Much has changed over the summer. The library and other facilities in the Physics building have been renovated. Seven graduate students and eleven faculty and staff have joined the department. Professor John Harer will resume his chairmanship of the Department after he returns from sabbatical study this year in Italy. In the interim, Professor William Pardon, the department chair from 1989 to 1992, will serve in this role.

Garrett Mitchener '99 continues as editor of *Duke Math News* for
the third year. He combines this job with that as head of the Duke
University Math Union. As Features Editor, Alan Bester '99 will
report in depth on developments in the department.
Undergraduates have many opportunities to get a taste of mathematical
research. Majors may attend summer research programs sponsored by the
National Science Foundation and other agencies. The graduate students
hold a weekly seminar to explore mathematical discoveries. Check your
email regularly for announcements about these and other opportunities
for math majors.
A special word to our majors. Our department strives to combine the best
features of a world class research university with the small classes
and personal attention more typical of distinguished liberal arts
colleges. It will be difficult to achieve this goal without your
help. Talk with your favorite professor about studying beyond the
syllabus. Consider doing independent study in your senior year with
the aim of graduation with distinction. The faculty are here to guide
you toward your maximum potential -- if you will let us.

*-- David Kraines, DMN Faculty Sponsor *

What do math and medicine have in common? Until recent years, not
much, but a group of Duke researchers is working to change that. The
Center for Mathematics and Computation in the Life Sciences and
Medicine (CMCLM) was established at Duke in 1986 to bring modern
applied mathematics to bear in solving questions in medical research.
This year, the Center received a $600,000 National Science Foundation
grant which will fund continued research and broaden the Center's
horizons in years to come. *Duke Math News* sat down with
Professor Michael Reed, a senior faculty member in the math
department, to discuss the origins of the CMCLM, and the exciting
prospects for its future.

The son of a chemist, Professor Reed was introduced to the life sciences at an early age; ``I've always been a closet physiologist,'' he told DMN. Although he never entertained thoughts of attending medical school, his interests in biology and medicine remained, even as he built up impressive credentials in pure mathematical research. Around age 40, however, he realized it was time for a change. Reed began by attending seminars at the medical center, many of which began as lectures and ended with considerable controversy as questions were raised.

Excited by the controversy and potential for discovery modern medicine offered, Reed became convinced that mathematics was the key to understanding medical questions, from the application of topology in analyzing cellular metabolism to the use of partial differential equations in modeling transport of signals in nerve axons. ``An awful lot [of modern] medicine is engineering, not science,'' he claims. ``Only in the last few years have we figured out how aspirin really works.''

Professor Reed and colleagues Harold Layton (Associate Professor of Mathematics) and J. Joseph Blum (Professor of Cell Biology) form the Center's core faculty. The CMCLM's chief goal, to facilitate the application of mathematics to biological and biomedical problems, has been realized in part by published research of these faculty and their collaborators. However, though support has always been available for individual research, it has been difficult to raise money for the broader educational goals of the Center. The recent $600,000 grant will enable the Center to increase its staff, to bring more visiting lecturers (often to speak at both the Math Department and the Medical Center), and to offer a summer workshop on mathematical biology. Most importantly, the new grant will enable the CMCLM to attract graduate students and post-docs from around the world. Reed emphasizes the importance of postdoctoral programs in connecting new mathematics Ph.D.'s with the Medical Center. The goal, Reed says, is to ``build bridges between [mathematicians] and the huge biological community, so that math expertise can be utilized in medical research.''

Math-Physics Librarian

Noise, dust, aching backs: the summer of 1997 saw the successful renovation of the Math-Physics Library. Beginning May 12th, a moving company and the staff shifted approximately 90,000 volumes, and all the bookcases, into eight classrooms and laboratories around the building. The library's staff moved across the hall into room 234 with the unbound journals, a couple of computers, and not much else.

The renovation began with the removal of the asbestos tile from the floors. Then construction crews removed the air conditioners, steam radiators, ceilings, and lights, and tore down the two back walls of the library.

The library reopened with a new air handling system (with air conditioning, humidity control, and heating), new lights and ceilings, carpeting in the reading rooms and staff areas, new tile flooring in the stacks, and new bookcases in the first two rooms. A beautiful class door replaced the old wooden door. In addition, several areas were rewired, particularly the staff area and the reference area, eliminating messy, dangerous cables crossing the floor and tripping people. The reference room was rearranged making the room less crowded. A new location for the copier allows better access to the fire door. Individual carrels were also cleared of various materials and moved, allowing several quiet, out-of-the-way study seats.

The Math-Physics Library reopened for business on September 3rd amid vases of congratulatory flowers.

An expert is a man who has made all the mistakes, which can be made, in a very narrow field.

--Neils Bohr

Director of Graduate Studies

This autumn seven new graduate students will begin working towards their Ph.D.'s in the math department. David Ambrose, a graduate of Carnegie Mellon University, will be pursuing his interest in analysis while becoming acquainted with geometry. Anne Collins, who has a master's degree in astronomy from Northwestern, will change directions a bit and explore the purer side of mathematics. Craig Grabowski, a graduate of Canisius College in Buffalo, New York, has expressed a possible interest in algebraic geometry. Chris Hale from Amherst College is interested in analysis and possibly number theory. Marianty Ionel comes to Duke after graduating from the University of Iasi in Romania. Her interests are in partial differential equations and geometry. Qing Li, a graduate of Beijing University, will begin by taking courses in a wide variety of areas. Darren Oldson from Florida State University got a bit of head start by working with Professor Mike Reed in July. He has expressed a possible interest in mathematical biology.

Chad Fargason recently received the 1996-1997 L. P. and Barbara Smith Award for Teaching Excellence. This award is presented annually to one or two graduate students who have demonstrated a long-term commitment to teaching and whose teaching has reached a consistent level of excellence. The Smith award carries with it the explicit recognition by the Mathematics Department of Chad's fine teaching as well as a substantial monetary prize.

Professor William Pardon, Acting Chairman of the Mathematics Department, presented the award to Chad Fargason at the opening department meeting of the school year. Pardon commented on the high praise that Chad receives from his students each term. Chad has taught calculus I, II, and III at Duke. He has designed syllabi and he regularly participates in the redesign and testing of course material.

The Smith teaching award was made possible by a generous donation from Captain L. P. Smith and Barbara Smith, who established the Smith Award in 1981. Captain Smith was Supervisor of Freshman Instruction in the Mathematics Department from 1973 until his retirement in 1982. The Smiths' goal was to reward those graduate students for their efforts to become fine teachers. The Smiths are now enjoying their retirement in the Seattle, Washington, area.

Chad's research, under the direction of Greg Lawler, concerns the geometric and fractal properties of Brownian motion and random walk in three dimensions, an area of probability theory. His dissertation, which he expects to complete this year, will analyze processes derived by erasing ``loops'' from random paths. He also pursues an interest in mathematical finance.

I wish to God these calculations had been executed by steam.

--Charles Babbage

Every Friday afternoon, the math graduate students host an informal
talk in which graduate students and faculty get a chance to share
their ongoing research or some mathematical gem they have discovered.
These talks are held every Friday afternoon at 4:00 in Room 120
Physics, preceded by tea at 3:30. Check the posted math calendar or
`http://math.duke.edu/seminars/graduate.html` for the
next speaker and title. No previous knowledge is assumed other than a
solid undergraduate math experience; everyone is encouraged to
attend.

DUMU, the Duke University Math Union, is a club sponsored by the
department for undergraduates. Our activities include social events,
such as the picnic on September 23rd, movies, frisbee games with the
Society for Physics Students, and our high-school math contest.
Additionally, we invite speakers for the entertaining and informative
Undergraduate Lecture Series. If you are interested in hearing about
DUMU events and are not already on our mailing list, contact Garrett
at `wgm2@acpub.duke.edu`. Read on to find out about our
current plans.

The Duke University Math Union is planning to host a contest in the spring for nearby high schools. We would like to have all the problems written before winter break, but it takes some time to come up with good ones, not too hard but not boring. The more people who contribute, the more varied and interesting the contest will be. So, start thinking, and keep you eyes open for intriguing ideas. Math may be a tool and a subject, but it can also be a sport, a game, a kind of art, and thought-provoking fun.

The problems should be limited to precalculus and below, but that does not mean they cannot be creative. We need all levels of problems, from quick-and-easy puzzles to short dissertations. Humor in good taste is most welcome. The format of the contest will likely be similar to the one used by the American Regions Math League.

If you come up with any promising problems, or are willing to help us
type them up, contact Johanna Miller at
`jlm6@acpub.duke.edu`.

Both of the following contests are open to all undergraduates. They take place on Saturdays, and are held in a math classroom in the Physics Building. If you are interested in participating in one of these competitions, please contact Professor Greg Lawler.

- Nov. 1
- The Virginia Tech contest. Problems requiring proofs. Linear algebra and multivariable calculus helpful. Two and one half hours long.
- Dec. 6
- The Putnam Competition. Problems requiring proofs. Two sessions of three hours each. The Duke team won this contest last year for the second time in four years!

The following are joining the math department this year:

Paul S. Aspinwall, Assistant Professor of Mathematics and Physics * Andrew Bernoff, Visitor * Lori Ann Carmack, Assistant Research Professor * Radu Constantinescu, Lecturer * Stephanie Fitchett, Lecturer * Ko Honda, Visiting Assistant Professor * Keener Hughen, Part-time Instructor * Lou Kondic, Post-doctoral fellow in Mathematics and Physics * Ronen Plesser, Assistant Professor of Physics and Mathematics * Andrew Schretter, Systems Programmer * Tom Witelski, NSF post-doctoral fellow.

Sunday, May 18, was graduation day for the class of 1997. Following the university-wide exercises, mathematics and physics majors, their families and friends, and a number of mathematics faculty gathered in the Levine Science Research Center Dining Room for a buffet luncheon, followed by a diploma ceremony. Director of Undergraduate Studies Harold Layton, assisted by Professors William Pardon and Richard Hodel, presented diplomas to the thirty-five first majors in mathematics. Applause, good cheer, and photo-flashes abounded as family, friends, and faculty expressed their congratulations and best wishes for the future.

Most of our first and second majors reported definite post-graduation plans. At least nine majors have entered graduate programs: two in mathematics and seven others in areas ranging from physics, to engineering, to theology. Three are attending medical schools and four have begun military service. Four have begun careers in computer services and fourteen have begun careers in financial services, including actuarial science.

Also featured is a ``math chat'' with Professor Frank Morgan of Williams College and Princeton University on his dedication to teaching and research. Morgan will present the Undergraduate Math Lecture at Duke early next semester.

Read about Professor Joe Gallian's very successful summer undergraduate research program (REU) in Minnesota. See the amusing article about amazing coincidences that have been collected by Persi Diaconis and others, and learn the simple rules from probability theory that explain them. Gallian and Diaconis have each spoken in our Undergraduate Lecture Series.

As a recent Duke Math graduate, I would like to tell you about some of the exciting career opportunities at Capital One, a rapidly growing and innovative international financial services company. Capital One is seeking quantitatively and analytically talented students who want to develop and implement business strategies in a competitive environment. Many recent Duke math majors -- Brent Baumbusch, Trip Hall, and myself -- have joined Capital One, and we hope to recruit many more this year.

Interested students should come hear our CEO, Rich Fairbank, present
on career opportunities with Capital One on Wednesday, October 15 in
Von Cannon C at 6:30 p.m. There will also be an information session
6:00 p.m., November 18 in the Reese-Jones room, Washington Duke.
Also, check out our website at `www.capitalone.com` for
additional information on our company.

If you have any questions please feel free to contact me at
`mike.rierson@capitalone.com` or (800) 641-6943 ext. 2780.

*-- Michael Rierson, Duke '96 *

The prestigious Goldwater Scholarship is intended for sophomores and juniors planning careers in mathematics, engineering, and the natural sciences. It is worth up to $7,500 annually, covering tuition, fees, books, and room and board. Ten math majors have won this award since 1992.

Preliminary applications are available now in room 04 Allen Building,
and the Premajor Advising Center, and should be turned in to room 04
Allen Building by Monday, October 27. For more information, please
see the Goldwater website
`http://www.act.org/goldwater`.

Greetings to all mathematics majors and minors from the Director of Undergraduate Studies!

Those of you who declared your majors and minors before September 1997
should have received the 1997--1998 edition of the*Handbook for
Mathematics Majors and Minors*. If you did not receive a
*Handbook*, you may pick up a copy in the Mathematics Office,
Room 121 Physics. The new version of the *Handbook* will soon
appear on the department's web site (`http://www.math.duke.edu`),
under the heading ``The Undergraduate Program.''

Registration for the spring semester begins on Wednesday, October 29. Before that date, advisor assignments will be distributed by electronic mail and posted on one of the bulletin boards near Room 117. I am currently assigning advisors for newly-declared first majors. Please let me know any information on interests or career plans that might help me in my assignments.

Mathematics courses suitable for majors and minors and scheduled to be offered in the spring semester include: MTH 114, 120S, 121, 126, 128S, 131, 133, 135, 139, 160, 197S, 201, 204, 206, 211, 216, 225, 232, and 239. (Instructor assignments are not final at press time.)

Please be cautioned that only math courses numbered 114 and above
count toward the math major requirements. Mathematics 111 (Applied
Mathematical Analysis I), however, may count toward the mathematics
minor (see the *Handbook*).

Mathematics 197S, Seminar in Mathematics, will will be a Seminar in Set Theory, offered by Professor Richard Hodel. The prerequisite for the course is MTH 104, though MTH 121 or 139 could prove helpful. Topics will include cardinal arithmetic, the Zermelo-Frankel axioms for set theory, and the axiom of choice. The topics will be developed in historical order. There will be student projects at the end of the semester.

Finally, I welcome comments, suggestions, and criticisms that may help the department offer a better mathematics program for our students.

Harold Layton

`layton@math.duke.edu`}

8 3 2 4 6 1 7 5

The sum of the numbers on each side of this square is constant. This is only one solution. There is no known systematic method for solving such problems.

These two problems are from *The Problem Solving
Competition*, run by the University of Oklahoma. You may submit
problems for consideration to Richard Neal, the editor. If your
problem is published, the prize is a wooden icosahedron paperweight.

Richard Neal, Editor *The Problem Solving Competition*

University of Oklahoma

Department of Mathematics

601 Elm Avenue

Norman, Oklahoma 73019

`rneal@uoknor.edu`

These problems were submitted by Stephen Harke and Andrew Hetzel of the University of Dayton.

Create a ten-digit number such that reading from the left, the first digit tells how many zeros are in the number, the second digit tells how many ones are in the number, the third tells how many twos, and so on.

*
Features Editor - Alan Bester,
cab7@acpub.duke.edu
*