Co-Presidents: Gena Boercker, Leanne Conaway

Treasurer : Sue Holt

Sponsored by the department and organized by graduate students, the club meets each Tuesday to eat pizza and discuss career opportunities, course work and general topics in mathematics. Guest speakers are invited to speak two or three times each semester.

**Puzzle Page by Dr. Jeno Lehel**

__New Puzzle:__ **Batting Average**

Batter A has a higher batting average than batter B for every single day of the season. Does it follow that batter A has a better batting average than B for the whole season?

__Old Puzzle__: **Traffic Light**

*At a certain corner, the traffic light is green for 30 seconds
and then red for 30 seconds. On the average, how much time is
lost at this corner?*

__Solution__ *by Jim Twohey (MA '95)*

The average time lost at the traffic light is 15/2 seconds. It is equal to the expected value of the time spent stopped at the light. The probability of being stopped at the light is 1/2. When not stopped by the light, the mean waiting time is zero. When stopped by the light, the mean waiting time is 15 seconds, because there is an equal probability of hitting the red light at any particular moment of the thirty seconds it is red. So 1/2 x 15 + 1/2 x 0 = 15/2 seconds is the mean waiting time.

*-Also solved by Paul Buckthal (MA '76), Samuel Carter (BA
'99), and Richard Farris (BA '72)*

Mail or e-mail your solution to: Dr. Jeno Lehel lehel@louisville.edu**
, **Math Dept, Louisville, KY 40292

**Chairman's Corner**

**Dr. Michael Jacobson**

This is shaping up to be a hallmark year for the department. Within the next six to nine months, I believe our Ph.D. proposal will finally get a review (hopefully positive) by the state Council on Post-Secondary Education. We expect that during this academic year to have awarded 14 M.A. degrees in Mathematics (an all-time high) and approximately 30 Baccalaureates. In spite of this, the department is under a microscope analyzing the efficiency of how we do our job. A significant reallocation review has been undertaken by the university in an effort to do an even better, more efficient job. I am optimistic that the department will fare well during this process and possibly see changes including a combining of Mathematics offerings across campus, and a true partnership in the training of mathematics teachers as we continue to work on an joint Center for Mathematics and Science Teacher Development, Education and Research in cooperation with the School of Education. These changes will help to strengthen the mathematical community in the area and help develop the scientific and mathematical literacy of the populace.

As always, I hope you find something interesting in this issue of the newsletter. Please feel free to contact me and let me know your thoughts - we appreciate all your support, and hope in some small way you are able to continue your mathematical experience.

**Faculty Activities for 2000:**

**Michael Jacobson **will be chairing a special session
at the KYMAA meeting in March for statewide department chairs.
He is also the featured speaker at the Fifth North Carolina Mini-conference
on graph Theory, Combinatorics and Computing in April. He will
give a Colloquium at Appalachian State University in April as
well. In May he will be co-organizer of the 14'th Cumberland Conference
to be held in Huntsville, Alabama.

**Udayan Darji **is currently visiting Caltech and will
be working at the Institute for Defense Analysis Center in Communications
Research in La Jolla, CA.

**Marianne Korten** one of our visiting professors, will
give a talk at the Arkansas Spring Lecture 2000 in Fayetteville,
Arkansas in March. She will also speak at the International Conference
on Generalized Functions, Linear and Non-Linear Problems, Pointe-a-Pitre,
Universite des Antilles et Guyane, Guadelope in April.

**Richard Davitt **will participate March 25-26, 2000 in
the semiannual meeting of ORESME (a group of Kentucky, Ohio, and
New York historians of mathematics who gather together periodically
to research a designated seminal mathematical work and the life
of the prominent mathematician who produced it) at Miami University
in Oxford, Ohio. This session is extra special in that Professor
John Fauvel, an internationally renowned historian of mathematics
from the Open University of Great Britain, will lead the discussion
of Sir Isaac Newton's fundamental text on integral calculus, De
Analysi, and the accompanying investigation of the life and times
of this most famous of mathematical scientists.

The Department of Mathematics is hosting the seventh annual Bullitt Lecture on Friday, April 7, 2000 at 7 p.m. in the Floyd Theatre located in the Swain Student Activities Center on UofL's Belknap Campus. This year's speaker is Professor Fernanco Q. Gouvea from Colby Collge. Dr. Gouvea's research interests are in number theory and arithmetic geometry, with a secondary interest in the history of mathematics. He is also the editor of FOCUS and MAA Online (the online newsletter of the Mathematical Association of America).

The talk will be a survey of the last 1000 years of mathematics focusing especially on how numbers moved from a peripheral position in mathematics to a central one, with some attention to how this has also influenced our way of thinking about the real world.

For more information please contact Professor Mike Jacobson (mikej@louisville.edu) or Professor Manav Das (manav@louisville.edu). Bullitt Lectures are open to the public and accessible to the non-specialist.

*****************************************************

For the last three years, our Department has hosted lectures by prominent scholars in insurance and mathematical economics, funded by the ARMS Financial Group. In 1997 our speaker was Dr. Jose Pinera, who discussed privatization of social insurance in Chile. In 1998, Dr. Stephen Ross presented the theoretical underpinnings of modern mathematical finance. In 1999, Dr. Hal Varian spoke about economic models of electronic commerce. Unfortunately, late in 1999, ARM Financial Group experienced financial difficulties and continued funding for the lecture became impossible.

This year, we will hold a special lecture in mathematical finance, without any external funding. It will take place on April 12, at 5:00 p.m. in Strickler Hall, Middleton Auditorium. The speaker is Dr. Richard Derrig, Senior Vice President of the Automobile Insurers Bureau of Massachusetts, and of the Insurance Fraud Bureau of Massachusetts. He will lecture on new mathematical methodologies of artificial intelligence helping in the discovery of insurance fraud.

Based on a proposal worked out by the Undergraduate Studies
Committee (Ewa Kubicka, Jenö Lehel, and Thomas Riedel) the
Mathematics Department has made essential changes to its undergraduate
degree program. Allowing students to specialize earlier than our
previous programs permitted, our graduates will have more choices
in the job market, or within their continuing studies.

We still offer the Bachelor of Arts and the Bachelor of Science
degrees. The B.A. requirements have changed slightly; it still
serves the purpose of getting a broad yet substantial background
in Mathematics, while allowing the student to take a significant
number of courses outside of Mathematics. Thus our B.A. program
best serves students who intend to enter the field of education
or continue their studies in other professional schools.

The B.S. provides a solid general background in Mathematics with
an in depth study of one area together with its applications.
This program serves students who enter into the technical job
market or who wish to continue their studies of Mathematics in
graduate school. The B.S. degree now contains a core curriculum
including traditional courses like Analysis, Linear Algebra, Abstract
Algebra, just to mention a few, and we offer four different concentration
areas:

**Actuarial Mathematics****Computational and Applied Mathematics****Probability and Statistics****Pure Mathematics**

These changes in our programs will better serve our students' and our community's needs.

**Faculty Highlight:**

**Manav Das**

**
**I received my Ph.D. in mathematics from The Ohio State University
in 1996. After spending a year at OSU as a postdoc, I joined the
University of Louisville as an Assistant Professor. I have taught
courses in trigonometry, college algebra, honors calculus and
linear algebra. Currently I am teaching a section of precalculus
and a graduate level course in real analysis.

My main interest is in measure theory and its interplay with other areas of mathematics such as dynamical systems, probability theory and real analysis.

Roughly speaking, measure theory deals with the various techniques of measuring geometric objects. Calculating areas and volumes are the classical roots of this area. Historically therefore, it dates back to the Greeks. Integration theory, as developed by Newton and Leibnitz, provide a backdrop for many modern developments. Riemann, Lebesgue, Carathéodory and Hausdorff, aided by the solid foundations in set theory laid by Cantor and Dedekind, were able to generalize and extend the notion of integration by introducing novel methods of measuring sets.

For instance, consider a piece of metallic wire. One way of
measuring this object would be its length. Another would be its
mass. If the wire is made up of a single metal and is of uniform
thickness, then its mass would be proportional to its length.
This is not very interesting. But suppose two or more metals are
combined into an alloy, then it is clear that the mass distribution
should vary with the relative compositions of these metals. Different
compositions would give rise to different mass distributions,
or *measure*s. Thus measure theory gives us a glimpse into
the intrinsic geometry of sets and not just their classical shape.

In the beginning of the 1900s, great minds like Poincaré
were trying to understand the notion of *dimension*. They
thought inductively: a line (which is 1-dimensional) has boundaries
that are points (which are zero-dimensional). A 2-dimensional
object such as a square has boundaries that are 1-dimensional
and so on. This dimension (termed *topological dimension*)
was then connected with the notion of measure. To measure a 2-dimensional
object *A*, length of *A* (denoted *l(A)*) is a
bad choice because it is infinite. On the other hand the volume
*l ^{3}(A*) is zero. Therefore area

Now imagine looking at an object under a magnifying glass.
As we change the order of magnification, certain features will
fall out of focus and certain others will become visible. This
is simply because a given object could have finer structures at
different scales. In order to understand the true geometry of
this object, we would want to view it under all possible magnifications.
Thus we would be compelled to study a multitude of fractals, each
coming into focus at a different scale. This is *multifractal
theory*.

The current research in multifractal theory is too vast for me to enumerate here.

There are numerous books on these topics. In particular there
is a book by M. Schroeder titled *Fractals, Chaos, Power Laws*
(W.H. Freeman, NY 1991) which gives a popular treatment of chaos
and fractals. For a philosophical approach one can read B. Mandelbrot’s
*The Fractal Geometry of Nature* (W. H. Freeman, NY 1983).

Please feel free to contact me if you have any questions. You can email me at manav@louisville.edu.

Department of Mathematics

College of Arts and Sciences

University of Louisville

Louisville, KY 40292

Tel. (502) 852-6826

Fax (502) 852-7132

E-mail: math@athena.louisville.edu

Chair of the Department:

Dr. Michael S. Jacobson

Professor of Mathematics

E-mail: mikej@louisville.edu

http://www.louisville.edu/a-s/math/msjaco01.html

Co-Editors of the Newsletter:

Dr. Robert C. Powers

Associate Professor of Mathematics

Diane Doby

Administrative Secretary