Title: Little by little
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Title: Little by little
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Language: English
Creator: Department of Mathematics, University of Florida
Publisher: Department of Mathematics, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: Fall 1998
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Volume ID: VID00003
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LITTLE BY LITTLE
UNIVERSITY OF FLORIDA DEPARTMENT OF NM_ iiE_4ii 'r NE\\. LE TER
VOLUME 12, ISSUE 1, FALL 1998


A new Chair for the Mathematics
Department
On July 1, 1998, Professor Krishnaswami Alladi
was appointed as the new chairman of the department
of mathematics. He received his Ph.D in 1978 from
UCLA and his field of specialization is uiii ,. r Theory.
He joined the department in December 1986. Professor
Joseph Glover who stepped down as Chair has now be-
come the Associate Dean for Faculty Affairs in the College
of Liberal Arts and Sciences. We wish Professors Alladi
and Glover all the best in their new assignments Editor.

Report from the Chair and vision for the future:
The mathematics department has an excellent fac-
ulty who are making significant contributions to research
while maintaining a sincere commitment to teaching. My
goal is to build on existing strengths and gain increased
recognition of our work both within the university and
internationally. With this in mind, I have initiated a
number of programs aimed at taking us to a higher level
of accomplishment and recognition.
Starting this academic year, our department will be
initiating two series of distinguished colloquia, one in
pure and one in applied mathematics. These special col-
loquia are to be given by persons of eminence and are to
reach a wide audience. The distinguished colloquium in
pure mathematics is named after Paul Erd6s, and the
one in applied mathematics after Stan Ulam. Profes-
sor Paul Erd6s, one of the legends of twentieth century
mathematics, died in September 1996. Author of over
1500 research papers, he had perhaps more influence on
mathematicians than any other person, by the original-
ity of his ideas, by the multitude of research problems
he proposed, and by the numerous collaborative research
papers he wrote. He visited our university each year
in the spring for two weeks and collaborated with many
of our members, thereby having a profound impact on
our department. Stan Ulam was an outstanding applied
mathematician who worked on a variety of problems and
projects. He served on the Los Alamos atom bomb project
during World War II, and was graduate research profes-
sor in our department for many years. Creating these
two distinguished colloquia is our way of remembering
these great mathematicians and building on our legacy.
The first Ulam Colloquium will be delivered on January
11, 1999, by Professor James Keener of the University
of Utah, an authority on mathematical biology. The title
of Professor Keener's talk is "The mathematics of sudden


cardiac death". It should attract a wide audience! The
first Erdos colloquium will be delivered on March 15,
1999, by Professor Ronald Graham of AT&T Research.
Graham, an outstanding researcher and speaker, was
former President of the American Mathematical Society.
Another distinguished visitor we will have this spring
is Professor Ingrid Daubechies of Princeton University,
who will be give a featured lecture under the Women in
Science series. There will be reports on these distin-
guished lectures in the next newsletter.
Starting in Fall 1999, our department will be con-
ducting two mini-conferences each year, one on the fall,
and one in the spring. By bringing established re-
searchers from around the world regularly to these con-
ferences, we will get increased visibility of our work and
benefit by the exchange of ideas that take place at such
meetings. We plan to publish the refereed proceedings of
such conferences.
We are very fortunate that on March 12-13, 1999, a
Regional MNt-lting of The American Mathematical Soci-
ety will be held in Gainesville. This conference will bring
more than two hundred mathematicians from all over the
USA and abroad to our campus. There are four featured
one hour invited plenary talks at this conference, two of
which will be given by our faculty by Graduate Re-
search Professor John Thompson and by Professor
Alexander Dranishnikov. There will also be several
invited twenty minute special session talks given in this
meeting. It turns out that our faculty are organizing 14
of these 16 special sessions an indication of our activity
in research and our enthusiasm. An announcement of
the conference is enclosed with this newsletter.
Our faculty continue to be recognized for their re-
search by invitations to speak at international meet-
ings, as can be seen from the Faculty N.itc- section. We
are especially proud that Professor Alexander Dran-
ishnikov gave an invited address at the International
Congress of Mathematicians in Berlin in August 1998.



INSIDE THIS ISSUE
A new Chair for the Mathematics Department... 1
Graduate Program Enhancement ................ 2
Graduate Working Seminar ...................... 2
Faculty N,,c- ................................... 3
Alumni of the 50's ................................ 4
Alumni Nc . . . . ............... 7








A New Chair (cont.)
This congress is the pre-eminent mathematics conference
and is held once every four years. To be invited to give a
talk at this conference is a great honor for a mathemati-
cian.
Two of our colleagues Professors Murali Rao and
Alexandre Turull won the prestigious PEP Awards
this Fall. These PEP Awards are given to faculty who
have been in the rank of full professor for at least seven
years in recognition of their scholarship, teaching and
service.
Our enthusiasm and commitment to teaching is
equally sincere and strong. The mathematics depart-
ment has always had a very good reputation in teaching.
This was further strengthened this year by six of our fac-
ulty winning the coveted TIP Awards, bringing the total
number of such awards won by our department to 29 since
they were instituted in 1993. The TIP award winners
this Fall are Douglas Cenzer, Yunmei Chen, David
Groisser, James Keesling, Li-Chien Shen, and Jane
Smith. Mathematics courses are required for almost ev-
ery student, and so we are proud to be of service to the
university and pleased by this recognition.
The department continues to hire new faculty of the
very highest caliber in its on going effort to expand in var-
ious active areas of research. Shari Moskow who spe-
cializes in partial differential equations, and and Pham
Tiep whose research interests cover algebra, especially
group representation theory, joined the department in
Fall 1998 as assistant professors.
The future will undoubtedly present new opportu-
nities, problems, and challenges. Our strength lies in the
fact that we are well balanced in our research, teaching,
and service. Thus I am hopeful that we have a bright fu-
ture and the events of Spring 1999 strengthen this hope.

Krishnaswami Alladi
Chair

Graduate Program Enhancement
by Neil 1\,:r, rc Associate Chair
As Professor Alladi assumed the office of Chair in
July, 1998, simultaneously three faculty members took
on new administrative roles in the department; Profes-
sor Neil White as Associate Chair, Professor Paul
Robinson as Graduate Coordinator, and Professor
Rick Smith as Undergraduate Coordinator-Editor.
These are exciting times for our graduate program.
The whole university is embarked on an initiative to in-
crease both the quality and quantity of our graduate stu-
dents. Additional funding has been provided to further
these goals. The keystone in this effort will be the Dis-
tinguished Alumni Fellows, who will receive $25,000 per
year for 4 years, with no duties besides their academic
work in some years and teaching and research duties in


other years. This program is in addition to various other
ongoing fellowship programs. Furthermore, money has
been provided directly to the department for stipend en-
hancement both for incoming and continuing teaching
assistants. We are all eagerly anticipating the positive
effects this initiative will have on graduate studies in
mathematics at UF!
Another item which I wish to mention is a summer
program for minority high school students. The Math-
ematics Department was awarded a GTE Focus Grant
of $30,000 to develop such a program over the next two
years. The program will begin this coming summer dur-
ing Summer B, and will involve about 25 minority stu-
dents from local high schools. The goal is to improve the
chances that they will eventually become interested in
majoring in mathematics (whether at UF or elsewhere).

Graduate Working Seminar in Ap-
plied Mathematics:
On a Successful Avenue
by Irene Hueter
Starting in January, 1997, a new seminar was added
to the current roster offered by the Department of Mathe-
matics, the Graduate Working Seminar in Applied Math-
ematics. This weekly seminar was launched by Professor
Gang Bao, and currently Bao and mathematics gradu-
ate student Tri Van are co-organizers of this seminar.
Recently, we were able to talk with them about this new
initiative.
Little by Little: Can you tell us about the purpose
and structure of the seminar ?
Gang Bao: The seminar is intended to be a forum for
students to participate in research activities. For exam-
ple, the students get exposed to research talks, mainly by
students, they get involved, learn on the spot, are pointed
and attracted to interesting subjects to explore, learn to
present their own research or talk about other people's
papers, have the opportunity to learn to give good talks,
they are encouraged to practice a presentation that they
plan to give at a local or national meeting, and impor-
tantly, they get exposed to questions. The seminar is
ideal to discuss and hear about projects that a student
pursued in summer internships. Everyone in the sem-
inar benefits from the discussion. \\ hliL-a- faculty are
welcome to attend or speak, the purpose of the semi-
nar is different from the Applied Mathematics Seminar,
where one person gets no more than one shot due to a
high number of speakers, time pressures to fly over de-
tails at times such that chances to learn something new
are given away, and the talks are on original research.
LbL: Different in which sense ?
Tri Van: The seminar is informal and a joint effort
between the speakers and the audience. Everyone here
understands that the best way to learn is to talk about a








subject, to try to convince the audience of its importance,
to get exposed to numerous questions, and to accept criti-
cism. The atmosphere is extremely friendly and fruitful.
There is enough time to stick to an interesting topic -
for instance, grating theory was of great interest to sev-
eral students to zoom in and view something from a
different angle, and to try again to do better next time.
In fact, I very well remember my first talk when certain
people were rattling my cage but luckily the talk that re-
ally counted, at Vanderbilt, went well (Gang Bao corrects:
'this was an excellent talk'). There is no doubt that all
students have learnt a great deal in this joint adventure.
Even though the working seminar is more difficult and
makes a student work harder than a regular class, the
7 8 students who regularly participate perfectly enjoy
the experience and count this seminar as a full success.
LbL: What are your visions for the future of the sem-
inar ?
Gang Bao: As our department continues to con-
siderably strengthen the program in Applied Mathemat-
ics and hopefully some of the submitted major research
proposals that include research assistantships will be
funded, it is important and timely to identify interested
students individually for these emerging opportunities.
The seminar is a mechanism to identify these students.
We always welcome new students at all levels to join us,
and thus, hope to see more faces soon. Hopefully, it will
continue be a good source of inspiration and a fruitful
learning ground for our students.
LbL: kindly thanks you for the interview!
This fall semester's topics have covered different ar-
eas in optics, ranging from grating theory to diffractive
and fiber optics.

Faculty Notes
by Paul Ehrlich
Professor Gang Bao had a busy summer, giving an
invited lecture on "Mathematical modeling of diffractive
gratings," to the 1998 Summer Topical Meeting of the Op-
tical Society of America in Kalilua-Kona, Hawaii in June.
Then in July, Bao attended the AMS- IMS-Siam Joint
Summer Research Conference on Mathematical Methods
of Inverse Problems for Partial Differential Equations
in South Hadley, NMl--dlchu--ltt-, delivering a lecture on
"Determination of locations of elliptic foci in the living
human brain." Also in July, Bao spoke on "Mathematical
modeling of diffractive optics" at the Air Force Institute
of Technology Distinguished Lecturers Series in Dayton,
Ohio. In August, Bao traveled to his native land, China,
and gave colloquim lectures on "Mathematics and com-
putation of diffractive optics" at Beijing University and
at Jilin University in Changchun.
Professor James Brooks was an invited speaker at
the long running annual Wabash Conference in Anal-
ysis, held this year in Indianapolis on October 10th.


Brooks lectured on "Weak compactness and applications
to stochastic processes."
Professor Yunmei Chen also traveled back to her
native China this past summer, and was pleasantly sur-
prised to receive the Third Prize of "Natural Science
Award" awarded by the National Science and Technol-
ogy Committee of the People's Republic of China. While
in China, Chen lectured at East Normal University, Jilin
University and Fudan University.
Professor Jean Larson has been participating in
an Association Review Group of the Mathematical As-
sociation of American studying standards being estab-
lished nation wide by the National Council of Teachers of
Mathematics. Larson is quoted in the NMia. Jun eL 1998 Fo-
cus NL \ -lt t LL of the M.A.A. discussing the creation and
use of algorithms by students in our mathematics course
MAE 3811 for prospective elementary school teachers.
Professors Jed Keesling and Neil White partici-
pated in a regional meeting of the American Mathemati-
cal Society held during March 20 21, 1998 at the Univer-
sity of Louisville in Kentucky. Keesling spoke in a Special
Session on Fractal Geometry and Related Topics on "A
practical algorithm for computing the Hausdorff dimen-
sion of boundaries of self-similar tiles", joint work with
Professors Andrew Vince of our department and Pro-
fessor Paul Duvall of the University of North Carolina
at Greensboro, who has been a visitor to our department.
\\hilte spoke in a Special Session on Algebraic Combi-
natorics on the topic of "Flag matroids", joint work with
Professor Alexandre Borovik of UMIST and Professor
Israel M. Gelfand of Rutgers University. \\hilt also de-
livered an invited lecture on "Symplectic Matroids" at a
Conference on Algebraic Combinatorics held at Oakland
University in Rochester, Michigan, during early May.
During July, White attended an international meeting
on combinatorics held in Porto, Portugal, and lectured
on "Flag matroids." During the summer, Keesling gave
an invited talk at the 13th Summer Topology Confer-
ence in Mexico City. This October, Keesling was involved
in organizing an international Conference on Geometric
Topology held in Dubrovnik, Croatia. Keesling spoke on
"Homeomorphisms of generalized Knaster continue" at
this meeting.
Professors Chat Ho and Peter Sin participated in a
Regional NM I- ing of the American Mathematical Society
held at the University of Kansas in Manhatten, Kansas,
during March 27 28, 1998, speaking in a Special Session
on Groups and Geometry. Ho spoke on "Collineations of
finite 1-.iL-cL li' L- planes" and Sin spoke on "The permuta-
tion modules for GL(n + 1, F))".
Professor Krishna Alladi participated in a Regional
N L-lt in of the American Mathematical Society held dur-
ing April 4 6, 1998, at Temple University in Philadel-
phia, lecturing in a Special Session on Modular Identities
and Q-Series in Number Theory on the topic of "On a par-
tition theorem of Gollnitz and quartic transformations."








Alladi also participated in a conference held by the
American Mathematical Society at Mt. Holyoke College
between June 21 and 24, in honor Professor Richard
Askey for his 65-th birthday. Alladi's talk at this con-
ference was entitled "G6llnitz' big partition theorem and
q-series identities".
During July 1998, Alladi gave colloquium talks at
The Raman Research Institute and at the Tata Institute,
both in Bangalore, India.
Alladi participated in two conferences held in honor of
Professor George Andrews for his sixtieth birthday. The
first was in Maratea, Italy, during August 31 September
6, when Alladi spoke on "A generalization and refinement
of an Andrews hierarchy of partition theorems". The
second conference was at Penn. State University during
October 22-24, where Alladi gave a one hour talk entitled
'\\L -ihtILd partition identities and applications".
Professor Nicolae Dinculeanu did research during
the summer of 1997 at the Laboratorie de Probabilites at
the Unversity of Paris, and also lectured at the Univer-
sity of Lille and at the Ecole Polytechnique in Lausanne,
Switzerland during June.
Professor Alex Dranishnikov gave an invited ad-
dress at the International Congress of Mathematicians
held in Berlin, in the section on Topology, lecturing on
"Dimension theory and large Riemannian manifolds."
Dranishnikov also participated in the Conference on Geo-
metric Topology in Dubrovnik mentioned above in which
Keesling was one of the organizers. Dranishnikov lec-
tured at this conference on the topic of "On coarse dimen-
sion of metric spaces."
Professor Paul Ehrlich participated in a Confer-
ence on Continued Fractions: From Analytic Number
Theory to Constructive Approximation" during May 20
- 23, 1998, held at the University of Missouri to mark
the retirement at age 70 of Professor L. Jerome Lange
of that institution, one of Ehrlich's best friends during
his eleven years at the University of Missouri. As well
as delivering a tribute to Professor Lange at the Retire-
ment Banquet, Ehrlich also spoke at the conference on
"The Emergence of the American Mathematical Research
Community: Florida, Illinois and Missouri." A few weeks
later, Ehrlich was off to St. John, New Brunswick, to par-
ticipate in the Summer Nlut..ing of the Canadian Mathe-
matical Society. Ehrlich spoke in a Symposium in Rela-
tivity and Geometry on "Bochner's technique for compact
Lorentzian manifolds (after Romero and Sanchez)."
Professor Gerard Emch participated in two confer-
ences in Europe this past summer. First, Emch delivered
the first plenary lecture at an International Workshop on
'NLw* Insights in Quantum Mechanics Fundamentals,
Experimental Results, Theoretical Directions," held in
Goslar, Germany, from August 31 to September 3. Then
Emch participated in the International VIENNA CIR-
CLE MNL-tini on "Philosophical and Experimental Per-
spectives on Quantum Physics" held from September 3 to


September 6th at the Schroedinger Institute in Vienna.
Graduate Research Professor John Thompson was
elected to the American Academy of Arts and Sciences
this past spring.
Professor Andrew Vince was an invited speaker
to an international conference on "Graphs, Maps and
Complexes" held in Flagstaff, Arizona this past summer.
Vince also was an invited speaker at a Workshop on "Ape-
riodicity" held at the Mathematisches Forschungsinstitut
in Oberwolfach, Germany, this past spring.
Professor Helmut Voelklein gave an invited lecture
at a Conference on Arithmetic of Fields at the Mathe-
matisches Forschungsintitut in Oberwolfach, Germany,
during July. He also visited Erlangen University.
The Center for Applied Mathematics held its First
Annual Fall Social on October 23, 1998. Faculty members
Gang Bao, Phillip Boyland, Yunmei Chen, Joseph
Glover, Bill Hager, Jed Keesling, Bernard Mair,
Shari Moskow, Tim Olson, Dave Wilson and grad-
uate student Aaron Brask made short presentations. A
tour of the UF Brain Institute was also offered.


Alumni of the 50's : Dr. John
Tilley
by Paul Ehrlich
I was very pleased to receive a long letter in April
from Professor Emeritus John Tilley of Mississippi State
University in which he reminisced about his years at
Florida. Tilley received the 39th Ph.D. in January, 1961,
from the department, with a dissertation written on
'.Slt i--- Distribution of a Rolling Limacon" under the su-
pervision of Professor C. Basel Smith. The Biographical
Sketch in Tilley's thesis reveals that
"John Leonard Tilley was born June 4, 1928, at Ja-
maica, New York. In June, 1964, he graduated from Jenk-
intown High School, Jenkintown, Pennsylvania. In June,
1950, he received the degree Bachelor of Science in Eco-
nomics from the University of Pennsylvania, Philadel-
phia, Pennsylvania. From January, 1951, through Jan-
uary, 1953, he served as an instructor in the 3rd Army
Supply School, Ft. Jackson, South Carolina. Following
his discharge, he enrolled at the University of Florida as
a Graduate Student in Education. He received the de-
gree Nla-t'r of Education in August, 1954. From then
until June, 1958, he taught in the public schools of St.
Petersburg, Florida; first in the Northeast High School,
and then in the St. Petersburg Junior College. At both
institutions he served in the mathematics departments.
During this period he returned each summer to the Uni-
versity of Florida as a Graduate Student in Mathemat-
ics. Having held a 1/3 time Graduate Assistantship
in Mathematics at the University of Florida in the school
year 1953 54, he applied for and received a 1/2 time As-
sistantship in that same department for the school year
1958 59 and again in 1959 60. He was appointed to








the faculty of that department as an Instructor for the
school year 1960 61.
John Tilley is married to the former Dolores May
Cope. He is a member of the Mathematical Association
of America. While at the University of Pennsylvania,
he was an active member of the Alpha Delta Chapter of
Beta Alpha Psi, The National Accounting Fraternity, and
served as student treasurer of that chapter in his senior
year."
In the Acknowledgements at the beginning of the
thesis, Tilley writes
"The encouragement received from Dr. F. W. Koko-
moor, now retired as Head of the Department of Math-
ematics, throughout the years of the author's graduate
study has been most helpful to the successful completion
of this work."
Let us see how Tilley himself remembers Kokomoor
in his letter to me of April 23, 1998, about 40 years later.
"Dear Dr. Ehrlich,
I have been thinking about writing this to you for
sometime now. I received my copy of the LITTLE BY
LITTLE newsletter this past week and decided that this
was a good time to write. Contained will be some of my
memories of the experiences I had from January 1953
through August 1961 with the Mathematics department.
In January of 1953 I enrolled as an MEd student,
after having 'fought the battle of Ft. Jackson (Columbia,
SC)' for two years. My wife and I had income from the
GI bill, $135 per month while in school on a full time
basis. My first introduction to the Mathematics Depart-
ment was with the first course in Calculus, a four hour
sophomore level course. As an undergraduate, major in
accounting, I had taken, as electives, a four hour college
algebra course, a four hour analytic geometry course, and
a three hour Introduction to the Calculus course at the
University of Pennsylvania. I had no trouble with the
first part of the Calculus course, but when it came to the
part dealing with trig functions, I was lost. It had been 6
and 1/2 years since I had had a trig course in high school.
When I asked the instructor for some help, he told me
to read the text (calculus) which I believe was Kells. It
was of little help as the only places the trig identities,
which I had forgotten, were used (explained ?) were in
the examples. I don't know how, but I managed to pass
the course.
In those days, the summer school was one ten week
term and you took three courses as a full load. This
ended about the middle of August and the Fall semester
did not begin until after the middle of September. By
this time we were living in Flavet III in a two bedroom
furnished apartment for $27.50 monthly rental which in-
cluded $2.00 worth of electricity. I would put $15.00 a
week in my wallet and that had to do for the entire week.
Hamburger was then 3 pounds for a dollar at the A &
P store! We spent the time between semesters at my
in-laws near Clearwater as we had no income for that


time.
We got back to Gainesville for the Fall semester and
registered for a full load of classes which included a geom-
etry course taught by Dr. Kokomoor. About the third day
of classes, I was out cutting the grass, a large area by the
apartment building, with the push mower the University
supplied, when Dr. Kokomoor rode up on his bicycle. I
had my first interview for a mathematics teaching posi-
tion sitting on the front steps of the building in shorts
and soaked in sweat with grass clippings all over me.
He was short of staff and asked if I would take a third-
time graduate assistantship for $900 for nine months,
mid-September through mid-June. He said that I was
supposed to teach six hours each semester, but that he
needed someone to teach the four hour integrated fresh-
man mathematics course. So he would assign me two
sections of that course in the Fall semester and one sec-
tion of it in the Spring and I would have to drop a course
I had signed up for that semester. I managed to drop
an Education course that was not required for teacher
certification. All went well until early November. Dr.
Kokomoor called me into his office and said that he had
'fought' with the Graduate Dean, but had 'lost the battle.'
This was the first time that the Dean had found out that
the third- time graduate assistants were teaching more
than six hours in a semester. He threatened to block my
GI-bill payments and my assistantship salary because I
'was over worked.' So I was removed from one of the sec-
tions I was teaching and given some help-session time to
make up the six hours.
In the Spring semester of 1954, I signed up for the
Calculus II course. Dr. South was the instructor. By
this time they had changed the text and the course out-
line. The new outline began the semester with integra-
tion techniques. I had a help session assignment the hour
before my Calculus II session. The other assistant for the
help session was a PhD candidate who thought that Cal-
culus was too low a level for him to help with. So all the
students who came in with calculus questions were auto-
matically handed to me. Several of them were taking the
Calculus II course and I would have to explain problems
and concepts that I would be exposed to the next hour.
Someone in my section learned of this, and the other
students in the class would ask me to work homework
problems as soon as I walked in the door of the class-
room. Dr. South would come into the classroom while I
was still trying to finish up the problems and would take
a seat to the side and wait until I had finished. I certainly
learned my Calculus II that semester!
I graduated in August of 1954 and took a job at
Northeast High School in St. Petersburg. With a Mas-
ter's degree and two years of experience credit, my salary
was $3600 for ten months! The school had just opened
that Fall. Each of the next several summers we would
return to Gainesville to take courses. I think it was the
first summer, 1955, when I took the differential equations








course. Dr. Hadlock taught it in the large second floor
classroom on the East side of Walker Hall. He had mem-
orized the number of slates that made up the blackboards
in the room and as soon as he walked in the door, he would
begin calling out names to go to the board to put up the
homework problems. The boards were on three sides of
the room. I remember one problem I was given that took
me more than my assigned slate. I finally crammed the
answer down at the bottom of the board next to the chalk
rail. The student next to me had a very similar problem
and finished his work in a very few lines. Dr. Hadlock
looked at my work and remarked that that was one way
to solve the problem but certainly the long hard way!
Each summer I used Dr. South as my advisor. I
admired him both as a teacher and a gentleman. I did
take his split-level statistics course and made an A grade,
but I did not really enjoy the course material, so I never
took any more math statistical courses. Later I did have
to take an education statistics course and had no trouble
with it.
I cannot remember whether it was before I came back
to campus as a full time PhD student in the summer of
1958 or one of the summers before that, but I signed up
for the split-level topology course. In those days, the full
time faculty taught for two summers and were off the
third. That particular summer, none of the regular fac-
ulty members who taught topology were employed. So
we had a man who was interested in Runga-Kutta tech-
niques as the instructor. He was a refugee from World
War II and had spent some time in Brazil planning and
building roads. NL-L-di -- to say, we learned little topology,
I think we got into the fourth chapter of the text. NL-, Lr
did take another topology course. I much preferred the
non-Euclidean geometry course I had at another time.
When I came back to work on my PhD in 1958, for
some reason Mr. Lewis put me on the committee that
made up the progress tests for C42 and the two semesters
of the integrated freshman course. I would get the cards
of questions and five answers that the various faculty
members had written and had the first pass at checking
to see that there was only one correct answer and that the
problems were appropriate. I soon learned the various
approaches of the different faculty members, including
the one who usually had mistakes in his solutions. I
soon learned to toss those cards and make up my own
questions and answers. When I finished my part, the
cards were sent to another faculty member, and then to
Mr. Lewis who made up the examination from those
questions sent to him. This was sent to the people in the
Segal Building and they printed and administered the
tests. We, the faculty, did not see the tests only the final
results in a print-out distribution after the tests were
given. The final exams were always late at night in the
two week exam period. After the results were ready we
would meet as a group for each of the three courses and
select the cut-off points for the various grades. It was


toward the end of my time there before any input from
the instructor was counted toward the final grade.
I can remember teaching a C42 class in the third
floor of Walker Hall, a large room on the West side that
had sloped ceilings coming down from the three dormer-
like window areas. The green painted chalkboards were
placed under the low ceiling in the corners. Since the size
of the class was determined by how many chairs were in
the room, this was a large class. Early in the semester, a
couple of woman students came to me and said that they
were graduating seniors in the College of Education and
had to pass the course. At that time their final grade was
strictly dependent on their two progress test scores and
their final exam score. We used Dr. Kokomoor's book for
the class which was written with the problems having five
given possible answers just as the exams were written. I
couldn't tell the women much more than to see me in my
'office' when they had questions.
My 'office' was one drawer in a desk in an L-shaped
room on the third floor of Walker Hall. All of the graduate
students shared the room and desks. The room was to
the left as you headed toward the front of Walker Hall.
There was a classroom at the very front of the third floor
that also had sloped ceilings to each side of the room with
green painted chalk boards on those walls. No one used
those boards as they were so low that it was difficult to
stand by, and also for the students to see, them. There
was a small green painted board beside the entry door
that was so covered with chalk that it couldn't be washed
off. That was where everyone had to write and it was
nearly impossible to tell what had just been written and
what was 'stuck' to the board.
My dissertation, 'Stress Distribution in a Rotating
Limacon', was done under the direction of Dr. C. B.
Smith. During my oral exam, I was asked to state the
Fundamental Theorem of Algebra. In my mind's eye, I
could see the theorem in my complex variables text book
and so stated it. When I looked up at the Committee, I
found heads making Yes' and 'No' signs. It took some dis-
cussion time among the committee members before Dr.
Smith told them I had stated the theorem correctly from
the complex variables text.
I was 'lucky' in that I had a closed form solution to
my dissertation problem. Dr. Smith had two other stu-
dents at that time and their problems had only infinite
series solutions with no apparent simple closed form of
a generating function. Dr. Smith sent them over to the
'new' computing machine to see if they could get some
numerical results. One student did finish 'on time' sum-
mer of 1960, but the other man was still struggling with
the programming of his problem when I left in 1961."
To be continued ....








Alumni News
by Paul Ehrlich
Professors Jane Maxwell Day, Ph.D. '64, of San
Jose State University and John Mayer, Ph.D. '82, of
the University of Alabama, participated in the Annual
\\Wink-r nl-uing of the M.A.A./A.M.S. in Maryland dur-
ing January, 1998. Day spoke in an MAA Session on
Innovations in Teaching Linear Algebra on the topic "As-
signments that stimulate thinking and writing." Mayer
spoke in an AMS Session on Topology in Dynamical Sys-
tems on joint work with Professor Lex Oversteegen on the
topic of "Recurrent critical points and typical limit sets of
rational maps." Our current graduate student Chawne
Kimber participated in a Graduate Student Poster Ses-
sion in the AWM Workshop, reporting on the topic "The
structure of prime ideal spectra in rings of continuous
functions."
John Gordon Moore, BS in Math '84, MS in ISE
'87, recently wrote us from Houston, Texas, where he is
a Senior Engineer at LIC Energy in Houston. He writes
"I reluctantly left my Math Department TA-ship in
1988, soon after Joe Glover jokingly u !-L-l ud that I 'get
a haircut and get a real job.' I began my career with
a defense contractor (Sverdrup Technology) and spent
my days at Eglin AFB and Edwards AFB as a software
developer and flight-test engineer.
I willing left DoD work in 1996 and moved to Hous-
ton. I did some consulting work at Compaq and then
worked at IMSL. I recently took a job with LIC Energy
where we develop modeling and optimization software
for the pipeline industry.
I married the former Sandra Petty Fonte on June 20,
1998. She is a kindergarten teacher and University of
Georgia graduate."
Leon Couch III (BS Phyics, BA Mathematics, BM
Organ Performance 1992) has accepted an Assistant Pro-
fessor of Music position at Luther College in Decorah,
Iowa. He will be teaching music theory and conducting
the collegium (a student choral ensemble). This past year,
he served as an Adjunct Professor of Mathematics at the
University College, a division of the University of Cincin-
nati. For the past three years, he has been Music Direc-
tor (organist/choirmaster) for a German-American con-
gregation at Concordia Lutheran Church in Cincinnati.
Last summer, his electronic music composition Sirens
was featured in an international conference in Thessa-
loniki, Greece and Montreal, Canada. He is completing a
DMA in Organ Performance and a PhD in Music Theory
at the College-Conservatory of Music in the University of
Cincinnati.
This summer Couch presented recitals in Cincinnati,
OH; Buffalo, NY; Gainesville, FL; and St. Augustine, FL.
The all-Bach organ recital at the University of Florida
Memorial Auditorium on June 8 at 8PM was part of the
Annual UF Summer Organ Festival. The program in-
cluded chorale singing along with the Passacaglia in C


Minor, the Schubler Chorales, Smucke dich, and the Pre-
lude and Fugue in E-flat Major ("St. Anne").
Warren McGovern, Ph.D. '98 with Professor Jorge
Martinez, has obtained a position at Bowling Green
State University.


Little By Little is published twice a year
to inform students and alumni of activities
of the Department of Mathematics, Uni-
versity of Florida. It is typeset using AMS-
TeX.
Chair ......................... Krishnaswami Alladi
Editor .................................. Paul Ehrlich
Co-editor .............................. Irene Hueter
Production...................... Arlene Williams








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