Duke Math News - March 1996


Three Graduate Students Win NSF Fellowships

Three of our finishing doctoral students, Jeanne Clelland, Rick Clelland, and Kevin Knudson, were awarded Postdoctoral Fellowships by the National Science Foundation. Only about 30 were awarded in mathematics nationally, so it is quite exceptional that three were awarded to Duke students.

Jeanne will take her fellowship at the Institute for Advanced Study in Princeton. She will work with Professor Phillip Griffiths, a former provost of Duke, and the current director of the Institute for Advanced Study. Her interests are in differential geometry and differential equations.

Rick Clelland will probably take his fellowship at SUNY Stony Brook where he will will work with Professor James Glimm. His interests are in numerical analysis and applied mathematics.

Kevin Knudson will take his fellowship at Northwestern University. He will work with Professor Andrei Suslin. His interests are in algebra and topology. A summary of his thesis follows this article.

Each year, the NSF awards between 30 and 40 mathematical sciences postdoctoral fellowships. American citizens and green card holders who are no more than five years beyond their Ph.D. are eligible. The awards my be used at any accredited institution in the United States in one of two options: either two years full-time research, or the instructorship option of one year full-time research and two years half-time research, half-time teaching. The fellowship also provides for three summers of support.

The application process includes writing a research proposal and finding a senior mathematician to serve as sponsor.

Kevin Knudson's Thesis
My sponsor is Professor Andrei Suslin at Northwestern University in Evanston, Illinois. Prof. Suslin is one of the world's leading researchers in algebraic K-theory. My dissertation is a study of the homology of special linear groups defined over Laurent polynomial rings (polynomials in t and over a field F). Along the way, I had to compute the homology of ; it turns out that homologically, is the same as . This is an unstable version of homotopy invariance in algebraic K-theory: the K-groups of are the same as those of F. I was also able to obtain some information about the low dimensional homology groups of .

Teaching Awards

by Lewis Blake

The winners of the 1994-1995 L.P. and Barbara Smith Award for Teaching Excellence are Beth Brooks and Jim Rolf. Both Beth and Jim were recognized for providing students with outstanding, enthusiastic teaching for a number of terms. This award carries with it both the recognition by the math department of their fine teaching and also a substantial monetary prize.

Beth came to this department from Florida, where she majored in math and computer science at Stetson University and was inducted into the Phi Beta Kappa honor society. At Duke she quickly distinguished herself as an excellent calculus lab assistant and went on the earn a reputation as an excellent classroom instructor. Her contributions to teaching calculus extend beyond the classroom, as evidenced by her participation in curricular review and reform. She has volunteered to conduct an experimental class, and she has been a valuable member of several calculus committees. She expects to finish her graduate work in 1996, and her goal is to find employment in a liberal arts college.

Jim studied mathematics at Baylor, and after four years of math, he went in a different direction. He entered Southwestern Baptist Theological Seminary, where he received a masters degree in divinity. He developed his teaching skills as a high school math teacher for a year and a half. He left that position to come to Duke, where he expects to finish in the next year. He has been a popular teacher among the undergraduates, and he has taught a variety of courses for the math department. He enjoys teaching, and after graduation he will look for a permanent teaching job.

The award itself was made possible by a generous donation from Captain L.P. and Barbara Smith, who established the fund in 1981. Captain Smith had been Supervisor of First-year Instruction in the department for many years prior to his departure in 1981. In setting up the award, the Smiths realized their goal of providing a substantial reward for those graduate students who work hard to become fine teachers. Each year one or two (or rarely three) graduate students are chosen for this teaching prize. Over the past 15 years, there have been 26 winners of the Award.

New Course in Financial Mathematics for Fall '96

Math 197S: Mathematics of Finance. Prerequisite: Math 135 (Probability) or equivalent. Taught by Lester Coyle.

Math 197S is an introduction to mathematical models used in finance with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models are derived from basic economic principles, and to provide the necessary probabilistic tools for their analysis.

Topics include trading strategies, hedging strategies, Wiener processes, Black-Scholes analysis, numerical procedures, and interest rate derivative securities.

Course on PDE's in Classical Physics

Math 211: Mathematical Methods in Physics and Engineering I: Partial Differential Equations and their Applications. Prerequisite: Math 114. Taught by John T. Scheick.

Math 211 will be a study of partial differential equations which arise from problems in engineering and physics. The primary tools for the construction of solutions will be eigenfunction expansions and Green's functions. Students will explore various representations of the solutions with the aim of understanding the qualitative aspects of the solutions as well as the suitability of the solutions for computations. In addition to developing computational skills, emphasis will be placed on understanding the underlying principles which unify the ideas and methods. Particular emphasis will be given to problems with source terms and inhomogenous boundary conditions.

Math 211 was previously offered as Math 230. Contrary to the current Duke Bulletin, Math 114 or its equivalent will be a prerequisite.

New Course on Fractal Geometry

Math 239: Fractal Geometry. For undergraduates, the prerequisite is Math 139 or Math 203. Taught by Greg Lawler.

Math 239 will introduce mathematical definitions of fractional dimension (Hausdorff, box, packing) and then investigate the use of fractals in mathematics, physics, computer science, and other areas. The second part of the course will consist of student presentations on examples of fractals; all students will write a term paper and make a presentation on their material.

The course is open to undergraduate math majors, mathematics graduate students, and graduate students in other departments.

This course was last taught in Fall 1993; two different master's theses in computer science had their roots in term papers presented in this class.

For more information, contact Greg Lawler.


Virginia Tech Contest

The results of the 1995 Virginia Tech Math Contest have been announced. Duke freshman Johanna Miller was the top scorer of the 175 contestants from 32 colleges and universities in the South. Akira Negi from UNC was second. Of the eight Duke undergrads who participated, six were in the top 17%. Johanna, Michael Rierson, and Tung Tran received certificates, and Johanna received a cash prize.

Mathematics Advanced Study Semesters

Pennsylvania State University announces a yearly semester-long intensive program for undergraduate students who are seriously interested in pursuing a career in mathematics. The Mathematics Advanced Study Semesters program (MASS) will start in Fall 1996.

The main goal of the program is to contribute to the future health of the U.S. mathematics research community by creating a highly charged, interactive, and friendly environment among a ``critical mass'' of talented and motivated undergraduates, a committed group of strong research faculty, and top graduate students.

The principal part of the program will consist of three core courses and a weekly working seminar. The courses are chosen from major areas in Algebra/Number Theory, Analysis, and Geometry/Topology respectively, and are specially designed and offered exclusively to MASS participants.

Additional features will include challenging problems from various fields of mathematics, colloquium-type lectures by visiting and resident mathematicians, and mathematical projects involving creative use of computers. The participants will be able to take part in the Putnam Competition on behalf of their home university while at the MASS Program.

The information about MASS program and the application materials can be obtained from the MASS home page on the World Wide Web at the URL: http://www.math.psu.edu/mass/

Notes from the DUS

Greetings to all mathematics majors and minors---and especially to newly-declared majors and minors!

Recently-declared majors and minors may pick up a copy of the 1995--1996 edition of the Handbook for Mathematics Majors and Minors in Room 217, Physics Building. The Handbook can be accessed electronically on the department's web site (http://www.math.duke.edu), under the heading ``Information for Math Majors and Minors.''

Registration for Fall 1996

Registration for the fall semester begins on Wednesday, March 27. As in former semesters, there will be an information session in which faculty teaching upper-level courses in the fall term will provide a brief introduction to those courses. Details will be announced after spring break.

Mathematics courses to be offered in the fall semester, with the scheduled instructors, include:

121, D. Reed; 123S, Harer; 124, Trangenstein; 131, Zheng & M. Reed; 132S, Layton; 135, Allard & Wolpert (ISDS); 139, Schaeffer; 149S, Kraines; 187, R. Hodel; 188, R. Hodel, Loveland (CPS), & Posy (PHL); 197S, Coyle; 200, Schoen; 203, M. Reed; 211, Scheick; 217, Burdick (ISDS); 231, Venakides; 238, Bertozzi; 239, Lawler; 241, Zhou.

Two sections of MTH 131 and MTH 135 will be offered. Mathematics 188, a new course called Logic and its Applications, will be team-taught by faculty from the Mathematics, Computer Science, and Philosophy Departments. MTH 197, Seminar in Mathematics, will be sub-titled Mathematics of Finance. MTH 238, Topics in Applied Mathematics, will be sub-titled Introduction to Incompressible Hydrodynamics: A Mathematical Perspective. MTH 239, Topics in Applied Mathematics, will be sub-titled Fractal Geometry.

Owing to a mathematics graduate course renumbering, MTH 211 is now Mathematical Methods in Physics and Engineering I (formerly MTH 230); MTH 217 is Linear Models (formerly MTH 241); MTH 231 is Ordinary Differential Equations (formerly MTH 296); MTH 238 and MTH 239 are unchanged; and MTH 241 is Real Analysis I (formerly MTH 281).

Graduate courses numbered below 245 are appropriate in many instances for undergraduate students.


The department has decided to change the way that advisors are assigned. Currently, most faculty members have two or three advisees. In the future there will be an advising committee of about eight faculty members, and each advisor will be assigned about eight advisees. Advisors will serve on the committee for two years, starting in the spring term. The new advising program will be phased in so that existing advisor-advisee relationships are not disturbed.

Latin Honors

Are you interested in seeking graduation with Latin Honors by way of an honors project? If you expect to graduate in spring 1997, then you must apply this spring to pursue a project during the 1996-97 school year. See additional requirements in the Handbook for Mathematics Majors and Minors, page 23.

-- Harold Layton



Solutions from December

Solution 1:

Solution 2:

New Problems

Problem 1: The Trouble with Triangular Squares

Find the first five numbers that are both perfect squares and perfect triangles. (Square numbers are of the form n x n and triangular numbers are of the form 1+2+3+...+n.)

Problem 2: Just for Fun

Express the speed of light in a vacuum in units of furlongs per fortnight.

A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction.

--Count Lev Nikolgevich Tolstoy


This newsletter is open to contributions from students, both graduate and undergraduate, and faculty. Information about the Mathematics Department, classes, degrees, and projects would all make good contributions. We are also looking for quotes, and of course problems and puzzles. Please send any ideas you might have to the editor, Garrett Mitchener: wgm2@acpub.duke.edu or talk to Harold Layton in the Mathematics Department.

Read It on the Web

Current and previous issues of Duke Math News are available online through the World Wide Web at: http://www.math.duke.edu

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

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