**The
Quaternion**

Volume 21: Number 1; Fall, 2006

*The Newsletter of
the Department of Mathematics and Statistics*

**An Old Answer
to an Old Problem**

Students have always had
difficulties with mathematics: when King Ptolemy asked

This has inspired a
number of reform proposals and experiments, and one experiment is being
conducted here at USF under the auspices of the *Mathematics Umbrella Group* (MUG), under
the direction of **Dr. Arcadii
Grinshpan**. The experiment is
motivated by changing the emphasis *from* the formal study of definitions
& theorems & proofs *to* using
algorithms in a realistic setting.
Specifically, in some Engineering and Life Science Calculus courses,
students may do a major project in lieu of a cumulative final. The project is selected from a list of
proposals from the local community submitted by businesses, private
organizations, and university faculty, and it is often a problem whose solution
would serve a very practical end.

For example, one
proposal from the Roskamp Institute (now in *is*, and then reformulating
the problem mathematically. Here,
the problem was how many mice the lab should expect to have over time, and from
that compute the total cost of housing the mice during that time. (This may sound to pet owners like a
trivial expense, but as one of the students observed about these genetically
engineered creatures: “if you think your car is expensive, try taking care of
lots of little mice!”) The core of
the mathematics was a recurrence formula that modeled the population growth over
time.

It may seem odd in
this era of “accountability” to dispense with tests in favor of projects, but
this is not a new idea. In many
medieval guilds, a craftsman would be promoted from *journeyman* to *master* based on a *masterpiece* (“meesterstuk”) the
craftsman created. European
universities and the Chinese civil service introduced standardized exams for
economic reasons: they required less expertise to grade. The debate between the two traditions
has raged for a millennium: exams minimize variation of evaluation and thus
allow for greater (mid-range) quality control, while masterpieces stress
practical (as opposed to formal) knowledge and skills exam-driven courses
ignore. In academia today, large
lower-division courses rely on exams, while the meesterstuk tradition can still
be seen in the term papers, honors and masters’ theses, and doctoral
dissertations of the upper division and graduate programs.

So far, the passing
rate for participants in the MUG program is about three fourths, a substantial
improvement over the regular course.
While the program is voluntary, it is seven years old, so we hope for
continuing success. Anyone
interested in the Mathematics Umbrella Group is invited to contact Dr. Arcadii
Grinshpan at the Department of Mathematics and Statistics, or visit the MUG at
<http://www.math.usf.edu/mug/>.

**Transition:
In Memoriam**

**Professor A. N. V. “Vijay” Rao** passed away on June 26 after an
illness.

He was born in

The young family then
moved to

Professor Rao was very active in the community. He founded a school, Gurukulam, was
founding president of the Hindu Temple of Florida, and first president of the
Telugu Association of Florida, the latter of which honored him with a Life Time
Achievement Award last year.
(Professor Rao read and wrote poetry composed in the Telugu language of Andhra Pradesh.) On campus, he organized the Urban
Scholars Outreach Program, which provided free tutoring to disadvantaged
children, and for which he was awarded the Time Warner Humanitarian Award. The faculty advisor for the Students of India Association, he was awarded the
Outstanding Faculty Advisor Award in 1990.
He was also awarded the INDO-US chamber of commerce
award.

He was very generous
with his time and energy to his students, and was committed to being the “ideal
guru.” At the funeral service on
June 30, there were many stories of his patience with students, his willingness
to spend great amounts of time with them, and his kind and even temper. He was a valuable member of the
department, of the university, and of the community, and will be sorely
missed.

**R. Kent Nagle
Lecture**

The Department of Mathematics
and Statistics sponsors a lecture series dedicated to the memory of our
colleague, R. Kent Nagle, who was very concerned about mathematics, mathematics
education, and mathematics in the community. We invite leading mathematical people to
come to USF and speak about issues of the day.

**Louis H. Kauffman**, Professor of
Mathematics at the *Unknots,
Collapsing tangles and DNA Recombination*. The talk began with a series of
accessible examples of knots in art, magic, and DNA, including demonstrations
with a piece of rope, and some computer animations. Professor Kauffman then talked
about the mathematics of knots, of diagrams of knots, and of the difficulty in
telling whether two diagrams of knots represent the “same” knot. In particular, what may appear to be an
immense tangle could actually be an “unknot”, i.e., something that could just be
pulled straight.

While knots in art and
magic can be compelling, the motivation for this work comes from DNA, which
often forms knot-like linked strands, contrary to the expectation that they
should separate during cell division.
There are biological mechanisms (e.g., enzymes) that deal with such
complications, and a mathematical model of knots is an important step towards
understanding these phenomena.

Professor Kauffman is
a leading mathematician in knot theory, having introduced many important
concepts and techniques, several of which bear his name. He has launched a leading journal and
authored many books and papers on knot theory and its connections beyond
mathematics.

For more information
on the series, consult the Nagle Lecture Series webpage at <http://www.math.usf.edu/Nagle/index.html>.

**Student
News**

Six math students received their Ph.D.s last year.

Gokarna R. Aryal, (under C.P. Tsokos), Dissertation title: *Study of Laplace and Related Probability
Distributions and Their Applications*.

Louis R. Camara, (under C.P. Tsokos), Dissertation title: *Statistical Modeling and Assessment of
Software Reliability*.

Jemal E. Gishe, (under M.E.H. Ismail), Dissertation title: *Finite Family of Orthogonal Polynomials and
Resultants of Chebyshev Polynomials*.

Abdelelah M. Mostafa, (under K. Ramachandran), Dissertation title: *Regression Approach to Software Reliability
Models*.

Joseph N. Quarcoo, (under A. Kartsatos), Dissertation title: *Contributions to the Degree Theory for
Perturbations of Maximal Monotone Operators*.

Lakshminarayan Rajaram, (under C.P. Tsokos), Dissertation title: *Statistical Models for Environmental and
Life Sciences*.

Thirteen students received M.A.s:
Anand R. Bhat, Vamsi K. Chikkam, Richard J. Decker, Sandra D. Draper
(under X.-D. Hou, thesis title: *Evaluation of Certain Exponential Sums of
Quadratic Functions over a Finite Field of Odd Characteristic*), Christina L.
Hamlet, Niluk John, Zahra Kottabi, Thucdoan T. Nguyen, Andrew Purcell (under T.
Bieske, thesis title: *Analysis of
Quasiconformal Maps in* **R**), Ziwen
Wei, Sue-Yen E. Wong, Ling Wu, Chunchun Zhao.

And 21 received baccalaureate degrees.

Graduating in summer, 2005: Glen Gonzalez, Karen Huria, and Alden Weddleton.

Graduating in fall, 2005: Travis Bronson, Shannon Evans, Christine Fitch (Magna Cum Laude), Nicole Hooper, Pauline Maiello, Ola Malas, Edward Navarro, Darshit Patel (Magna Cum Laude).

Graduating in spring, 2006: Amber Age (Cum Laude), Seth Ascher (Summa Cum Laude), Gary Bachner, Tyanne Campbell (Magna Cum Laude), Serde Marcelin, Ryan McLaughlin, Marek Merlak, Jaclyn Shepard (Summa Cum Laude), Caleb Sparkman, Nicole Trapp.

And the vast majority of students passing through our classrooms major in other subjects, and take mathematics courses to construct the toolkit they will need later in life. We wish all of them well in their future adventures.

**Center for
Mathematical Services**

Thirty-eight gifted and high-ability 8th – 12th grade
students participated in the summer program of the Center for Mathematical
Services this summer. Students
listened to lectures by Carol Williams and Mile Krajcevski and took courses in
mathematics, computer science, and biomedical sciences and worked on projects
with Arun Mukherjea and Brian Curtin.
Two students were supported by a grant from the

**Mathematics
Clubs**

The USF Student Chapter of the MAA and Pi Mu Epsilon (the Math Honor Society) are sponsored jointly by Fernando Burgos and Mile Krajcevski.

The clubs met every other Friday and featured speakers who addressed topics from “The Mathematics of Viruses” to “Using Statistics to Model Software Failures” and “Applying Operations Research to Efficient Organ Transplantation and Allocation”. Six presentations were made by USF students, five of them undergraduates.

Student members of the clubs traveled to the MAA/PME MathFest in August,
the Suncoast Regional Meeting of the MAA in December, the AMS/MAA Joint Meetings
in January, and the Math Awareness Conference organized by

Matt Williamson, a math major and last year's PME president, delivered the student presentation “Twist Number of Links from the Jones Polynomial” at the AMS/MAA meetings, based on his REU research.

The math clubs continued the “The Math Problem of the Month” contest, which is open to all USF undergraduate students. Each month, a problem is posted and students have the month to submit their solutions; the winner receives a math book. This year’s prizes were purchased with a grant from the USF Council of Honor Societies. At year’s end the “Outstanding Problem Solver” was Vien Van Truong.

The Florida Epsilon Chapter of PME inducted 18 new members on April 28,
almost all undergraduate math students. The 40th annual PME Induction Banquet
was attended by inductees, their families, and math department faculty. The
speaker was Robert C. Eslinger, Professor Emeritus from

The 2006 PME Outstanding Scholar was Darshit J. “DJ” Patel, a double major in math and computer science. DJ now works at Raymond James Financial Services.

In February, 2006, two teams of undergraduate mathematics and engineering students participated in the Mathematical Contest in Modeling sponsored by the Consortium for Mathematics and its Applications. Professor Brian Curtin coached the team of Clayton Beardsley, Brent King and Brian Vohaska, while Professor Nan Kong of the Department of Industrial Engineering coached the team consisting of Egor Dolzhenko, Scott McDermott and Gabriel Zayas Cabán.

All 23 county high schools participated in the two PME and Math & Stat Department-sponsored Hillsborough County Math Bowls. Each school sent four teams, bringing more than 350 very bright math students to our campus. The overall fall winner was Plant High, with Middleton winning in spring.

**Miscellany**

**We’d Like to Hear from YOU!**

The Department of
Mathematics & Statistics would like to hear from alumni, friends,
collaborators, members of the community, and fellow explorers of and guides to
the world of mathematics. Contact
us at: 974-2643, or fax
974-2700. E-mail <file://file1/home/mccolm/publicity/quaternion2006/mathdept@math.usf.edu>. We have a web-page at <http://www.math.usf.edu/>. Snail-mail address is Department of
Mathematics & Statistics,

**New
Faculty**

We are pleased to announce the arrival of three new faculty this year, Catherine Beneteau, Dmitri Khavinson, and Brendan Nagle.

**Appeal for funds**

We are a new department in a new university, and developing new programs to meet the needs and provide opportunities for our students and our community to fulfill their aspirations. With all due respect to Benjamin Franklin, many of the best things in education and scholarship cost money. We would appreciate any assistance we can get from alumni and the community. Feel free to contact our chair, Marcus McWaters, at the above address for details.