Department of Mathematics

Box 90320

Durham, North Carolina 27708-0320

Each spring, the department takes pride in acknowledging the accomplishments of its majors. You are invited to attend the awards ceremony following a talk by graduating senior and DUMU president, Paul Dreyer, at 2:00 on Thursday, April 27, in the Math-Physics Building, room 120. Refreshments will follow.

Freshman Noam Shazeer placed sixth among the 2314 contestants in the 55th annual William Lowell Putnam Mathematical Competition. Sophomore Robert R. Schneck ranked 57th, just one point shy of Honorable Mention. Two other freshmen, Gretta Bartels and James Harrington, ranked in the top 15%. The team members, Paul A. Dreyer, Jr. '95, Tung T. Tran '97, and Noam M. Shazeer '98, and eight other Duke students worked individually on 12 challenging mathematics problems for six hours on December 3, 1995. According to this year's coach, associate professor David Kraines, the team finished a bit higher than the [men's] basketball team, just as last year.

Undergraduates at more than 400 colleges and universities throughout the United States and Canada participate in the Putnam Competition each year. The median scores on this prestigious exam have ranged between 2 and 10 out of a possible 120 points and was 4 points this year. Harvard University won the Competition this year for the 18th time. Last year, Duke became one of only 15 different institutions to have captured first place since the Competition began in 1938.

On Friday, March 31, Noam Shazeer was honored with a check for $100 from the Mathematical Association of America at the southeast sectional meeting in Asheville as the highest Putnam scorer in the area. In addition, Noam will receive $500 from the American Mathematical Society.

At the awards ceremony on Thursday, April 27, the top three Putnam contestants from Duke, James Harrington, Robert Schneck and Noam Shazeer, will each receive the $250 Karl Menger Award. Menger was a well-known twentieth century mathematician who held academic positions in Europe and the U.S. and was widely published. The Karl Menger Award was established by a gift to Duke University from George and Eva Menger-Hammond, the daughter of Karl Menger.

Julia Dale was an Assistant Professor of Mathematics at Duke University who died early in her career on January 13, 1936. In her honor, the department of mathematics awards cash prizes to those seniors who have most clearly demonstrated excellence in mathematics. The winners this year, Paul A. Dreyer Jr. and Craig B. Gentry, will each receive $350. A second place award of $200 will be given to Mark Miller.

Math majors, Elizabeth Ayer and Michael Rierson, were awarded the Barry M. Goldwater scholarship for excellence in education. This scholarship pays up to $7,000 to students who have demonstrated special talents in mathematics, science and engineering. This year, of the 285 scholarships awarded, 37 were to mathematics majors. Since the inauguration of the scholarship in 1989, eight math majors from Duke have received this coveted award.

The mathematics department entered two teams in the 1995 Mathematical Contest in Modeling. This contest, organized by the Consortium for Mathematics and its Applications and supported in part by the National Security Agency,``offers students the opportunity to compete in a team setting using applied mathematics in the solving of real world problems'' The students picked up their problems at 12:01 a.m. on Friday, February 17, and turned in their elaborate reports at 5 p.m. on Monday, February 20. The team of Nathan Bronson, Paul Dreyer, and Scott Harrington produced a computer algorithm supported by solid mathematical reasoning which was one of the fifteen percent declared Meritorious. The team of Robert Schneck, Noam Shazeer and Tung Tran received Honorable Mention for their clever contribution to this problem.

Over the weekend of March 25 in Austin, Texas, the undergraduate Duke Programming Team made up of Gregory Badros '95, Nathan Bronson '96, and Scott Harrington '95 won the IEEE National Programming contest. This is a two day contest in which each team writes a program that competes against programs written by other teams. Scott and Nate are triple Math, CPS and EE majors while Greg is a double Math and CPS major.

The department offers its majors the opportunity for graduation with Latin honors by honors project. Students are expected to make their intentions known to the Director of Undergraduate Studies in the spring of their junior year. The student will usually take an independent study course (Math 193-194) with their faculty advisor as they strive to produce a paper demonstrating significant independent work in mathematics.

This year, seniors Paul Dreyer and Paul Koss have successfully completed undergraduate honors projects. Paul Koss will present his results at 4 PM on Tuesday, April 25, and Paul Dreyer will make his presentation at 2 PM on Thursday, April 27, each in room 120 of the Math-Physics building. All intersted parties are encouraged to attend.

Dreyer's paper is entitled Knot Theory and the Human Pretzel Game. Assume a group of people randomly join hands. What is the likelihood of various topologically distinct knots and links being formed? Professor John Harer has been Dreyer's advisor.

Koss has studied the iterated Prisoner's Dilemma, a classic paradigm of Game Theory. What strategies would help ensure that cooperation will evolve when selfishness has a greater short term appeal? Koss has devised modifications of the Tit For Tat strategy which performs quite well in a noisy environment. Professor David Kraines has been Koss's advisor.

Math majors Jason Samuels '96 and Tung Tran '97 have been invited to participate in REU programs this summer. Jason will study at Tulane University in an eight week program which emphasizes Differential Geometry. Tung will work for six weeks at Rose-Hulman University on Computational Group Theory. Each will receive a stipend of at least $2000 in addition to expenses for room and board. Tung Tran and David Vanderweide '95 each participated in the REU program at the University of Washington during the summer of 1994.

Real estate in hyperbolic space? Investment opportunities for the '90's. On March 20, real estate agent, Mel Slugbate described some of the fascinating world of hyperbolic space. Slugbate, who bears an uncanny resemblance to Professor Colin Adams of Williams College, showed the appreciative audience that, in the hyperbolic world, the notion of distances and areas make living far more spacious. The Undergraduate Mathematics Colloquium series is supported in part by a grant from the Cigna Foundation.

Have you gone surfing lately? Check out the new pages provided for first-year students on the World Wide Web. We now have detailed information on placement, AP credit, transfer credit, mathematical assistance, courses, and recent changes. There have already been some incoming students and parents who have found this information, even though it was not advertised in any mailings from Duke! As you surf, you can make a contribution by thinking of ways to improve and expand the information that's there. Please pass along your suggestions to Lewis Blake.

This year fifty-nine students will graduate with a major in mathematics. Of these, twenty-nine are double majors and six have triple majors. Economics was by far the most popular second major, with ten students.

The graduating class and their families will be honored at a luncheon on Sunday, May 14, in Room 157 of the Math Physics Building.

* Prerequisites:* Mathematics 103 or the equivalent. (Many upper-level courses assume programming experience at the level of Computer Science 1. Students without programming experience are encouraged to take Computer Science 4.)

*Minor requirements:* Five courses in mathematics to include either Mathematics 104 or Mathematics 111, but not both, and four additional courses in mathematics numbered above 111, to include at least one course (or its equivalent) selected from the following: Mathematics 121, 132S, 135, 139, 160, 181, 187, and courses in Mathematics numbered at the 200 level.

* Rationale.* As with the major, a preparation in calculus is required. Thus the prerequisite for the minor is mathematics through MTH 103. Furthermore, since some majors already require several courses in mathematics, and students pursing these majors are likely to minor in mathematics, at least five courses beyond MTH 103 are needed to formulate a meaningful minor in mathematics. (For example, Chemistry requires MTH 31, 32, and 103; Computer Science (BS) requires MTH 31, 32, 103, 104 and two additional courses in mathematics; the School of Engineering requires MTH 31, 32, 103, and at least one additional course in mathematics; Physics requires MTH 31, 32, 103, and 111.)

In addition, at least one course of the five numbered above MTH 111 must be selected from courses that the department judges to be suitably challenging and central to modern mathematical science.

* Advising.* A student minoring in mathematics will usually receive formal advising in the department of his or her major. However, the Department of Mathematics will provide supplementary advice through its publications and faculty.

The Handbook for Mathematics Majors will be revised as a * Handbook for Mathematics Majors and Minors*. The revised Handbook will contain recommended course selections to complement majors in other disciplines, and that information will also be made available through the Mathematics Department World Wide Web (WWW) site. Both the Handbook and the WWW site will contain statements that encourage students to seek advice from the mathematics faculty or to consult the Director of Undergraduate Studies for advice or for referral to an appropriate member of the mathematics faculty.

Clarence Burg and Sukhee Han expect to get their MA degrees this spring while Khaled Furati and Keener Hughen plan to get their Ph.D. degrees by September.

Emily Puckette has accepted a position at Occidental College. She received her Ph.D. from Duke in 1994 and has been a part-time instructor here for the past year.

The entering graduate class consists of six students from some distinguished undergraduate programs around the country. They are Phillip Riley, who joins us from the University of Chicago; Ben Jones, from the University of Massachusetts at Amherst; Andrew Schretter, from the University of Georgia at Athens; James Ott, from the University of Kentucky; Aaron Ashford, from MIT; and Ted Welsh, from Williams College. Their expressed interests range from biomathematics and dynamical systems to geometric topology and differential geometry.

Andrea Bertozzi has recently accepted a position as associate professor of mathematics. She wrote her Ph.D. thesis with Andrew Majda, a prominent applied mathematician at Princeton University and then taught for four years at the University of Chicago. Dr. Bertozzi's research has earned her several honors, including an N.S.F. Postdoctoral Fellowship and an Alfred P. Sloan Research Fellowship. Most of her recent work is concerned with the behavior of thin films of viscous liquid (like a liquid spilled on a table) and especially the pinching off of droplets. She will be on leave in 1995-96 to continue her research as Maria Goeppert-Mayer Distinguished Scholar at the Argonne Lab and will join our department in fall, 1996.

Former Duke professor, William W. Elliott, created an endowment fund to support a research assistant professorship in the mathematics department. Elliott joined the math department in 1925, just one year after the University was created. He retired in 1968 and died in 1993.

Dr. David Reed has accepted a three year term as the first Elliott research assistant professor. Reed completed his undergraduate work at the University of Chicago and received his D. Phil from Oxford University. His area of expertise is in the topology of conjugate algebraic varieties.

Professor John Harer will continue as department chair with professor William Pardon as associate chair. Professor Richard Hain will be the Director of Graduate Studies, associate professor Harold Layton will be Director of Undergraduate Studies and assistant professor of the practice Lewis Blake will continue as Supervisor of First Year Instruction.

After forty years of distinguished service to Duke University, including eleven years as department chair, Professor Seth Warner will retire this summer. Warner received his B.S. from Yale and his Ph.D. from Harvard. In addition to numerous journal articles, Warner has written several books, including a popular text on abstract algebra.

Richard Hain, Gregory Lawler and David Morrison will return to teaching this fall after their sabbatical leaves. David Kraines will be on sabbatical leave for the year and William Allard, Richard Hodel, David Schaeffer, Chad Schoen, and Fang Yang Zheng will each be on leave during a term in 1995-96.

Please send information about your plans for the summer and/or next year to Joan McLaughlin (joan@math.duke.edu). We would like to share your news in our next issue.

**See also** the previous issue of Duke Math News, dated February 1995 and the next issue, dated October 1995.