- MATHEMATICS COLLOQUIA
- MATHEMATICS STUDENT COLLOQUIA
- OFF-CAMPUS COLLOQUIA
- POSTGRADUATE PLANS OF MATHEMATICS MAJORS

The Mathematics Department has had another great year. This spring, we saw a record 43 sophomores signing on to be majors. With the 37 soon-to-be seniors, this easily sets a new record for the total number of math majors on campus. Total enrollments in math classes continue to be at record levels.

Both Richard De Veaux and Frank Morgan were on leave this year, with Dick having spent the year at the French National Institute for Argonometric Research (I.N.R.A.) in Montpellier, France, and Frank having spent the year as the 250th Anniversary Visiting Professor for Distinguished Teaching at Princeton. Dick will be back in time for next Fall, while Frank will be taking one more years' leave, after returning to Williams for the summer to participate in the SMALL undergraduate research program. Ed Burger will be on leave next year at the University of Colorado. Deb Bergstrand will be on leave in Philadelphia, and Victor Hill will be on leave with lots of travel plans but a base in Williamstown. Both Stewart Johnson and Cesar Silva will take semester long leaves next academic year. Both of their leaves are well deserved, with Stewart having shouldered the burden of the statistics courses during Dick's leave, and Cesar having chaired our hiring committee so effectively.

With all the leaves coming up, we were pleased to appoint two visitors for next year. Steve Wang is finishing a Ph.D. in Statistics at the University of Chicago and is particularly interested in the statistics of handwriting recognition, such as might be required when the post office tries to decipher that zip code you wrote. He will teach a variety of courses for us, including a course on statistical graphics. Jorge Calvo is finishing his Ph.D. in Mathematics at the University of California-Santa Barbara. He studies questions related to knots constructed out of sticks. His courses will include Algebraic Topology and Geometry.

This past year, we were lucky enough to be joined by David Morgan, who was on leave from the Bishop's School in San Diego, CA. He taughtOne sad note this year was the passing of Wally Jordan. A member
of the Williams Mathematics Department from 1946-1977 as well as the
valedictorian of Williams Class of 1937, Wally worked as an actuary
before becoming a member of the Faculty. He was the author of *Life
Contingencies* that can still be found on the bookshelves of
actuaries throughout the country. Over the years, he contributed
greatly to the Mathematics Department, in addition to helping
innumerable students who had an interest in actuarial science.

As always, we were extremely proud of the accomplishments of our graduating seniors this year. Kariane Calta `98 was awarded a National Science Foundation Fellowship for graduate study in mathematics. She will attend the Ph.D. Program at the University of Chicago. She also received the Rosenburg prize given to the best graduating major by the mathematics department. Past major, Deborah Greilsheimer `97 received honorable mention in the NSF Graduate Fellowship competition. She will be attending the University of Pennsylvania next Fall. Andrew Raich `98, who is going to the University of Wisconsin to study math, received the Morgan Prize for teaching and/or applied math. Tristan Smith `98 received the Goldberg Prize for having given the best colloquium and the Witte Problem Solving Prize for his excellent showings on both the Green Chicken Exam and the Putnam Exam. Tristan is speaking at the Toronto SIAM meetings this summer on his joint work with Prof. Deborah Bergstrand and will be teaching mathematics in Morocco next year. Kari, Andy and Tristan were all elected to the Sigma Xi Research Society on the basis of the research they did for their theses. All three received highest honors from the department. Heath Dill `98 and Mimi Huang `98 received honors from the department, based on their accomplishments on their theses. The Benedict prize for outstanding sophomore went to Anthony Ndirango `00.

We are very grateful to the members of the Student Mathematics Advisory Board (SMAB) for their help with hiring, advice on departmental issues and organization of events. This year, the members were Patrick Anderson `00, Catherine Bagley `99, Garren Bird `99, Zack Grossman `99, Sang Pahk `99, Audrey Watkins `98 and Aaron Weinberg `99. Also, Kariane Calta `98 and Andy Raich `98 did a great job as our senior advisors.

All of the faculty had a busy and productive year. Highlights of the year's faculty activities follow:

Colin Adams became chair of the Mathematics Department in July 1997, taking over from Prof. Olga R. Beaver. In summer of 1997, he directed four students on research in alternating graphs as part of the SMALL program. The students spoke on their work at the Atlanta Mathfest in August. The paper that Adams and the students jointly produced has been submitted to a math research journal for publication.

In January 1998, Adams was awarded the Deborah and Franklin Tepper Haimo Distinguished Teaching Award, given annually to three recipients nationwide. He is the second winner in the department. Frank Morgan won it in 1993, the first year that it was awarded. Only one other department in the country has as many recipients of this award as we do, and that is the Purdue Math department (which incidentally has three times the number of faculty).

Adams also became a Polya Lecturer for the Mathematical
Association of America, making him one of two nationally and the
seventh appointed so far. He gave over 20 talks around the country,
including a second production of the mathematical play, co-authored
and performed jointly with Edward Burger, entitled *Casting About:
About Casting* at the National Mathematics Meetings in Atlanta,
GA, Aug. 4, 1997. He wrote several papers and had several others
accepted for publication. He edited a special issue of the *Journal
of Chaos, Solitons and Fractals* devoted to "Knot Theory and Its
Applications." His new book *How to Ace Calculus: the Streetwise
Guide*, co-authored with Joel Hass and Abigail Thompson, will
appear in July 1998. His National Science Foundation research grant
has been renewed for the next three years. As of July 1998, he
becomes the Mark Hopkins Professor of Mathematics at Williams
College.

Professor Ollie Beaver was on sabbatical leave in the fall. In November, she gave a Bronfman Bag Lunch talk on Williams' Summer Science Program. Also in November, Beaver was an invited speaker at the 1997 Fall Conference of the Northeastern Section of the Mathematical Association of America, presenting a lecture, "The Williams Summer Science Program - Not With a Whisper But a Bang." In the spring she was a panelist in the Connecticut Association of Independent Schools Math Forum Calculus Panel Discussion, held at The Hotchkiss School in Lakeville, Connecticut. She has continued her long association with the Summer Science Program, again teaching in the mathematics component.

Deb Bergstrand continued her work in graph theory. She spoke on "Graceful Graphs" at the Williams Faculty Seminar. She served as the Director of the 1997 SMALL Project. She was also Chair of the Faculty Steering Committee until January when she took a leave of absence to care for a newly adopted daughter, Julia Michelle Stanley, born February 11, 1998. Mom, dad, and daughter are enjoying life in Philadelphia.

Professor Edward Burger spent the summer of 1997 as a Visiting Scholar at the University of Texas at Austin. This past academic year he advised three honor's thesis students: Kariane Calta `98, Heath Dill `98, and Mimi Huang `98, on various number theory research projects. Next year Professor Burger will be on sabbatical at the University of Colorado at Boulder where he was named the Ulam Visiting Research Professor of Mathematics.

Burger published "Mathematics Beyond the Ivy-Covered Hall" in The
Mathematical Intelligencer (vol. 20, 1998), and completed his text,
*The Heart of Mathematics: An Invitation to Effective Thinking*,
co-authored with Michael Starbird, to be published by Springer-Verlag
in 1999. He is also completing the first-ever virtual interactive
video WEB calculus textbook. It may be found at
http://www.thinkwell.com/.

Burger was the Chair of the Program Committee for the Fall 1997
Northeastern Mathematical Association of America Meeting, held on
November 21 and 22 at Western New England College in Springfield. He
reviewed numerous articles for Mathematical Reviews, and served as
referee for the *Journal fur die Reine und Angewandte*, the
*Fibonacci Quarterly*, Columbia University Press, and W.H.
Freeman Press. He also was a reviewer for the National Science
Foundation.

Professor Burger gave numerous invited lectures throughout the country. (See the list of talks at the end of this section.) Here at Williams, Professor Burger lectured on mathematics during the Summer Open House in August, at the Williams College Faculty Club and in the Mathematics Faculty Seminar in September, at a Mathematics Colloquium in October, and again in the Mathematics Faculty Seminar in April. Also in April, Burger delivered a lecture in the Williams Writers on Writing Lecture Series.

Professor Mikhail Chkhenkeli continued his research in Four Dimensional Topology and Gauge Theory. In particular he investigated the problem of determining the genera of homology classes of 4-manifolds and representing them by smoothly embedded 2-spheres. Chkhenkeli wrote two papers: "Homology Classes of K3" and "Homology Classes of 4-Manifolds."

At Williams, he gave Mathematics Faculty Seminars in November and
May. In the Fall of 1997 he taught a new senior
seminar,*Differential Topology* MATH 427. He organized the First
Annual Purple Cow High School Math Contest, the Twentieth Annual
Green Chicken Math Contest, and monthly mathematics conundrums. He
was the coach of the Williams College team in the national Putnam
mathematical competition.

In the summer of 1997 he taught an accelerated course,
*Mathematical Logic and Reasoning* at the summer program
organized by the Institute for the Academic Advancement of Youth (The
Johns Hopkins University). In the summer of 1998 he is an invited by
the IAAY to teach a course in Mathematical Reasoning and Probability
Theory.

Professor Richard D. De Veaux spent the year as a visiting scientist at the French National Institute for Argonometric Research (I.N.R.A.) in Montpellier, France. He gave a variety of talks in the United States and France. He will give the J.S. Hunter Lecture in Australia at the International Environmetrics Meeting this July on "Hybrid Neural Networks for Environmental Process Control."

Dick continued as Associate Editor for *Technometrics*,
*Environmetrics* *and Journal of Environmental Statistics*.
He will serve as General Methodology Chair for the ASA 1998-99 and
was elected Program Chair Elect for the Section on Statistics in
Sports. His paper "Prediction Intervals for Neural Networks via
Nonlinear Regression" will appear in *Technometrics* in
November. This paper, with co-authors Jason Schweinsberg `97 and
Jennifer Schumi `97, is based, in part, on research performed by
Jason and Jenny when they were undergraduates. They are both
currently enrolled in Ph.D. programs in Statistics (at Berkeley and
Iowa State respectively).

Professor Thomas Garrity has continued his research in higher
codimensional CR structures and classical algebraic invariant theory.
His paper "Vector-valued Forms and CR Geometry" written with R.
Mizner, has appeared in a collection *CR Geometry and
Overdetermined Systems*, *Advanced Studies in Pure
Mathematics,* published by the Mathematical Society of Japan. He
has spoken a number of times at Williams and at the Hudson River
Undergraduate Mathematics Conference.

Victor E. Hill IV, Thomas T. Read Professor of Mathematics,
developed a new senior seminar on Axiomatic Set Theory, offered in
the fall. He continued as a History of Mathematics reviewer of books
for Scott Foresman and of articles for *Mathematics Magazine.*
He also participated in the spring meeting of the Northeastern
Section of the Mathematical Association of America, held in Keene,
N.H.

Professor Hill continued his work as a free-lance professional harpsichordist and organist. The 30th anniversary season of his Griffin Hall Concerts at Williams College featured the inaugural in January and a varied program in May using his new double-manual Franco-Flemish harpsichord, completed by Richard Kingston (Asheville, N.C.) in October; additional programs on the series were an all-Bach organ recital and a harp/organ concert with Teresa Mango. Professor Hill completed his 16th year on the Board of the Association of Anglican Musicians; he also serves on the Editorial Board of this Association, on the Board of Trustees of the Berkshire Unit of Recording for the Blind & Dyslexic, and on the Executive Board of the Berkshire Chapter of the American Guild of Organists.

Professor Stewart Johnson continued his research in dynamical systems and control theory, focusing on the dynamics and optimality of controls that have continuous and discrete components. His research is in the new area of "passive controls." These controls have no feedback loops and are not self-monitoring, but maintain stability by a dynamic design that is inherently self-correcting. This work was the subject of his Faculty Lecture Series talk given in March titled "Dynamics, Noise and Chaos." Professor Johnson taught his senior seminar on math modeling to a large group of 25 students, in addition to teaching the two core statistics courses while Professor De Veaux was on leave and a tutorial on Numerical Methods.

Professor Susan Loepp continued her research in commutative
algebra. Her paper "Excellent Rings with Local Generic Formal Fibers"
appeared in the *Journal of Algebra*. During the year, she
attended several conferences including the annual Joint Mathematics
Meetings, the Mathematics and Statistics Centennial Celebration of
the University of Nebraska, the fall Mathematical Association of
America conference, and the Hudson River Undergraduate Mathematics
Conference. She gave talks at three of these conferences. Loepp gave
several other talks during the year including colloquia at Smith
College, Colgate University and Williams College.

Loepp served on the steering committee for the 1998 Hudson River Undergraduate Mathematics Conference, held at Union College. Eleven Williams students and three faculty participated in the conference.

Professor Frank Morgan has spent the year as Princeton University's new 250th anniversary Visiting Professor for Distinguished Teaching. Over 100 graduate students, faculty, and undergraduates, from Mathematics and other departments (notably Molecular Biology), participated in his innovative teaching seminar, videotaped model teachers and each other, and discussed strengths and weaknesses. Professors Colin Adams and Edward Burger of Williams College, the sensations of recent national mathematics meetings, came to Princeton to produce their imaginative mathematical play and conduct teaching workshops.

Morgan took his call-in Math Chat TV show to Princeton, where it
was broadcast before a live audience off a dining hall. The volunteer
staff of graduate and undergraduate students directed the show,
operated the camera and control booth, screened the calls, and took
turns as co-host. Special guests included John Conway, Freeman Dyson,
and the young winners of Morgan's Soap Bubble Geometry Contest at
Riverside Elementary School. (Check out the March 9 show on the web
via Morgan's homepage at
http://www.williams.edu/Mathematics/fmorgan,
where you can also find his Math Chat newspaper column from *The
Christian Science Monitor.*) An interview of Morgan was featured
as the cover story of the September 1997 issue of *Math
Horizons.*

Morgan studies the geometry of soap bubble clusters and other structures in nature and in materials. He is currently writing two papers with two former undergraduate research students, Hugh Howards `92 and Michael Hutchings, on the most efficient enclosures of prescribed area ("soap bubbles") in curvy surfaces. This summer his SMALL undergraduate research Geometry Group will study efficient enclosures on the surface of the cube and other surfaces.

During the year Morgan published three papers and has five others
in press. He has given some forty talks, ranging from mathematics
seminars to his popular Soap Bubble Geometry Contest. A write-up of
the contest, written jointly with undergraduate research students Ted
Melnick and Ramona Nicholson, was published in The Mathematics
Teacher (December 1997). A second edition of Morgan's *Riemannian
Geometry *appeared this spring.

Morgan is planning a number of visits for his upcoming sabbatical, including three months in Spain at the University of Granada.

Professor Cesar Silva taught a course on chaotic dynamics and
fractals along with his other courses, and continued his research in
ergodic theory (measurable dynamical systems). He supervised a group
in the SMALL summer `97 research program. His group completed
research in ergodic theory and a manuscript was submitted for
publication "Power Weakly Mixing Infinite Transformations," with S.L.
Day, B.R. Grivna, and E.P. McCartney `99. (See their site at
http://front.math.ucdavis.edu/math.DS/9803105
.) He also supervised Andy Raich `98 who wrote a thesis in ergodic
theory. Andy presented his work
http://front.math.ucdavis.edu/math.DS/9803105
at the Hudson River Undergraduate Mathematics Conference, in April
1998. Andy's thesis together with the work of previous research
students are part of a paper that has been submitted for publication
"Infinite Ergodic Index Z^{d }Actions in Infinite
Measure",* *with E. Muehlegger `97, B. Narasimhan `97, A. Raich
`98, M. Touloumtzis `96, and W. Zhao). Silva also submitted two other
papers and published three papers, one of them based on research from
SMALL `96.

In January, Silva attended the annual meeting of the American Mathematical Society in Baltimore. He delivered a Faculty Lecture titled "Determinism and Randomness in Kneading Dough" and "Fractals and Dynamics," Bronfman Science Summer Lunch, Williams College. He also was a reviewer for Mathematical Reviews. During September, Silva hosted Professor Philippe Thieullen from the University of Paris at Orsay; they continued their long term collaboration on entropy characterization of distal dynamical systems.

In summer `98, he will be preparing a course on fractals to be taught in the fall. This work is being supported by a college Mellon grant, which is also supporting a student, Jonathan Kallay `00, who will write some programs for the course.

- Colin Adams
- Williams College
- "Alternating Graphs"

"Bus Tours of the Universe and Beyond"

"Living on the Cusp (of a hyperbolic 3-manifold)" - Williams College
- "Some Math of Finance Not in Victor Hill's Courses: Probability Distributions of Stock Prices"
- Williams College
- "New Math for Non-Math People"

"Wolfgang Schmidt: The Man and His Mathematics"

"Further Remarks on Simultaneous Diophantine Approximation" - University of California, Santa Barbara
- "Geometric Knot Theory: The Classification of Base Polygons with Small Numbers of Edges"
- University of Pennsylvania
- "Homology Classes of K
^{3}"

"Homology Classes of 4-manifolds" - Williams College
- "Designing Contracts for Interacting Parties"
- University of Maine
- "So, You Want to be an Applied Topologist?"
- Williams College
- "On Writing Numbers"

"On Godel, Tarski, Geometry and Robotics"

"On Flag Manifolds and CR Structures"

"On Minkowski and Algebraic Numbers" - Dartmouth College
- "Index Theory: The Tip of an Iceberg"
- Williams College
- "A Critical Look at Some Old Story Problems"

"Rigor and Oversight in the Work of Regiomontanus (1464)"

"The Problem of the Points" - Harvard University
- "Two Related Problems: The Distribution of Prime Numbers, and Counting Lattice Points"
- Williams College
- "What Can Electric Dipole Moments Tell Us About Space-Time Symmetries?"
- Williams College
- "Some Recent Results in Communicative Algebra"

"Back to Basics: A Lesson in Division"

"Formal Fibers at Height One Prime Ideals"

"Commutative Rings, Polynomial Rings, and Their Completions" - Williams College
- "This is the Title of My Talk"
- Williams College
- "Do Minimal Surfaces Minimize Area?"
- University of Wisconsin, Madison
- "Bicircular Matroids: Bicycles, Wheels, and Trees"
- Franklin and Marshall College
- "A Horse is a Horse, but Not to Morse. (It's a __________, of Course)"
- Middlebury College
- "Seven Shuffles Suffice"
- Williams College
- "The Secrets of `Two': Esoteric Numbers in Japanese Buddhism"
- University at Albany, SUNY
- "When Do Averages Converge and When Do They Diverge"
- Williams College
- "Mixing Actions of the Integer Lattice Group"

"2^{7}= 128 Starts with a 12, Does 2^{n}Start with 1998 for Some n?" - SUNY, Stony Brook
- "Symplectic Matrices and Why They Can't Squeeze"
- University of Colorado, Boulder
- "The Average Shape of a Lattice"
- University of Paris at Orsay
- "Ergodic Reduction of Random Products of Two-By-Two Matrices"
- University of Chicago
- "Mountains Out of Molehills, with an Application to Computer Handwriting Recognition"

Roger Bolton

Edward Burger

Jorge Calvo

Mikhail Chkhenkeli

Jonathan Conning

Robert Franzosa

Thomas Garrity

Erik Guentner

Victor E. Hill IV

Kamal Khuri-Makdisi

Dennis Krause

Susan Loepp

David Morgan

Frank Morgan

Nancy Ann Neudauer

Barbara Nimershiem

William Peterson

Fabio Rambelli

Karin Reinhold

Cesar Silva

Jennifer Slimowitz

Wolfgang M. Schmidt

Philippe Thieullen

Steve Wang

- SMALL 1997 Participants
- "How We Spent Our Summer Vacation: Reflections on SMALL 1997, the Summer Undergraduate Research Program in Mathematics at Williams College"
- "Immiscible Fluids: How They Meet to Minimize Interface
Energy"

"Can You Reduce Energy by Adding Two Immiscible Fluids?" - "Connect the Dots, La La La"

"On Outer-Crossing Numbers of Complete Tripartite and Hamiltonian Graphs" - "Lightly Mixing, Rank One Transformations: Chacon, Not
Stirred"

"On Power Cartesian Weakly Mixing Transformations and Rigid and Non-Rigid Flows" - "Covariant Transformations of Canonical Finite Sets of
Points in Complex Projective Space"

"Points from Polars" - "Compositions of Alternating Graphs"

"Crossing Number for Alternating Graphs" - "Fractal Attraction: The Iterated Function System Theorem, with Examples"
- "Catalan Numbers"
- "Group Presentations, Free Groups and Subgroups: A Presentation of an Algebraic Free for All"
- "The Fibonacci Sequence, Modulo n"
- "An Ideal World: Polynomials, Notherian Rings, and the Hilbert Basis Theorem"
- "Give It Up: A Good-Looking PDE with No Solution"
- "Quadratic Reciprocity: Sometimes the Issue Isn't Staying Together, But Splitting Apart"
- "Lots of Sticks Make Lots of Knots -- But How Much is `Lots?'"
- "Continued Fractions and Chaos"
- "Hartog's Theorem: Why Multivariable Complex Functions are Special"
- "Quadratic Forms, and Why They Mean So Much to Me"
- "An Introduction to Knot Theory Using Crayons"
- "The Five Color Theorem"
- "Proof That e Is Transcendental"
- "Mathematics in Architecture"
- "An Idyllic Chinese Remainder Theorem"
- "This Old Math: Designing Brick Walls and Patios Using de Bruijn's Theorem"
- "This Ain't Your Grandma's Sundial"
- "The Natural Numbers: How to Pair Them Up, Make Money, and Fall in Love"
- "Diophantine Approximation and Differentiability"
- "Mathematics for Economists: Dynamic Optimization with an Application to Growth Modeling"
- "Don't Move! The Brouwer Fixed Point Theorem (And Implications For Coffee)"

SMALL Geometry Group

SMALL Graph Theory Group

SMALL Dynamical Systems Group

SMALL Higher Co-dimensional Geometry Group

SMALL Knot Theory Group

Amrita Ahuja `98

Daniel Anello `98

Kariane Calta `98

Heath Dill `98

Clay Elliott `98

Steven Ellis `98

Victoria Fang `98

Katherine Hedden `98

Mimi Huang `97

Edward Johnson `98

Paul Kari `98

Jeremy Kay `98

Adrian Ludwig `98

Linden Minnick `98

Jonathan Novita `98

Andrew Raich `98

Catherine Riihimaki `98

Derek Sasaki-Scanlon `98

Tristan Smith `98

Adam Sterns `98

Surach Tanboon `98

Audrey Watkins `98

- Colin Adams
- "Systoles of Hyperbolic 3-Manifolds"

Wasatch Topology Conference, Park City, Utah - "Bus Tours of the Universe and Beyond"

Gulf Coast Consortium Mathematics Conference, Houston, Texas

Union College

Moravian College Undergraduate Mathematics Conference, keynote address

Leonard Sulski Lecture, Holy Cross College, Worcester, Massachusetts - "Casting About: About Casting"

Mathematical play, with Edward Burger, MAA Mathfest, Atlanta, Georgia - "Hyperbolic 3-Manifolds: A Photo Album"

"Mel Slugbate's Real Estate in Hyperbolic Space"

"What the Mathematicians and Scouts have in Common: Knot Theory"

University of Georgia - "Real Estate in Hyperbolic Space: Investment Opportunities
for the Next Millennium"

Western New England College(MAA Conference)

Lafayette College, Easton, Pennsylvania - "Why Do We Teach Mathematics"

Distinguished Teaching Award Talk, AMS/MAA Meeting, Baltimore, Maryland - "Waist Size for Knots and Hyperbolic 3-Manifolds"

"Teaching as Performance Art"

Improve Teaching Workshops, Princeton University - "Why Knot"

State University of New York, Albany - "What Cusps Have To Say About Knots, Links, and 3-Manifolds
and How They

Repay the Favor"

Birman 70th Birthday Conference, Columbia University - "Alternating Graphs"

AMS Sectional Meeting, Louisville, Kentucky

Hudson River Undergraduate Mathematics Conference, Union College - "Real Estate in Hyperbolic Space"

Keynote Lecturer, New Jersey Sectional Meeting of the MAA Ocean County Community College, Tom's River, New Jersey - "Waist Size for Knots, Links and Hyperbolic
3-Manifolds"

"Real Estate in Hyperbolic Space"

University of Connecticut, Storrs - "The Williams Summer Science Program - Not With a Whisper
But a Bang"

1997 Fall Conference of the Northeastern Section of the MAA - "Calculus Reform: Good or Bad"

Independent Schools Math Reform Calculus Panel Discussion, The Hotchkiss School - "Graph Crossing Numbers"

Combinatorists of New England, Smith College - "The SMALL Project: What Works After Ten Years"

National Joint Meetings of the AMS and MAA, Baltimore, Maryland - "Casting About: About Casting" (with Colin Adams)

MAA Summer Meeting, Atlanta, Georgia - "The Invisible Art: Abstract the Clouds"

Contemporary Artists Center, North Adams, Massachusetts - "Can You Sum Some of the Series all of the Time?"

MAA Colloquium, Amherst College - "Why I Hate Mathematics but Love Museums"

Berkshire Athenaeum, Pittsfield, Massachusetts

Williams Alumni, Napa Valley, California and Chicago, Illinois - "Confessions of a Mathematics Professor"

Simmons College - "Innovative Experiments in Mathematics and Beyond... and
How I Survived Them"

MAA Seaway Sectional Fall Meeting, Sienna College

MAA D.C., Maryland, Virginia Sectional Spring Meeting, Virginia State University - "Transcendental Numbers with Diophantine Structure"

Princeton University - "Teaching as Performance Art" (with Colin Adams)

Princeton University - "Simultaneous Diophantine Approximation"

Santa Clara University - "Magic with Mathematics: Is the Equation Faster Than the
Eye?"

University of Hartford - "Having Undergraduates Discover the Uncharted"

Discovery Learning Seminar, University of Texas at Austin - "Infinity and Beyond"

University of Hartford - "Preliminary Remarks on Simultaneous Diophantine
Approximation"

Number Theory Seminar, University of Texas at Austin - "This is Not the Title of My Lecture--Paradoxes... the Dark
Side of Mathematics"

Hamden Hall Country Day School, Hamden, Connecticut - "Discovering Symmetry and Beauty Through Excessive
Drawing"

Illinois Institute of Art in Chicago

Olga R. Beaver

Deborah J. Bergstrand

Edward B. Burger

Richard De Veaux

"Re'seaux de Neurones De'mele's"(Neural Networks Untangled)

French National Institute for Argonometric Research, Montpellier,
France

"Neural Networks Untangled"

American Statistical Association Joint Meetings, Anaheim, California

- "Hybrid Neural Networks for Process Control"

Iowa State University - "Hybrid Neural Networks for Environmental Process Control"

J.S. Hunter Lecture, International Environmetrics Meeting, Australia - Thomas Garrity
- "Number Theory and Geometry"

Hudson River Undergraduate Research Conference, Union College - "The Hypercube and Bach: Seeing Things We Can't See,
Hearing Things We Can't Hear"

Emma Willard School, Troy, NY - "Story Problems: Their History, Purposes, and Solution"

Mathematical Association of America, Northeastern Section, Spring Meeting, Keene State College (NH). - "An Introduction to Error Correcting Codes"

Science Colloquium Series, Colgate University - "Formal Fibers at Height One Prime Ideals"

Joint Mathematics Meetings, Baltimore, Maryland - "Rational Numbers and Polynomial: The Complete Story"

Undergraduate Mathematics Colloquium, Smith College - "An Algebra Secret: What They Don't Tell You in High
School"

Hudson River Undergraduate Mathematics Conference, Union College - "Integral Domains with Local Generic Formal Fibers"

Mathematics and Statistics Centennial Celebration, University of Nebraska - "New Isoperimetric Theorems"

Geometry Conference, Lehigh University

University of Pennsylvania - "Isoperimetric Theorems Redux"

Geometry Conference, Lehigh University - "The Soap Bubble Geometry Contest"

Southern Vermont College, Duke University, NCTM Meeting, Long Island,

Stuart Country Day School, Princeton University, Rotary Club, Princeton, New Jersey

Riverside Elementary School, Princeton, New Jersey

University of Hartford, Morehead State University, Cod Community College

Cedar Crest College, John Carroll University, Princeton High School - "New Classical Isoperimetric Theorems"

Duke University

Brigham Young University - "The Three Secrets of Good Teaching"

Princeton University

Oklahoma State University - "New Isoperimetric Inequalities"

Princeton University - "The Double Soap Bubble Breakthrough and Fallout 1998

Oklahoma State University - "The Isoperimetric Problem and Freshman Calculus"

Milton Academy - "Math Chat Contest TV"

Morehead State University - "Soap Bubbles `98"

Morehead State University - "Generalizing the Circle and Undergraduate Research"

Cape Cod Community College - "Acquainting Calculus Students with the Frontiers of
Research"

MAA Meeting, Brigham Young University - "The Soap Bubble Geometry Contest for Teachers"

Cedar Crest College - "Bubbles and Crystals in Surfaces and in Space"

John Carroll University - "The Double Soap Bubble Breakthrough"

Princeton University - "Acquainting Undergraduates with the Frontiers of
Research"

Princeton University

Victor E. Hill IV

Susan Loepp

Frank Morgan

- Amrita Ahuja
- Working at Monitor Company in London
- Daniel Anello
- Working as a Buyer for Filenes in Boston, Massachusetts
- Kariane Calta
- Pursuing a Ph.D. in Mathematics at the University of Chicago
- Heath Dill:
- Unknown
- Clay Elliott:
- Unknown
- Steven Ellis
- Working for Foree Consulting in Austin, Texas
- Victoria Fang:
- Unknown
- Katherine Hedden
- Volunteering with IVCF (Williams Christian Fellowship) and substitute teaching in local schools
- Mimi Huang:
- Unknown
- Edward Johnson
- Working for management consulting firm, Hamilton Consultants, in Cambridge
- Paul Kari:
- Unknown
- Jeremy Kay
- Teaching math at the Delbarton School in Morristown, New Jersey
- Adrian Ludwig:
- Unknown
- Linden Minnick
- Working for Intel in Portland, Oregon
- Jonathan Novita:
- Unknown
- Andrew Raich
- Pursuing a Ph.D. in Mathematics at the University of Wisconsin
- Catherine Riihimaki
- Pursuing a Ph.D. in Geology at the University of California, Santa Cruz
- Derek Sasaki-Scanlon
- Working as an Internet Systems Developer for Comstock in New York City
- Tristan Smith
- Intern/math teacher at the Casablanca American School in Casablanca, Morocco
- Adam Sterns:
- Unknown
- Surach Tanboon
- Pursuing a Ph.D. in Economics at Stanford University
- Andrew Watkins
- Attending Harvard Graduate School of Education in a Ed.M. program