October 1994

Duke Math News

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


It is time to think about courses to take in the spring. Dick Scoville, Director of Undergraduate Studies, will send out information about advising toward the middle of October. Look over your check sheets and review your long range plan. The Handbook for Math Majors suggests courses to take for various career goals. Instructors of most of the courses for mathematics majors will discuss their plans for these courses at a meeting in Room 120, Math-Physics Building at 4:00 on Tuesday, October 25.

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.

MATH 120S Introduction to Theoretical Mathematics

Math 120S includes topics from set theory, number theory, algebra and analysis. It is recommended for prospective mathematics majors who feel the need to improve their skills in logical reasoning and theorem-proving.

Changes in Major Requirements

The Mathematics Department has recently changed the requirements for an A.B. in mathematics from 6 courses to 6.5 courses beyond Math 111, effective with the class entering in 1995. The requirements for a B.S. in mathematics are unchanged. Students who need to improve their skills with proofs are encouraged to take the half credit seminar, Math 120S, before they take Math 121 or Math 139. This spring, Math 120 will meet Mondays and Wednesdays or Mondays and Fridays from 10:30-11:20. This course is best taken concurrently with Math 104. Alternatively, students may take 7 full courses beyond Math 111 for the A.B. degree.
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.

Project CALCulators by Lewis Blake

All Math 31L sections will be using the HP 48G and HP 48GX calculators. We have chosen calculators over computers because of their mobility and versatility. Teachers can use them in the classroom. The classroom does not need to be specially equipped; therefore, it is easy for teachers and students to take full advantage of this technology.

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.


The Virginia Tech Math Contest will be held from 9:00 to 11:30 a.m. on Saturday, October 29. The W.L. Putnam Mathematics Competition will be held from 10:00 a.m.-1:00 p.m. and 3:00-6:00 p.m. on Saturday December 3. All Duke undergraduates, regardless of major, are eligible to compete. If you would like to take one or both of these competitions, please contact David Kraines (135D Math-Physics, phone: 660-2820, email: dkrain@math.duke.edu.)


From time to time, potential employers send information to the department encouraging math majors to apply to them. Several of these companies will be interviewing students here. See Joan McLaughlin in room 135 of the Physics Building for more details.

CIGNA and Prudential

Both CIGNA and Prudential insurance companies are seeking Duke Math majors.

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.

First Union of Charlotte

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.''

Programmers Needed
by Professor John Trangenstein

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.


On Wednesday afternoon, October 21, Professor Robert Devaney of Boston University entertained an audience of over 50 students with pictures and computer animation of the Mandelbrot set and related topics. Devaney explained how to understand various of the distinguishing intricate features of this beautiful mathematical object and of the related Julia sets. Many students stayed after the lecture for quite a while at the DUMU reception in order to talk with Devaney about his work.

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.


The Graduate General Seminar began this year with the goal of bringing students together to enjoy the many exciting ideas alive in mathematics today. The talks are designed to be accessible to many undergraduates as well as graduate students. Yet the approach of the talks is fresh enough to be interesting even to the experts. Below is a list of speakers so far.

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.


Many programs for graduate study in mathematics send us brochures and other information about their school. If you are considering graduate work in mathematics, see Cynthia Wilkerson in Room 116 or the student worker in Room 117 about the files on graduate schools.


Several alumni, who have been recipients of the North Carolina Mathematics Scholarship, have written about their careers or their graduate studies as well as their personal lives. If you would like to let the Duke mathematics community know a bit about what you are up to, please write to David Kraines or Joan McLaughlin at Department of Mathematics, Duke University, Box 90320, Durham, NC 27708. Or send an e-mail message to dkrain@math.duke.edu or joan@math.duke.edu.


My life at Duke included a B.S. in 1985 in Computer Sciences and Economics, along with entry into the 3-2 program resulting in an M.B.A. at the Fuqua School of Business in 1986.

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.


After working for a computer software company for four years, I decided to go to law school. The lure of a scholarship brought me to Chicago and Northwestern University, and I ended up staying here to practice law (although I return to North Carolina frequently because of family). I have enclosed some items about my current law firm, which specializes in Information Technology Law. My undergraduate education in Mathematics and Computer Science has been very helpful throughout my career on a number of different levels.


I graduated Duke with a B.S. in Math in 1985, after which I went to Oxford on a Marshall Scholarship, to study philosophy. Most of my time in Oxford was spent studying Wittgenstein and Frege, concentrating on issues in the philosophy of language. Two years later, and a much improved philosopher, I left Oxford with a B.Phil. (which is a graduate degree) and went to MIT to complete my Ph.D. There, my focus shifted towards issues in ontology and the philosophy of logic and, under the guidance of my supervisor George Boolos, the philosophy of mathematics. I completed my Ph.D. in 1991 and accepted a job as an Assistant Professor at Harvard University, where I have been since.

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.


Kathy Benson and I went to grad schools in Cambridge MA: she in Harvard in theoretical physics, I in MIT Applied Math (theory of computation). In 1991 we both graduated and we married in the Duke Gardens. This year we are both finishing postdocs at UCSD (I have a NSF Math Sci postdoc), and we will be looking for jobs again in 1995. Although the academic job market looks tough, I would say we have enjoyed our years together so far.


I graduated from Duke in 1987 with a triple major in: Electrical Engineering, Mathematics, and Computer Science. I obtained my masters in Electrical Engineering in 1988 from the University of Pennsylvania, then worked for General Electric in New Jersey for two years as a combat systems engineer. In 1992 I graduated from Duke with my MBA.


I am very grateful for having received a NC Math Scholarship. Since that scholarship was based upon past achievement (I placed third in the NC Math Competition in 1982) rather than on future commitment to mathematics, it allowed me to pursue my interests in the humanities at Duke, from which I graduated with an A.B. in Germanic Languages and Literatures in 1987. After a year of driving buses for Duke University Transit, I entered graduate school in geological sciences at Brown University, from which I obtained an M.Sc. in 1990 for work on volcanic rocks from Mount St. Helens.

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 graduated in 1988 with a double major in math and physics. I spent the following year doing research in medical imaging at the Duke Medical Center, working in a juvenile detention center and as a bicycle messenger in Washington, DC and traveling in India. I spent 1989-1994 at NYU's Courant Institute working with Stephane Mallat (of wavelet fame) and completed my PhD, " Adaptive Nonlinear Decompositions " in June. While at NYU I founded NYU Outreach, a community-service based freshman orientation program modeled after Duke's Project BUILD, and I developed virtual reality video games which won several national awards for a local advertising agency.

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 am currently working for the IBM PC Company as a Software Engineer. I am on the ThinkPad Subnotebook development team here in Durham. I also married a Duke Math graduate this past June, Cindy Green ('89).

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.


This is in response to your letter to former NC math scholars. As you probably remember, I finished my PhD at Duke last year. I am starting the second year of a two-year postdoc at NC State, working on PDE's governing granular flow.


I graduated in 1992, and am now just starting my third year of graduate school in the math PhD program at UC Berkeley. I took my qualifying exam last spring, and am now studying galois representations, elliptic curves, modular forms, etc. . . with Ken Ribet. I really enjoy the department here; everyone is very easy to work with, and I have somehow managed to avoid slipping through the cracks and getting lost in the shuffle.

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.)


Marc Starnes of the class of 1993 taught high school math last year at the Hopkins School in new Haven, CT. He is taking the year off to ponder graduate school or teaching.


David Kirsch, class of '93, is currently at Johns Hopkins on a seven-year plan to receive his MD and PhD. He is on a full scholarship all the way.


I'm in Houston at Baylor College of Medicine (not affiliated with the Baylor University in Waco!) working towards a Ph.D. in cell and molecular biology. I've been told that my address that shows up on e-mail doesn't actually work, so my real address is LC691279@express.ssctr.bcm.tmc.edu. And in case anyone wants to know, it's not any hotter in Houston in the summer than in Durham - summer just seems to last a few months longer here!


I had a really good summer working for IDA [Institute for Defense Analysis], but I can't tell you a thing about it, what with security and all. It's easily the best paying job of its type for math students. Classes [at Princeton University] start today. I think I'll sit in on Wiles' Number Theory, although I don't plan to take it. Lots of fun classes to choose from. It's a pretty impressive place.


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.