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The next issue of the Duke Math News is dated December 1995
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The Duke University Press will publish a special volume of the Duke Mathematical Journal in honor of Nobel Laureate, John Nash. Nash was awarded the 1994 Nobel Prize in Economics for his seminal work in game theory. He also made fundamental contributions in more classical areas of mathematics such as the Nash blowups and the Nash embedding theorem. The volume of the Duke Mathematical Journal will contain a previously unpublished paper of Nash still of research interest, a transcript of the Nobel prize seminar on Nash's work in game theory, as well as contributed papers in mathematics and economics of top research caliber.
Throughout October, the display cabinet in the lobby of the Physics building will feature an exhibit on Nash and his work.
A math degree gives a good background for many different occupations and areas of study. For instance, several math graduates are planning to go on to law school and medical school, where their reasoning and analytical skills will give them an edge. Many other are going on to graduate school in such areas as physics, computer science, economics, engineering, biology, and of course mathematics.
Banks and other businesses are always looking for financial advisors, and who better to advise them than math students? The second largest group of responses to the survey came from people anticipating jobs with such companies as Nations Bank and Merrill-Lynch. Companies that do extensive computation, such as AT&T, often hire math majors, too.
Other students are planning to teach, at least for a year or two, travel, or do research.
Tung Tran has been working on this problem through the Research
Experience for Undergraduates (REU) program, which is open to any
undergraduate student interested in a mathematical career. The program
offers paid summer research opportunities at various locations around
the country. The applications are usually due in February.
Tung presented his paper at the joint MAA/AMS meeting in August.
The problem consists of determining the flow in the interior of a network by making measurements on the outside edge. Examples of this include finding currents and resistances inside a network of resistors but measuring only the outermost wires, and finding out how much oil is in an area from information on its boundary.
Here is the abstract:
The paper attempts to find 
the n-extent of certain lens spaces. The paper includes a
conjecture as to the actual formula of the n-extent, the maximum
average distance of n points for a given compact metric space, of
these spaces, as well as a proof of a lower bound. The evidence
provided by running a computer program supported the conjecture. The
value of the n-extent has a correlation with the Euler
characteristic of 4-dimensional manifolds of positive sectional
curvature with nontrivial isometric 
actions. The lower
bound for the n-extent places certain bounds on the Euler
characteristic. The latter bounds would be stricter if our conjecture
of equality for the n-extent holds.
The best way to have a good idea is to have a lot of ideas.
-- Dr. Linus Pauling
The 17th Annual Virginia Tech Regional Mathematics Contest will be held on Saturday morning, October 28, 1995. The hours are from 9 AM to 11:30 AM.
Universities and colleges from throughout the southeast take part--each participating school, under the direction of a faculty member, gives the test to its own entrants. Duke has done very well in the contest, producing first, second and third prizes in 1993.
If you would like to enter the contest please contact Dick Scoville, 225 Physics before-hand to reserve a place. You may also simply show up around 8:30 on October 28th in Room 120 Physics Building. However, the number of Duke entries is limited to 20, so don't get left out.
The fifty-sixth William Lowell Putnam Mathematical Competition will be held on Saturday, December 2, 1995. The Eastern Time Zone hours for the two sessions are 10 AM to 1 PM and 3 PM to 6 PM.
A list of all students taking part in the competition must be mailed in by October 8!
Please let Dick Scoville know before then if you plan to participate. You can reach him at ras@math.duke.edu or at his office, 225 Physics.
In the past ten years, only two schools have taken first prizes: Harvard nine times and Duke once. Wouldn't it be great for Duke to do it again?
The biggest undertaking is the all-day math contest we host for high schools. It's in the ARML format, which includes team, power, individual, and relay rounds, and requires problem writers, graders, and lots of people in general. Watch for more about this.
For more information, contact Tung Tran at trantt@acpub.duke.edu or Michael Rierson at rierson@math.duke.edu.
One cannot conceive anything so strange and so implausible that it has not already been said by one philosopher or another.
-- René Descartes
Le Discours de la Mé thode [1637], I
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
-- Bertrand Earl Russell
Recent Work on the Principles of Mathematics [1901]. In International Mathematical Monthly, vol. 4, p. 84.
Here are some problems you might enjoy working. The solutions will appear in the next issue.
Define the ``hole'' operation 
to be a real number for all
x and y not equal to zero which obeys the following rules:
if and only if x + y = 0
Find a formula for
which uses only addition, subtraction,
multiplication, and division of real numbers.
Find all solutions in natural numbers x and y:
Find a general method for solving:
for any given natural number a.
If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.
-- Roger Bacon
Opus Majus, bk.1, ch4.
Greetings to all mathematics majors and minors from the Director of Undergraduate Studies!
Those of you who had declared your majors and minors as of early September should have received the 1995--1996 edition of the Handbook for Mathematics Majors and Minors. If you did not receive a Handbook, you may pick up a copy in Room 217, Physics Building, near where my office (217B) is located. The new version of the Handbook will soon appear on the department's web site (http://www.math.duke.edu), under the heading ``Information for Math Majors and Minors.''
As you know, registration for the spring semester begins on Wednesday, October 25. My predecessors have sometimes organized sessions in which those faculty teaching upper-level courses in the upcoming term provide a brief introduction to those courses. Following in that tradition, I have tentatively scheduled a one-hour meeting for Tuesday, 24 October, at 4:00 PM in Room 120, Physics. At recent meetings, student attendance has been low, so if you would like these sessions to continue, please come! Refreshments will be served.
Mathematics courses to be offered next semester, with the currently scheduled instructors, include: 120S, Scoville; 121, Lawler; 126, Trangenstein; 128, Pardon; 131, Zhou; 133, Beale; 135, Coyle & Schaeffer; 139, Moore; 196S, Layton; 201, Yang; 204, Reed; 206, Saper; 238, Schaeffer; and 240, Lawler.
I am currently assigning advisors for newly-declared first majors. Please let me know any specific requests and any information on interests or career plans that could help me in my assignments.
Finally, I want to do all I can---within the limits of the resources and time that I have available to me---to help you get the most out of your study of mathematics at Duke. I am delighted to receive suggestions on how to best accomplish that goal.
-- Harold Layton
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're 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 or Joan McLaughlin in the Mathematics Department.
Until we come up with a better way, just submit them to Harold Layton, or the editor wgm2@acpub.duke.edu.
To see the next issue of the Duke Math News click here for December 1995
To return to the Duke Math News Home Page
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