Duke Math News - May, 1996


Ayer Wins Churchill Scholarship

Elizabeth Ayer '96, a math and computer science student, was one of about ten students nationwide to win the prestigious Churchill Scholarship. Elizabeth is an active member of the mathematical community, having served as the features editor for Vertices, the Duke science magazine, and co-founder of the Logic Club. She has participated in a number of research programs. She also helped create the ACES Online web page.

The Churchill Scholarship is sponsored by the Winston Churchill Foundation in New York City. The winners each receive a $22,000 fellowship for one year of study at Cambridge University in England. The application process is extensive. Students must be nominated by a committee at their college. The Churchill Foundation narrows down the candidates, and finally a committee at Cambridge selects the winners. The process requires an interview and personal essay.

Two Math Students Win
Goldwater Scholarships

Tung Tran '97 and Gretta Bartels '98, both double majors in math and computer science, were awarded Barry M. Goldwater Scholarships this year. Students pursuing research careers in mathematics, natural science, and some fields of engineering are eligible to compete for these grants. The winners receive scholarships for use during their junior and senior years, worth up to $7000 per year. This year the award was given to 264 sophomores and juniors from a field of 1200. Since 1989, when the scholarship was founded, 26 Duke University students, including 10 math majors, have won this distinguished award.

Faculty Scholar Award
Goes to Math Major

Robert Schneck '97 was one of three students to win the Faculty Scholar Award, the highest honor granted by the Duke University faculty. Each department nominated one or two rising seniors, who submitted essays, transcripts, and letters of recommendations. Seven applicants were chosen to be interviewed, and of those, three won the award. The criteria include high G.P.A., independent work, potential as an innovative scholar, the intention to pursue a scholarly career, and strong faculty support.

The Karl Menger Award and
the Putnam Contest

The Karl Menger Award is given primarily in recognition of performance on the Putnam exam. This year's awards go to the members of Duke's Putnam contest team, Johanna Miller '99, Noam Shazeer '98, and Tung Tran '97. The prize consists of $250 for each winner.

Karl Menger was a well-known twentieth century mathematician who held academic positions in Europe and the United States and was widely published. The Karl Menger Award was established by a gift to Duke University from George and Eva Menger-Hammond. Karl Menger was Eva Menger-Hammond's father.

The 56th Annual William Lowell Putnam Mathematical Competition was held on Saturday, December 2, 1995. The competition is open to all undergraduates in the U.S. and Canada. Each school also selects a team of three students, and their performance determines the school's ranking. A total of 2,468 students from 405 colleges and universities participated in the competition. The team of Johanna Miller, Noam Shazeer and Tung Tran placed among the top ten this past December. This is the fourth time since 1990 that a Duke team has placed in the top ten. The Duke team finished first in 1993 and second in 1990.

Overall Putnam Results: The top five teams overall were: Harvard, Cornell, MIT, the University of Toronto, and Princeton. The top five individuals were Dodis, Grossman, Kedlaya, Levin, and Ng. (Lenny Ng is from Chapel Hill, NC, and is currently attending Harvard.) Akira Negi of UNC Chapel Hill placed within the next four. The Elizabeth Lowell Putnam Prize was won by Ioana Dumitriu of NYU.

Julia Dale Prize Winners

The winners of the 1996 Julia Dale Prize for excellence in undergraduate mathematics are Elizabeth Ayer '96 and Michael Rierson '96. They have each received $350 for their hard work. Congratulations to them both!

Julia Dale was an Assistant Professor of Mathematics at Duke University who died early in her career on January 13, 1936. Friends, relatives, and colleagues of Professor Dale established the Julia Dale Memorial Fund in 1938. It was the first memorial fund established in honor of a woman member of the Duke University faculty. The fund provides income to support the Julia Dale Prize.

The Mathematical Contest in Modeling

Duke's math modeling team won a rating of ``Meritorious'' for their paper ``Using Ambient Noise Fields for Submarine Location.'' This puts their paper in the top sixteen percent nationwide. This year makes the fourth year in a row in which one of Duke's teams has earned a ``Meritorious'' rating.

This year's team consisted of Frederick Wang '99, Garrett Mitchener '99, and Gretta Bartels '98. The team's paper is available on the World Wide Web in PostScript form at http://www.duke.edu/~ wgm2/.

The math modeling contest takes place every spring, usually in February. Teams of three students at colleges across the nation spend four days working on a single problem in applied mathematics, and write a paper reporting their results. The papers are graded in the next few months and given ratings of ``Outstanding,'' ``Meritorious,'' ``Honorable Mention,'' or ``Successful Participant.'' The teams who write the top few papers are often invited to present their work at national meetings, and the ``Outstanding'' papers are published in The UMAP Journal. All undergraduates interested in mathematics, particularly applied mathematics, are encouraged to participate. Contact Dr. Scoville at ras@math.duke.edu for more information.

This year's contestants had a choice between two problems: The first was to develop a fair but efficient method of grading the math modeling contest. The second was to determine if it is possible to locate submarines under water using only the noise naturally present in the ocean.

To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

--Pierre de Fermat


AMS Convention in Iowa City

During the weekend of March 22-24, the American Mathematics Society hosted a convention in Iowa City, Iowa, where recent research was presented, covering topics in mathematics from analysis to algebra. On Saturday morning, a special session organized by Dr. Carl Cowen of Purdue focused on undergraduate research. Jason Samuels '96 was one of a handful of undergraduates from around the country to present recent original research. His paper, entitled ``,'' established bounds for the generalized diameter of various lens spaces, conjectured an equality, and discussed the topological implications for certain 4-dimensional manifolds. After the talks, all the speakers were treated to lunch by Dr. Cowen at Pizza Hut. Jason Samuels's travel expenses were paid in part by a grant from the Cigna Foundation.

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work.

--Richard Philips Feynman


Revision of Course on Nonlinear ODE's

The course description for Math 132S has been revised, and its title has been changed from ``Qualitative Theory of Differential Equations'' to ``Nonlinear Ordinary Differential Equations.'' The new description, which more closely conforms to the course offered in recent years, is given at the end of this article.

Math 132S will be taught in the fall by Dr. Harold Layton. He reports that the first part of the course will be similar to a lecture course, with problem sets and quizzes, although there will probably be more discussion and class participation than in non-seminar courses. In the second half of the semester, each student will select a project, write a brief paper on it, and make a presentation.

The texts will be Nonlinear Dynamics and Chaos (with applications to physics, biology, chemistry, and engineering) by S. H. Strogatz, and Differential Equations with Maple by K. R. Coombes et al.

For more information, contact Harold Layton by e-mail at layton@math.duke.edu.

Math 132S: Nonlinear ordinary differential equations. Theory and applications of systems of nonlinear ordinary differential equations. Topics may include qualitative behavior, numerical experiments, oscillations, bifurcations, deterministic chaos, fractal dimension of attracting sets, delay differential equations, and applications to the biological and physical sciences. Instructor: Harold Layton. Prerequisite: Mathematics 111 or 131 or the consent of the instructor. One course. Area of knowledge: QR.

In Memory of Francis J. Murray

by Seth L. Warner

Francis J. Murray, professor of mathematics at Duke from 1960 until he retired in 1980, died March 15, 1996 at Duke Hospital. Born in New York in 1911, Dr. Murray received his A.B. in 1932 and his Ph.D. in 1935 from Columbia University. He joined the faculty of Columbia in 1936 and was promoted to professor in 1949. He is best known for his series of papers with John von Neumann, from 1936 to 1943, on rings of operators, and for his proof of the complex version of the Hahn-Banach theorem of functional analysis From 1953 to 1957, he was chairman of the Committee on Applied Mathematics of the American Mathematical Society. In 1957, Dr. Murray went on leave from Columbia to become Director of Special Research in Numerical Analysis at Duke, and in that capacity served as mathematical consultant to many Army agencies. In 1967, he was awarded the Outstanding Civilian Service Medal by the U. S. Army. Dr. Murray served as Director of Undergraduate Studies from 1974 to 1980.

Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up.

--Leopold Kronecker

Math Majors and Minors
Graduating This Year

(Multiple majors are listed in parentheses.)

Mathematics First Majors

Mr. Nathan Brian Almond * Ms. Elizabeth Carol Ayer (Computer Science) * Ms. Jennifer Detlef Barba * Mr. Matthew Seth Cohen * Ms. Cammey Elizabeth Cole (Computer Science) * Mr. Michael Philip Epstein (Biological Anthropology & Anatomy) * Ms. Jessica Erdmann-Sager * Mr. Jonathan James Frankel (Economics) * Mr. David Ryan Heinen (History) * Mr. Jonathan Daniel Jackson * Mr. Jonathan Eric James * Ms. Sherri Jennifer King * Ms. Preeti Prakash Kulkarni (History) * Ms. Kimberly Page Lacey * Ms. Virginia Hart Pike (Music) * Mr. Thomas Burton Rees, III * Mr. Michael Allen Rierson * Mr. Jason Forrest Samuels * Ms. Brenda Catherine Schindler * Mr. John Louis Seelke, III (History) * Mr. Vincent Michael Sipowicz * Mr. Eric Michael Storey

Mathematics Second Majors

Ms. Susan Kelley Chasnov (Public Policy) * Mr. Burak Tamer Karacam (Economics) * Mr. Daniel Kiwon Kim (Computer Science)

Mathematics Minors

Mr. James Harold Bankston (Biology) * Mr. Kevin Randolph Gross (Biology) * Mr. Robert Jason Parsley (Mechanical Engineering)

Congratulations to all of you, and good luck in the years to come!


Solutions from Last Issue

Solution 1:

Solution 2:

Faculty Sponsor - David Kraines, dkrain@math.duke.edu
Student Editor - Garrett Mitchener, garrett@math.duke.edu

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