Department of Mathematics

Box 90320

Durham, North Carolina 27708-0320

Among the mathematics courses offered this spring, listed with those teaching them, are: Math 120S, R. Hodel; Math 121, Pardon; Math 124, M. Hodel; Math 128, Kitchen; Math 131, Donaldson; Math 135, Puckette and Scoville; Math 136, Mueller; Math 139, Yang; Math 160, Trangenstein; Math 197S, R. Hodel; Math 201, Allard; Math 204, Schoen; and Math 206, Kraines. Math 197S will be a seminar in mathematical logic with a prerequisite of Math 187 or permission of the instructor. Make your appointment with your advisor to talk about these and other courses.

Rigor is to the mathematician what morality is to man. It does not consist in proving everything, but in maintaining a sharp distinction between what is assumed and what is proved, and in endeavoring to assume as little as possible at every stage.

--Andre Weil Quoted in ``Mathematical Teaching in Universities,''Amer. Math. Monthly 61 (January 1954) 35.

There are also some experimental sections of Math 32L underway. Three sections of Math 32L are devoted to first semester students. We hope to demonstrate that we can successfully assimilate into laboratory calculus students who have completed one semester of calculus in the traditional format. These sections will be using MathCAD for Windows.

CIGNA asks that your resume be delivered to the Career Development Center by December 7. A CIGNA representative will be on campus on February 9 and 10 to discuss both permanent employment possibilities and summer internships. CIGNA had a Duke math major last summer in its intern program.

Prudential seeks sophomores and juniors for its summer program and seniors and graduate students for full time positions in their Actuarial Executive Development Program. Resumes should be sent to Paul Piechnik ASA, Prudential Insurance Company of America, 213 Washington St., Newark, NJ 07102-2992.

Derivatives are not just for calculus any more. According to Terry Turner of First Union National Bank of Charlotte, ``derivative products are the newest and most intellectually challenging of financial products'' He will visit Duke on Tuesday, November 1, to interview seniors and graduate students for associate positions. A successful candidate ``will need to be aggressive, highly motivated and have excellent communications, math, computer and analytical skills. No prior banking experience is required.''

I am looking for one or possibly two more people to help with programming. I need someone to work with refinement of a graphical user interface and someone to help with 3D graphics. Both require a background in object-oriented programming (C++), and the latter could benefit with a background in geometry. (I need to visualize vector fields in clever ways.) Contact John A. Trangenstein at johnt@math.duke.edu for more information.

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious...

--Eugene Wigner

Quoted in ``The Unreasonable Effectiveness

of Mathematics in the Natural Sciences,''

Comm. on Pure and Appl. Math. 13 (February 1960) 2.

DUMU plans to sponsor the next undergraduate mathematics lecture early in the spring term. This lecture series is supported in part by the Cigna Foundation.

Mathematics and Music, the most sharply contrasted fields of intellectual activity which one can discover, and yet bound together, supporting one another as if they would demonstrate the hidden bond which draws together all activities of our mind, and which also in the revelations of artistic genius leads us to surmise unconscious expressions of a mysteriously active intelligence.

--H. Helmholtz

Quoted in R.C. Archibald, ``Mathematicians and Music,'' Amer. Math. Monthly, 31 (January 1924) 1.

- Dax Mitchell, The Mathematics of Elastic Bands in Honey

(Evolution of curves in the plane according to curvature) - David Mills, Newton's Method on Banach Spaces

(Generalization of Newton's method for finding zeroes of functions to infinite dimensions together with numerical applications) - Sharad Chaudhary, We are the Robots

(Using algebraic geometry, in particular Groebner bases, to solve problems arising from robotics) - Rick Clelland, Godunov, MD, and Some of Greg's Appliances

(Using partial differential equations and numerical methods to study problems arising from granular flow) - Leon Moser, A Tale of Three Cities: Introduction to Automatic Groups

(A visual approach to the word problem in group theory as well as a geometric characterization of automatic groups) - Clarence Burg, Data Compression: Breaking the Entropy Barrier?

(A description of some approaches to data compression together with considerations of each approach's effectiveness)

Future speakers for the Fall will be Paul Horja, Kevin Knudson, Emily Puckette, Chris Michael, Jim Rolf, and Andrew Barnes. Everybody is welcome to come and hear these folks give their talks. The Graduate General Seminar meets every Friday at 4:00 in Room 114 of the Math-Physics building.

Following Fuqua, I joined the firm of Price Waterhouse LLp in Washington, DC as a financial auditor. I am still with Price Waterhouse as the Manager in charge of Information Systems Auditing for the Washington, DC practice office.

I was glad to hear that the math department at Duke is flourishing. Here is a brief synopsis of my life since Duke.

I graduated in 1985 with a BS in Mechanical Engineering. From there I went to George Washington University where I completed my MS work in 1987. That year I was also married and moved to Virginia to work at the NASA Langley Research Center in the Spacecraft Controls Branch.

In 1992-1993 I spent a year taking classes at NCSU toward my PhD in the area of spacecraft controls. I am currently back at NASA working on my dissertation. I have recently transferred to the Vehicle Analysis Branch where I am working on the control system for a single-stage rocket designed to be an eventual replacement for the Space Shuttle.

I have a 14-month old son and I enjoy sailing and Ultimate Frisbee.

Though I am now a professional philosopher, my mathematical training has hardly proved worthless. For one thing, logic plays a central role in current philosophical work, and my general facility with mathematics has been invaluable.

In 1991 I entered the doctoral program in History of Science at Johns Hopkins University, where I am now researching a dissertation on the history of seismology and earthquake engineering in the United States from the 1860s to the 1930s. My eventual career objective is to become a professor of history.

I am presently a John Wesley Young Research Instructor at Dartmouth College. My current research focuses on image compression and on medical imaging applications. My Duke mathematics education was excellent preparation for my subsequent work, and my attending Duke would not have been possible but for the NC mathematics scholarship.

Congratulations on the department's recent Putnam performance!

I'm getting kind of tired of private industry and am seriously looking into going back to school. We'll see which schools accept me before I know where I'm going (or what I'll be doing.) :-)

Anyway, it was great to get some academic news from the alma mater. I keep up with the athletics so much, it's easy to forget the reason I chose Duke in the first place.

I am also spending a lot of time involved in outdoor adventures and outdoor education. I have been working for a group called Cal Adventures, leading backpacking, sea kayaking and rockclimbing trips. I have also been involved with the UC hiking club, doing a lot of backpacking and rockclimbing on my own. Last spring my roommate and I climbed El Capitan in Yosemite Valley. This past summer I returned to Duke to work at the TIP program, teaching Algebra II to academically gifted kids. It was good to be back at Duke, if only for a short month. (Basically my life is math and rockclimbing.)

## NICOLAS BOURBAKI

Most mathematicians today are still convinced that Nicolas Bourbaki does not exist. Instead, they consider Bourbaki simply to be the pseudonym for a group of French mathematicians. Mr. Boas, executive editor of the Mathematical Reviews, went so far as to print this opinion in an article for the Encyclopedia Britannica. The publishers of the Encyclopedia Britannica soon found themselves in an acutely embarrassing position, for they received a scalding letter signed by Nicolas Bourbaki in which he declared that he was not about to allow anyone to question his right to exist. And to avenge himself on Boas, Bourbaki began to circulate the rumour that the mathematician Boas did not exist, rather that the initials B.O.A.S. were simply used as a pseudonym for a group of the Mathematical Reviews' editors.

--Henri Cartan Quoted in ``Nicolas Bourbaki and Contemporary Mathematics,''

Math. Intell. 2 (No. 4, 1980) 175.

**See also** the previous issue of Duke Math News, dated August 1994, and the next issue, dated February 1995.