversary conference.

involved in research in order to be able to identifysuitable thesis topics.

A department with so many high-poweredpersonalities could easily become fractured. Butthe Williams department has not. “Somehow, wehave gotten faculty who are very dedicated to thedepartment,” Loepp noted. “There are no politicalgroups. We have opinionated people, but when wevote, we don’t vote according to who we like. We voteon the issue.” Sometimes discussions in departmentmeetings become heated, but afterwards, everyonehas lunch together. And they don’t bicker over thesmall stuff. A department can easily get embroiledin arguments over, for example, whether calculusshould be taught by lecturing, by using “reform”methods, by using computers, and so on. But,Morgan noted, if the focus is on whether studentsare learning, and faculty are free to use whateverteaching methods they personally find effective,“What’s there to argue about?” Whether studentsare happily learning “is all we care about,” he said.“That’s all we had to agree on. That is the sharedvision.”

Building an Academic CommunityOlga (Ollie) R. Beaver, a beloved member of theWilliams department and recipient of the 1992Louise Hay Award of the Association for Women inMathematics, died in 2012. In a memorial tribute toBeaver, posted on the department website, Loepprecounted a story from her first weeks at Williams,when Beaver was department chair. Loepp washeading to a reception for women faculty andstopped by Beaver’s office to ask if she was goingto the “chick event”. “I was immediately horrifiedthat I had mistakenly used the possibly offensiveword ‘chick’ in the presence of my departmentchair,” Loepp wrote. “As I stood paralyzed, tryingto figure out how to get out of this one, withoutmissing a beat, Ollie leaned over to me and said,‘Some of us are hens.”’

This anecdote captures Beaver’s inimitablecharm. An enormously popular teacher, she co-founded the college’s new Summer Science Program

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(SSP) in 1987, serving as director of the programfor ten years and teaching in it until her death.SSP identifies Williams freshmen who expressan interest in mathematics and science and whoare from underrepresented minorities or are thefirst in their families to attend college (Williams’policy of need-blind admissions and full needfor all American students has brought more suchstudents to campus in recent years). SSP is not aremedial program; the SSP participants are talented,high-achieving individuals.

However, some of them come to Williams withthe idea that they have to “go it alone”. “The mainthing SSP does is develop a sense of academiccommunity,” Morgan explained. Over the courseof the five-week program, the SSP students areencouraged to ask questions of the instructorsand to work together with their peers when theyget stuck. “This spirit has been transmitted toother, non-SSP students,” Morgan wrote in a letternominating Beaver for the Hay Award. “Now thereare successful role models; students help eachother. Word gets around that people care here.”The majority of SSP participants opt for science-related majors, and a large number enroll ina mathematics course. Some have gone on tocomplete the mathematics major.

Through the SSP, Beaver touched the lives ofaround 500 students, conveying a welcoming andencouraging message and transmitting to themher ethic of hard work and perseverance. Silva,who is originally from Peru, has also taught in theSSP since the mid-1990s; other faculty, includingLoepp, have taught in it as well. Calling the program“fantastic”, Loepp nevertheless acknowledges thatprogress in bringing underrepresented studentsinto mathematics has been slow. “It’s hard,” shesaid. “We are not the best at it. But we are makingprogress, and I hope we can continue.”

Everyone Loves MathThe faculty of the Williams College Department ofMathematics and Statistics are almost unbelievablyenergetic. How does the department inspire thefaculty to work so hard? “We love what we’re doing,”Morgan said. “Mathematics is an honor and a thrillto be part of. People come here excited to taketheir place in what we are doing.” With its open,creative atmosphere, the department providesfertile ground for new ideas for pursuing its maingoal: communicating and enjoying mathematics.For his part, Silva hopes the department willcontinue to spread its message: “Everyone lovesmath, even if they don’t know it yet.”

Digging into the Numbers

Bethany McLean at SMALL 20th anniversaryconference.

Bethany McLean, whose article in Fortune mag-azine was the first to report on the Enron fraud,received her bachelor’s degree in mathematicsfrom Williams in 1992 (see main article). Askedabout how studying mathematics influencedher career, she made the following remarks.

Math was easy for me until I hit abstract algebra.And then it became impossible. I struggled forBs and definitely was not going to go on tograduate school. The really great thing aboutthe Williams math department is that theydidn’t discourage people like me from stillmajoring in math—in fact, they encouraged it.I think the department has long had the viewthat they want more students than those whoare going to go on to get Ph.D.’s. Math is arelevant degree for so many careers!I gave a talk at the college a few yearsago entitled “Why math made me a betterjournalist”. Part of my argument was thatmath taught me inescapable logic. I am notnaturally a tough, confrontational person. Butwhen A doesn’t lead to B, I dig in. I can’t getaround it any more than I could skip a step ina proof. That’s made me ask questions until Iget answers.I also think that it’s good to do somethingin college that isn’t easy for you. Math washumbling for me. But I learned what it was liketo have to work at something that didn’t comeeasily. That’s an incredibly important lessonfor any career.

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