August 1994

Duke Math News

Duke University
Department of Mathematics
Box 90320
Durham, North Carolina 27708-0320


Please take some time to read this issue about your mathematics department. We hope that Duke Math News will make a regular appearance in your mailbox. We would like to include news about you and your activities in future issues. Please send your mailing and/or e-mail address and any information you would like to share to Joan McLaughlin, Box 90320, Durham, NC 27708, phone 919-660-2807 or use e-mail:


This year 38 students graduated from Duke with a major in math. Three of these undergraduates will be beginning graduate school in mathematics: Russell Jackson at UNC-Chapel Hill; John Kelley at UCLA; and Jeff Vanderkam at Princeton. Alex Hartemink will begin studies for a MPhil in Economics at Oxford as a Rhodes Scholar. Several of our majors have taken jobs in actuarial work and financial analysis. One student will become an officer in the USAF specializing in logistics. Other majors will pursue graduate studies in medical school, biomedical engineering, physical oceanography, and civil and environmental engineering.

The CIGNA Foundation has once again made a generous contribution of $7500 to the Duke Math Department. Last year, several students took advantage of our offer to pay their actuarial exam registration fees and two of our majors interned with CIGNA in Philadelphia last summer. The CIGNA Foundation contribution has allowed us to continue our popular Undergraduate Mathematics Colloquium Series with Persi Diaconis from Harvard in the fall of 1993 and Joseph Gallian from Minnesota the spring of 1994. This series will continue with Robert Devaney giving a lecture on the Mandelbrot set and dynamical systems on Wednesday, September 21, 1994.

These funds have also been used to cover expenses of undergraduates who attended national mathematical society meetings for the purpose of reading papers and of accepting awards. They have provided nine majors with complementary memberships to the Mathematical Association of America.


Hello everybody! I'm Paul Dreyer, and on behalf of the Duke University Mathematics Union, I would like to welcome all mathematics students old and new to Duke for what should be an exciting year. I have just returned from a year studying abroad in England and I am really psyched to get the Union running again.

Now in its third year, the Duke University Mathematics Union (or DUMU for short, pronounced "doo-moo") provides students with an interest in mathematics the opportunity to learn more about the subject outside the classroom. Several undergraduate students and professors have discussed their research on topics spanning the mathematics spectrum. DUMU also provides information on careers and summer research internships in mathematics. This fall, we will hold the third annual Duke University Mathematics Contest, a one-day student-run contest for high schools from throughout the southeast.

Most importantly, DUMU is FUN. We now have a lounge for our use and I plan to organize some social events and possibly some friendly competition against the other club in our building, the Society for Physics Students. In any case, we are going to have a great year ahead of us, and I hope you will become a part of it by joining DUMU. The first meeting will be during the first week of September, so be sure to keep your eyes open for announcements.

If you have any questions, I can be reached by e-mail at Box 91628 or by e-mail at I hope to hear from you soon!


On the first Saturday of December last winter, over 3000 undergraduates around the country participated in the 53rd annual William Lowell Putnam Mathematics Competition for six hours. Students struggled over 12 very challenging math problems to win honors for themselves and their school. Harvard University had been a dominating presence for most of the history of the Competition, including 8 straight first place finishes. But their streak was broken this time by stellar performances from Freshman Andrew Dittmer, Junior Craig Gentry and Senior Captain Jeff Vanderkam. When the news of the victory leaked out in early March, team coach Professor Greg Lawler and associate chairman David Kraines ordered team shirts displaying one of the problems and the announcement of victory. The news spread from the local papers and appeared in an amusing story in the Lexington Herald-Leader. Governor Jim Hunt sent a warm congratulatory note to the department. President Nan Koehane awarded the Putnam prize money to the team members and then ``retired'' Jeff's shirt citing his valedictorian status, his second place individual finish in the 1992 Putnam Competition and his several publications while at Duke.


For years, the word was that young Americans couldn't do math: In a 1991 assessment of math skills in 15 countries, the average test scores of America's 13-year-olds lagged behind all but Jordan's. But while critics have long lamented the educational achievement of the average U.S. student, America's best are as bright as whiz kids anywhere. Last week, six American high school students returned triumphantly from the International Mathematical Olympiad in Hong Kong. There, the U.S. team out-calculated math geniuses from 69 countries, including perennial powerhouses Russia and China.

The Americans became the first team in the competition's 35-year history to achieve a perfect score on the Olympiad's nine-hour test, which included this challenge: ``Show that there exists a set A of positive integers with the following property: For any infinite set S of primes there exist two positive integers m in A and n not in A each of which is a product of k distinct elements of S for some k greater than 1.'' (Half the Chinese team, which trained for a year, missed that one.)
( U.S. News August 1, 1994)

One of these Olympians, Noam Shazeer of Swampscott, MA, will enter Trinity College this fall. Noam will be the third gold medalist and the fourth Olympian to enter Duke since 1988.


As 4 p.m. on Wednesday, September 21, Robert Devaney will give a multi-media talk in the Undergraduate Mathematics Lecture Series entitled The Fractal Geometry of the Mandelbrot Set. Professor Devaney, of Boston University, is a distinguished researcher in dynamical systems and a very popular lecturer. See what goes into generating the pretty pictures that you can see in many commercial advertisements. Check out the display case in the Math-Physics lobby soon for more details.
Before you enter on the study of law a sufficient ground work must be laid. . . . Mathematics and natural philosophy are so useful in the most familiar occurrences of life and are so peculiarly engaging and delightful as would induce everyone to wish an acquaintance with them. Besides this, the faculties of the mind, like the members of a body, are strengthened and improved by exercise. Mathematical reasoning and deductions are, therefore, a fine preparation for investigating the abstruse speculations of the law.
                   Quoted in Cajori's Teaching and
                   History of Mathematics in the 
                   U.S.(Washington, 1890), p.35.



The Mathematics Department at Duke University congratulates four PhD graduates of spring 1994. They are Emily Puckette, Henry Suters, Vince Moulton, and Christopher Peterson.

Emily Puckette's thesis title is Critical Exponents for Intersections of Random Walks in Dimensions Between 1 and 2. As for her immediate plans, she will remain at Duke, teaching in the Math Department and working with Project NExT (New Experiences in Teaching).

A Numerical Study of the Instability of Vortex Rings with Swirl is Henry Suters' thesis title. He has a job at Carson-Newman College in Jefferson City, TN.

Vince Moulton, whose thesis is entitled Vector Braids, will hold a postdoctoral position at the University of Bielefeld in Germany.

Chris Peterson's official title at Notre Dame is Visiting Assistant Professor. His thesis title is Applications of Liaison Theory to Schemes Supported on Lines, Growth of the Deficiency Module, and Low Rank Vector Bundles.


Sharad Chaudhary has been nominated and selected for a teaching fellow appointment for the Center for Teaching and Learning at Duke University for 1994-1995. Departments from Duke submitted the recommendations. There were 23 applications from 15 departments. Only six fellows were selected.

Responsibilities as a Fellow will begin Tuesday, August 23. Recipients will coordinate aspects of the Fall, 1994 Orientation for graduate students on August 26 and 27, stressing pedagogical issues and dilemmas. They will serve as small group discussion leaders in the afternoon. Fall semester, participants will meet twice a week with Center staff to plan a follow-up session in their department, using what they learned at the Orientation Program, emphasizing innovative approaches in the teaching and learning process. Duties will cover only five or six months. The appointment also includes a stipend of $1000 for professional development.

Kevin Knudson and Keener Hughen are this year's recipients of the L.P. and Barbara Smith Award for Excellence in Teaching. This award was established by Smith, Supervisor of Freshman Instruction (predecessor of Lewis Blake). Professor Smith set up the award in April, 1982 to give graduate students recognition for being good teachers. It also includes a cash prize.


  NAME                        NAME OF INSTITUTION
Timothy D. Culver B.S., 1994 University of Notre Dame Charles D. Fargason B.A., 1994 Rice University Benjamin W. McKay B.S., 1993, University of Toronto, Canada Alexander M. Solodovnikov Diploma, 1993, Odessa State University, Ukraine Laura A. Taalman B.S., 1994 University of Chicago Kirsten E. Travers B.S., 1994, St. John's College, Oxford University Liya A. Zhornitskaya Diploma, 1993 Moscow State University


This fall, Professors Richard Hain, Gregory Lawler, and William Pardon will be on sabbatical leave. Professor Hain will visit the Institute for Advanced Study in Princeton and Professor Lawler will join the University of British Columbia in Vancouver each for the full academic year. Professor Pardon will remain in Durham in the fall and resume his teaching at Duke in the spring.

Professors Robert Bryant, David Morrison, and David A. Smith have returned to Duke after their own busy sabbatical leaves.

Among the visiting faculty at Duke this year are Professor Xabier Garaizer from NCSU and George Majda from Ohio State U. Each are experts in differential equations.


By John Harer

Greetings to all. I begin my term as department chair in a time of budget tightening within the division of Arts and Sciences. Dean Weintraub has asked all department chairs and program directors to submit proposals for 2% and 5% permanent budget cuts for the coming fiscal year. This is motivated by the fact that against a reserve of $2.3 million, the division is running at a $1.1 million deficit this year and a projected $2 million deficit next year. So far we don't know what affect this will have on our program, but a 5% cut will certainly result in the loss of at least one faculty position (and the corresponding course offerings). But Duke is in better shape than many other schools. The Berkeley newsletter from fall 1993 talks about another round of 5-8% cuts and schools like Columbia, Cornell, Stanford, Chicago, ... have had to face much larger budget problems than ours. We are all hoping that this is a one time thing!

This year we will begin a new and exciting program by hiring the first of three Research Assistant Professors. These will be three year, non-renewable, positions for new PhD's in Mathematics. Programs like this exist at most major Universities where they provide a great source of stimulation for the research and teaching environments of the departments. The first of these positions will be funded by a donation from the late Professor William Elliott, who served as department chair from 1929 until 1937 and retired in 1968. The other two will be paid for by the University. Since they will be replaced as they come to an end, we will hire one new person each year once the program is established.

I wish you all a good year.

See also the next issue of Duke Math News, dated October 1994.