Math/Stats at Williams

Our nation needs to interest a wider group of students in mathematics and science. Here at Williams we have developed a variety of strategies to inspire students to pursue mathematics, strategies that transcend our department and that have had an impact well beyond our own institution. Over the last three decades, we have seen a dramatic increase in the number and diversity of mathematics majors, students, and undergraduate research participants. In 1985, we had six senior majors. In the class of 2014, we have 67 majors, over 12% of the senior class, as compared to the national average of about 1%. Although there is no college requirement for students at Williams to complete a course in mathematics or statistics, over 84% of Williams students in the recent graduating classes completed at least one course in mathematics or statistics and 48% completed Multivariable Calculus. Our summer undergraduate research project has grown to be perhaps the most prolific in the nation, with over 400 students and over 100 papers accepted for publication and with increasing numbers of women and minorities. Our students carry their understanding and appreciation of mathematics into every department of society, including a Presidential speech writer. One of our notable alumni is Curt McMullen, a Fields Medalist.

Our department currently has 14 full-time faculty members in mathematics and four in statistics. Six of us have won the National MAA Haimo or Alder Distinguished Teaching Award for excellence in mathematics teaching and two have won the Robert Forster Cherry Award for Great Teaching in any discipline in the English speaking world, including Ed Burger who has just left to become President of Southwestern University. As a department we publish an average of three books and 19 journal articles per year.

In addition to the standard undergraduate offerings, we offer a wide variety of pure and applied courses, from “The Beauty of Numbers” through advanced tutorials and senior seminars such as “Geometric Measure Theory” not usually found in undergraduate programs. Meanwhile in the past ten years the number of students taking statistics at Williams has increased from approximately 70 to over 400 a year.  In 1994 approximately 15% of the graduating class had taken a statistics course. Today over 60% of the graduating classes have completed at least one course in statistics. The department has four statisticians, perhaps a first for liberal arts colleges.

Each senior major must prepare and deliver a mathematics colloquium on a new topic.  The student works with a faculty advisor and after considerable preparation and practice presents the lecture to an audience of 20 – 50 students, faculty, and often family and friends in our twice weekly Undergraduate Mathematics Colloquium. Many students have reported to us that this exercise was one of the most important educational experiences in their undergraduate careers.

We have two undergraduate research programs and perhaps they best capture our belief that teaching and research are naturally interconnected. The first is our nine-week summer program named “SMALL”—an acronym formed from the names of the program’s founding faculty members. Since its inception in 1988, SMALL has grown to be one of the largest undergraduate research programs in the nation, an REU site funded jointly by the National Science Foundation and Williams College. Each summer approximately 30 undergraduates—about one third from Williams and the remainder from other institutions—work in small groups under the supervision of a faculty member on problems of current research interest. Recent areas of study include algebra, geometry, number theory, ergodic theory, mathematical physics, and topology. The goal of the SMALL program is for undergraduates to discover the excitement and challenges of pursuing original research while learning advanced mathematics. Each group produces a paper based on their summer work. In most cases, these papers lead to published articles. Over 100 publications resulting from student work in the SMALL program have appeared or have been accepted for publication.  Students present their work at numerous conferences including the MAA summer MathFests, the Joint Mathematics Meetings, research conferences, and various national and regional meetings. They have written reviews for MathSciNet, refereed papers for journals, talked to high school students in programs such as PROMYS and Hampshire, made presentations at our street fair, and even marched in our July 4 parade.

SMALL alumni now hold regular faculty appointments at colleges and universities throughout the country, including Berkeley, Bowdoin, Brown, Duke, Grinnell, Illinois Central College, Illinois Institute of Technology, Macalester, SUNY Potsdam, Toronto, University of Arkansas, Vassar, Wake Forest, Westfield State, William and Mary, and Yale.  Many others currently hold postdoctoral or visiting positions. Currently, there are over 60 SMALL alumni who are in the process of completing their Ph.D.’s in mathematics. The table below shows the demographic breakdown between the current and previous grant (the number in each category is given in parentheses). There were 144 students from 2009—2013, and 111 from 2004—2008.

2009—2013

2004—2008

Percentage of students from outside Williams

68% (98)

53% (59)

Percentage of students who are women (overall)

38% (54)

29% (32)

Percentage of non-Williams students who are women

42% (41)

31% (18)

Percentage of students who are minorities (overall)

13% (19)

4% ( 4)

Percentage of non-Williams students who are minorities

18% (18)

2% ( 1)

In the last five years, 38% of participants are women (42% among the non-Williams students). Further, 13% are minorities (18% of the non-Williams students).

Our second research opportunity is the Senior Honors Thesis option. Typically about ten seniors each year decide to embark on a thesis. These projects usually involve publishable original scholarship. Recent topics include Regression with Missing Data, Perimeter-Minimizing Tilings, Formal Fibers of Height-n Primes, Diophantine Approximation over Algebraic Curves, Class Groups of Function Fields, Hyperbolic 3-manifolds, Measurable Dynamical Systems, Analytic Number Theory and Minimal Blow-ups of Coxeter Complexes.

Through our teaching and research we hope to continue to attract students to mathematics and to inspire them to understand its beauty and to move its frontiers forward.

 

Williams College is a liberal arts institution with approximately 2100 students. Our activities have been recognized by various news outlets (see, for example, The New York Times (8/01/99), Newsweek (6/05/00)) and The Boston Globe (10/16/05)).

Scholarship. Since 2000, the members of our department have published an average of three books and 19 journal articles per year. Books include The Heart of Mathematics, Making Transcendence Transparent, Exploring the Number Jungle, Coincidences, Chaos and All that Math Jazz, Extending the Frontiers of Mathematics, The Knot Book, How to Ace Calculus, How to Ace the Rest of Calculus, Introduction to Topology, Why Knot?, All the Mathematics You Missed, Matrix Groups for Undergraduates, The Mathematics of Encryption: An Elementary Introduction, Calculus Lite, Beginner’s Guide to Riemannian Geometry, Geometric Measure Theory: A Beginner’s Guide, The Math Chat Book, Real Analysis, Applied Real Analysis, Protecting Information, Invitation to Ergodic Theory, Groups and Characters, An Invitation to Number Theory, Mathematics and Politics: Strategy, Voting, Power and Proof, Protecting Information: From Classical Error Correction to Quantum Cryptography, Stats: Data and Models, Stats: Modeling the World, and Intro Stats. Several of the books have been adopted and started new courses at other colleges and universities.

Since 2000, faculty members have also received 12 research grants from the National Science Foundation. We have had NSF-REU grants to support our summer research program since 1988. We run a department-wide weekly faculty seminar, at which we describe our current interests. This seminar has stimulated not only our individual research but also collaboration among ourselves and with others, including economists and biologists.  Members of our faculty travel widely and deliver nearly 200 talks at conferences and other institutions annually.

Meanwhile our students have published papers in the following 30 journals among others: Acta Arithmetica, Acta Crystallographica, Sect. A, American Mathematical Monthly, American Scientist, Colloquium Mathematicum, Communications in Algebra, Computational Statistics and Data Analysis, Discrete and Continuous Dynamical Systems, Ergodic Theory and Dynamical Systems, Fibonacci Quarterly, Geometriae Dedicata, Illinois Journal of Mathematics, Journal of Algebra, Journal of the Australian Mathematical Society, Journal of Combinatorial Theory, Journal of Differential Geometry, Journal of Discrete and Computational Geometry, Journal of Geometric Analysis, Journal of Knot Theory and its Ramifications, Journal of Number Theory, Journal of Pure and Applied Algebra, Nonlinearity, New York Journal of Mathematics, Pacific Journal of Mathematics, Pattern Recognition Letter, Proceedings of the AMS, Real Analysis Exchange, Technometrics, Topology and its Applications, Transactions of the AMS.

Several of our SMALL students have won the Alice T. Schafer Prize: Kate Gruher, MurphyKate Montee, Charmaine Sia, Fan Wei, runner-ups were Sami Assaf, Jennifer Nova, and honorable mention was awarded to Sonya Mapes, Amy Marinello, Jessica Polito, Laura Starkston, Grace Wang, Yinghui Wang, and Mary Wooters.

Advanced Curriculum. Recent offerings include Hyperbolic 3-Manifolds, Transcendental Number Theory, Analytic Number Theory, Linear Algebraic Groups, Matrix Groups, Riemannian Geometry, Ergodic Theory, Diophantine Analysis, Algebraic Geometry, Tiling Theory, Polynomial Arithmetic and Fuchsian Groups.  Our applied offerings include Biological Modeling, Game Theory, Mathematical Physics, Protecting Information (Applications of Abstract Algebra and Quantum Physics), Control Theory, Categorical Data Analysis, Algebraic Error Correcting Codes, Applied Topology, Investment Mathematics, Bayesian Statistics, Mathematical Modeling of Ecological Systems, and Computational Statistics and Data Mining.

We participate in various competitions. In last three years we have had 25, 13, and 23 students take the Putnam exam and our team placed 19th, 10th, and 25th in the nation, one of the highest for a small liberal arts college. Last year we placed second in the Chicago Quantitative Alliance stock trade competition. We have a weekly math puzzle night and a monthly conundrum. Steve Miller’s puzzle page gets 4000 hits a month.

Department Activities. Due to our many student-related activities outside of the classroom, our department has developed a reputation on campus as lively, fun, and social. We host monthly dinners for students and faculty.  We also hold Ice Cream Socials during course registration, at which students can receive informal course advising while eating ice cream sundaes. We also have entertaining events on Pi Day and even Skewe’s Day (March 4th).  These include the Great Pi/e Debate (which is now a DVD on sale through the MAA) and game show antics with attendance well into the hundreds. In the summer, faculty and students from SMALL hold community activities in a program called Summer Sundays.

Summer Science Program. Williams’ Summer Science Program (SSP) identifies talented pre-first-year students from groups underrepresented in math and science. The students are invited to campus for a five-week intensive summer program in science and mathematics. The program was cofounded by a member of the department, and two members of the department have taught in the program for most of its existence; the director of the program for its first ten years was a member of our department. The participants are mentored by faculty members who include them in research programs. The main goal of the SSP is to begin to prepare and inspire these students to pursue a Ph.D. in science or mathematics. While the majority of the participants go into science-related majors, a large number continue to enroll in mathematics courses and some have completed the mathematics major.  One SSP participant went on to pursue graduate studies in mathematics and published three papers in The Pacific Journal of Mathematics.

Hudson River Undergraduate Mathematics Conference. Williams College is one of the four founding members of the Hudson River Undergraduate Mathematics Conference (HRUMC)—a one-day mathematics conference held each spring. HRUMC, the first of its kind, founded in 1994, has since been the inspiration for many other such regional undergraduate mathematics conferences around the country. HRUMC is the largest such undergraduate conference and regularly draws well over 400 students and faculty members from a wide variety of universities, colleges, and community colleges in New York and New England. Following the tradition of HRUMC, one member of the department is a co-principal investigator on an NSF grant to the MAA to support dozens of undergraduate mathematics conferences around the country. This past spring we hosted the 20th annual conference at Williams, with over 200 talks, 60 by Williams students, the keynote by Manjul Bhargava, and some 500 attendees.

Outreach and Service. Our department is committed to sharing with our students and the community at large our sense of the beauty, power, and pleasure of mathematics.  To that end, we have given many popular public lectures on campus (our Parents’ Weekend lectures, for example, draw crowds of hundreds on Saturday afternoons). We have also brought to campus a long list of renowned mathematicians to speak and interact with our students.  That list includes John Conway, Shizuo Kakutani, Benoit Mandelbrot, Roger Penrose, Ken Ribet, Gian-Carlo Rota, Wolfgang Schmidt, and Jeff Weeks. As part of our outreach to the community, we developed MathBlast!—a one-day event for high school students and their teachers from Massachusetts, New York, and Connecticut.  Participants enjoy hands-on workshops, games, and entertaining lectures. Recently, in the fall we have invited the whole 10th grade of our local high school for a morning of workshops by members of our department. Last summer Allison Pacelli inaugurated a MathCamp for gifted high school students. Steve Miller gives continuing education talks to teachers.

Faculty Honors. Department members have received a variety of honors. Two of our faculty members have been MAA Polya Lecturers, two are recipients of the Kenan Trust Professor of Distinguished Teaching at Princeton and six are recipients of the national MAA teaching awards. Other honors include Fellowship in the ASA or AMS, the AWM Louise Hay Award, Sigma Xi Distinguished Lecturer, the Residence Life Teaching Award of University of Colorado, two winners of the Baylor University Robert Foster Cherry Award for Great Teachers, the University of Texas Robert W. Hamilton Book Prize, and the MAA Chauvenet Prize.

Leadership Within the Mathematical Community. The faculty members of the Department of Mathematics and Statistics have served in a variety of roles in the scientific community and have held various leadership positions. These include Second Vice President of the MAA, Vice President of the AMS, members of the AMS Council, national committee chairs, editors, and members of numerous visiting committees.

Service to the Mathematical Community. Our faculty have served in a variety of roles to help faculty at other institutions, including an NSF sponsored Chatauqua summer workshop, MAA PREP courses (five times), an MAA PMET course, an MAA Allegheny Mountain Section short course, two MAA Ohio Section short courses, two Park City Mathematics Institute Faculty Workshops, MAA Mini-courses at many national joint meetings, MAA Short Courses, and a variety of teaching workshops at conferences. In October 2001 we hosted an AMS Section Meeting at Williams. In summer 2011 we hosted a mathematics research conference with speakers from six different countries where two undergraduates from SMALL spoke. Last summer Dick De Veaux and Bernhard Klingenberg organized a conference on Big Data for Mathematicians. We have had Williams students co-organize AMS sectional sessions on undergraduate research. Faculty have given a great number and variety of talks throughout the world, including invited addresses at the joint meetings, keynote addresses at the regional and national NCTM meetings, AMATYC meetings and keynote addresses at annual meetings of 25 out of the 29 sections of the MAA. We have given talks at over 600 colleges and universities as well as a variety of public lectures, talks at high schools, and addresses at international conferences. For all this and more, see our new webpage http://math.williams.edu.

 

Appendix: Alum Fellowships and Awards

** CLAY FELLOWSHIP
Ivan Corwin, SMALL ’04
Sam Payne, SMALL ’97

** FIELDS MEDAL
Curt McMullen, Williams ’80

** NSF POST-DOCTORAL FELLOWSHIP IN MATHEMATICS
Curt McMullen, Williams ’80Jeff Brock, SMALL ’90,
Brian Street, SMALL ’02
Daniel Kane, SMALL ’04
Anatoly Preygel, SMALL ’05
Thomas Koberda, SMALL ’06
Kathryn Lindsey, SMALL ’06
Jeff Danciger, SMALL ’04

** RHODES SCHOLARSHIP
Jeff Brock SMALL ’90
Jason Zimba Williams’90, SMALL’90
Ben Ebert Williams ’91

** SLOAN RESEARCH FELLOWSHIP
Curt McMullen, Williams ’80, Sloan ’88
Jonathan Mattingly, SMALL ’91, Sloan ’05-07
Jeff Brock, SMALL ’90, Sloan ’96-97