MATH CONNections In This Issue

MATH
CONNections
A Newsletter from the UConn Department of Mathematics
Volume 7, Summer 2004
In This Issue
From the Department Head
Undergraduate Mathematics at UConn
The Graduate Program
Actuarial Science Update
Colloquium News
Actuarial Center
Professional Master’s Degree/Financial Mathematics
Changes in Computing: A Bold New Direction
Faculty News
Visitors
Alumni News
Sarah Glaz Receives Teaching Innovation Award
Regina Speicher Receives University Award
Mathematics Club
Undergraduate Competitions
Undergraduate News
Post-Doctoral Program
Mathematics Awards Day
Puzzle Corner
Feedback
Miki Neumann
Jeff Tollefson
Manny Lerman
Dick London
Vadim Olshevsky
Jay Vadiveloo
Jim Bridgeman
Kevin Marinelli
Jim Hurley
Manny Lerman
Keith Conrad
Stu Sidney
FROM THE DEPARTMENT HEAD
by Miki Neumann
Welcome to the seventh edition of Math CONNections. As I approach the end of my first
year as Head of the Department, I owe a big debt of thanks to my predecessor, Prof. Chuck
Vinsonhaler, who has given me so much support, encouragement, and good advice in my
new position. Chuck has been on sabbatical in the Spring semester, a well-deserved break
from the busy job of department head. I know that when he returns to his regular duties in
the fall, he will play a big part in various future missions of the department, particularly
those concerning education, both graduate and undergraduate.
As a new Head of Department, I should like to acknowledge here the dedication of our
administrative staff, Arcelia Bettencourt, Sharon McDermott, and last but not least, Tammy
Prentice, my personal assistant, for all their help in getting me settled into the new position
and for making it possible for the department to run so smoothly during the year.
The past year has seen intense activity in our undergraduate program. At the beginning of
the year we learned that the administration planned to initiate a pilot project for the
renewal of the undergraduate program in two departments, History and Mathematics. The
first step that we took was to appoint two undergraduate directors, Professor Andrew Haas
and Professor Jeffrey Tollefson. Andy is responsible for our service mission to the
university – we teach close to 4800 students each semester. Jeff is responsible for the
studies for the major in mathematics. I assigned them the task of working together with the
Undergraduate Program Committee and other programs in the University such as the
Honors Program, the Institute of Teaching and Learning, and the Center for Undergraduate
Education. Andy and Jeff did an outstanding job in spearheading the development of the
proposal. If our proposal for the pilot study is accepted by the administration, it will
increase the operating budget of the department, allowing us to fund many important
projects.
It would be remiss for me not to mention David Gross, our Undergraduate Program
Coordinator. In addition to serving on several educational committees of the University,
David does outstanding work advising the many students who come to him for help.
I would like to emphasize two other very positive developments in our undergraduate
program. First, let me mention the reviving of our Undergraduate Mathematics Club under
the energetic guidance of Keith Conrad. The second is the very strong performance of our
students who participated in the William Lowell Putnam International Mathematics
Competition. They were trained by Professor Stuart Sidney, who is currently the President
of UConn's chapter of the Phi Beta Kappa Society. Read about both activities inside.
Jeff Tollefson will describe elsewhere the detailed activities of the Undergraduate Program
Committee, but I would like to return for a moment to the pilot project for the renewal of
the undergraduate program. One of the several committees that we have decided to create is
designed to strengthen the relationship between the department and its alumni. Let me just
mention that this year we graduated 28 students with a BA or a BS in Mathematics and 36
students with a minor in Mathematics. Currently we send this newsletter to over 1800
alumni addresses. One of our major goals is to strengthen and increase the number of
students majoring and minoring in math. We would especially like you, our alumni, to feel
very comfortable in recommending our university and our department as a place to obtain a
solid degree in mathematics. We feel that a way to achieve this level of comfort for you is
through better knowledge of and stronger ties with our department. Therefore I call on you
to volunteer to set up an alumni-faculty committee. If 5–10 of you will be ready to think of
concrete ways to determine the activities of this committee, we will match you with faculty
members who will be your partners on this mission.
In addition to our undergraduate teaching mission we are, as you know, a very active
research department. A department that seeks to be strong in research needs a
correspondingly strong graduate program. The last two recruitment seasons have shown a
very positive turnaround in our situation. In recent years we have had fewer applicants
from the Far East and from Eastern Europe, probably because of the opening up of their
societies and markets, but the improved quality of our domestic applicants has more than
compensated for this. Later in this letter, you will find a report from our superb Associate
Head and Director of Graduate Studies, Manny Lerman. I would like to highlight here one
activity of the graduate students and the Graduate Committee. For the first time, we applied
for substantial sums to fund invitations to prospective students for a two-day stay on
campus to meet with our faculty and our current graduate students. All 7 of the students
who came for the visit accepted our offers to become graduate assistants in our department.
Let me add that this year 4 students completed their studies towards the PhD degree in
Mathematics and 5 completed studies towards the Master's degree in Mathematics.
Inside you will find a report on Regina Speicher, who won UConn's 2004 Outstanding
Teaching Assistant Award as well as our department's Connie Strange Graduate
Community Award. It is also a pleasure to recognize Minerva Catral for winning our
department's Louis J. DeLuca Memorial Award for Outstanding Teaching Assistant. You
will also read about the very active graduate student weekly Sigma Seminar run so well by
our student Lance Miller.
To maintain the growth in the number of our undergraduate and graduate students we need
a corresponding growth in the number of faculty and postdoctoral students. This year we
have hired two new faculty members. One, Louis Lombardi, comes to us with much
experience from the insurance/actuarial industries. He will replace Richard London who
has done an outstanding job as our Director of Actuarial Science, and who will be leaving
us in 2005. A comprehensive report on the program, written by Richard London, can be
found inside these pages.
The second person whom we hired is Ralph Kaufmann, who comes to us from Oklahoma
State University in Stillwater. Ralph, who will be an Assistant Professor in Mathematics,
earned his PhD from the University of Bonn, Germany, and did Postdoctoral work at the
University of Southern California. His areas of expertise are geometry and topology.
Ralph's wife will be teaching in the Physics Department. They are the proud parents of a
very young baby.
In addition to the hiring of faculty, we also hired 6 new Postdoctoral Fellows. Three of our
current Fellows will be leaving us, Edlira Shteto, Yasar Sozen, and Moritz Kassmann, and
we wish them all the best in their new careers. The new Fellows are: Stephen Binns, James
Borger, Dmitry Glotov, Jesse Ratzkin, Leonid Slavin, and Xudong Yao. They will
contribute much to research and teaching in our department.
Receiving research grants from national agencies or awards for their teaching were Evarist
Giné (two year Department of Defense grant ), Reed Solomon (three year National Science
Foundation grant ), Sarah Glaz (AAUP Excellence in Teaching Innovation award), Joe
McKenna (Distinguished College or University Teaching Award of the Northeast Section
of the MAA), and Miki Neumann (the Provost’s Research Excellence Award for 2004). We
salute them all. Their activity clearly enhances the reputation of our department.
The past year has seen a complete revamping of the computing and technological resources
of the department. More on this is in the report by our Systems Director, Kevin Marinelli.
We acknowledge the Dean of the College of Liberal Arts and Sciences, Ross MacKinnon,
for providing our department with some $200,000 for the renewal of our system, and we
thank Kevin for all the hard work that he put in to install both the new system and all the
new computers in the offices of our faculty and graduate students.
Finally, we have had a very active colloquium program this year. This included
collaboration with the Computer Science and Engineering Department on the selection of
several very distinguished speakers whose work straddles both areas. This brought us
together with the faculty and students of those departments, which was very positive. A
comprehensive report on our colloquium activity can be found in the write-up by our very
energetic colloquium chair, Vadim Olshevsky.
UNDERGRADUATE MATHEMATICS AT UCONN
by Jeffrey Tollefson
The department is embarking on a major effort to dramatically improve the undergraduate program
from top to bottom. Special emphasis will be placed on calculus and the major. This project is still
in the planning stages but will begin this fall and will extend over a four or five year period. We
will briefly mention some of the highlights.
We expect to develop and implement procedures to assess the effectiveness of each course,
measuring its success against its mission statement. Math 101 will be completely revolutionized
following the highly successful model at the University of Maryland. We will develop a new
calculus curriculum with more emphasis on the fundamental ideas of the subject, as well as on the
essential skills of reading and writing mathematics, problem solving and logical reasoning.
Considerable resources will be devoted to making the major an attractive and worthwhile endeavor
for mathematically talented students at the University. Looking at other schools with successful
majors, one sees how the system builds upon itself. It begins with a calculus sequence that engages
the students, challenges their imaginations and creates a strong feeling of camaraderie. At the same
time, the students have opportunities to mix and become acquainted with more advanced students
who speak highly of their own experience with the program. They meet faculty who take pride in
the major and the whole package becomes something they want to be part of.
We have been encouraged by recent events. This past fall an undergraduate mathematics club and
an undergraduate colloquium were both brought back to activity through the efforts of an energetic
junior faculty member. Their success has been beyond what any of us would have imagined.
Some of the things we want to accomplish for our majors include: a weekly undergraduate
mathematics colloquium series leading to a W credit, research opportunities for undergraduate
mathematics majors, continuation of the development of an active math club, career talks and inhouse job interviews, department computer accounts, tutoring and grading jobs, a web page
newsletter, a math major lounge, field trips to events such as the Connecticut Valley Undergraduate
Mathematics Symposium.
We will be reviewing all of the upper division mathematics courses. We expect to include an
increased emphasis on writing in all of our courses since communicating mathematical ideas with
understanding is essential for learning and using mathematics after graduation. We will also
develop a comprehensive 4-year Honors Program experience for math majors.
We will begin active recruitment for the major program by first making it an exciting program that
sells itself. We also plan to establish a merit-based scholarship program for students in the High
School Coop Mathematics program who are planning to major in mathematics at UConn, and will
welcome financial assistance from alumni toward this scholarship.
[Editor’s note: The College of Liberal Arts and Sciences is undertaking pilot projects to transform
the undergraduate experience in Mathematics and History. Jeff Tollefson is spearheading the pilot
in the Department of Mathematics.]
THE GRADUATE PROGRAM, 2003-04
by Manuel Lerman, Associate Head for Graduate Studies
2003-04 has been an especially productive and rewarding year for the mathematics graduate
program. As in every year, we began a week before classes with PhD prelims for continuing
doctoral students and orientation for the incoming class. Many students were successful with
their prelims, but the difference from previous years hit home when we got to meet our incoming
students – that cohort of twenty-two students was about twice the size of our normal one, with
many highly qualified students. This new group of students is a sociable and friendly group, and
as the semester progressed, I was pleased to see some of them assume leadership roles for
graduate student-sponsored activities. These activities include the SIGMA Seminar, a weekly
seminar run by the graduate students, monthly movie nights combined with pot luck dinners, and
the TA Network, a group of senior teaching assistants who are available for consultations and
classroom visits to help the newer TAs become acclimated. I would particularly like to note the
contributions of Lance Miller, a first-year student who assumed the role of coordinating the
SIGMA seminar, and Rachel Schwell, who coordinated the movie nights and pot luck dinners,
and all members of the TA Network.
One of the greatest pleasures inherent in coordinating the graduate program is to interact with
large numbers of students, both on a professional and personal basis, and observe their
maturation both as mathematicians and as responsible citizens. The Graduate Program
Committee works closely with representatives elected by the graduate students, meets with them
on a regular basis, and tries to implement some of their suggestions to enhance the program. We
began to implement one of those suggestions last year, getting input on the courses the graduate
students would like us to offer, rather than relying solely on faculty preferences. This input,
together with changes we were able to implement which allow us to get early indications of the
courses the students wish to take, and those they wish to teach, has enabled us to provide a much
larger and richer selection of graduate courses than previously. I thank and recognize Marc
Corluy and Regina Speicher, who have served ably and conscientiously as the graduate student
representatives for the past two years.
Two new programs were implemented this year. The first was a recruiting effort at the end of
March, supported through a grant from the UConn Graduate School. The grant enabled us to
bring in a group of students being recruited to learn about our program first-hand. These students
were also invited to attend some graduate courses, and undergraduate courses taught by TAs, to
speak to faculty members about their interests, and to socialize with faculty and graduate
students. Seven students accepted our offer to visit together, and all decided to join us in Fall
2004. Other recruits visited at other times, and most of them decided to come to UConn. We look
forward to having another excellent entering cohort next year, a group of mathematically bright
and very personable people.
In the middle of April, we co-sponsored a program entitled “Preparing Future Mathematicians”
with the Institute of Teaching and Learning. This program brought together senior faculty
members from some of the local community colleges, colleges and universities and senior
graduate students from UConn. The faculty members participated in an excellent and informative
panel discussion, conveying the expectations their schools have of faculty. In addition, our own
Reed Solomon ran a seminar discussing the job application process. It is our hope that the
students will be able to make themselves more attractive on the job market after attending this
program.
I should note that the Mathematics Department cooperates with the ITL in other ways. Several of
our faculty members are, or have been recognized as fellows of that institute, and the institute is
also instrumental in assisting us with the preparation of teaching assistants for their classroom
responsibilities.
Finally, I would like to recognize our graduate students who received PhD degrees in 2003 or
will be receiving them in Spring/Summer 2004: Peng Zhou, Gabriela Bulancea, Jianhong Xu,
Molli Jones, Jonathan Keiter, Alexander Lavrentiev and Ermek Nurkhaidarov.
PH. D. DEGREES GRANTED, 2003-2004
•
•
•
•
Molli R. Jones (adviser E.P. Spiegel), “Group Gradings of Incidence Algebras.”
Jonathan Keiter (adviser J.L. Tollefson), “One-vertex Triangulations and Heegaard
Splittings.”
Alexander Lavrentiev (adviser R. Bass), “Uniqueness for the Martingale Problem for
some Degenerate Elliptical Operators.”
Ermek Nurkhaidarov (adviser J.H. Schmerl), “On Automorphisms of Models of Peano
Arithmetic.”
ACTUARIAL SCIENCE UPDATE
by Richard L. (Dick) London, FSA
Director of Actuarial Science
This is the sixth in a series of annual articles describing the status of the Department's Program in
Actuarial Science.
A. The Past Academic Year
We have just completed the academic year 2003-04 at the time of this writing. The program
continues to be healthy in terms of total student enrollments (both undergraduate and graduate), the
undergraduate scholarship program ($76,500 awarded to 28 students this year), summer internship
opportunities, and full-time positions for those of our graduating students who have passed at least
one of the SOA/CAS professional qualification exams.
Our core faculty group remained at five this year, although Chuck Vinsonhaler was on sabbatical
leave during the Spring 2004 semester. In his absence we were fortunate to have recent grad Paul
Navratil (BS 2000, MS 2001) help us out in an adjunct capacity.
B. Future Faculty Changes
I anticipate that the upcoming 2004-05 academic year will be my last one as Director of Actuarial
Science at UConn. Accordingly, we undertook a search over the past year to find a replacement for
both my teaching and administrative responsibilities. The result of this search was the hiring of
Louis J. Lombardi, FSA, MA, who will be joining our full-time actuarial faculty group for the
2004-05 academic year. Professor Lombardi is a graduate of Central Connecticut State and did
graduate work in mathematics at Tufts University. He has been employed in both life insurance
companies and actuarial consulting firms for the past 26 years.
In addition to Professor Lombardi, the actuarial faculty group will receive the half-time services of
a new post-doctoral fellow next year: Dmitry Glotov will receive his Ph.D. from Purdue University
this summer and join our group in the fall.
The addition of Professors Lombardi and Glotov means that we will actually have a surplus of
teaching resources for the 2004-05 academic year, as I will be overlapping for one year with the
new additions. In particular, we will use this expansion of resources to establish separate sections
of several of our core courses that have heretofore combined both undergraduate and graduate
students in the same section. These combined classes have been reaching total enrollments of up to
50 students, which is inappropriately large for such advanced topics.
Over the next several years, however, as the "three old men" of Bridgeman, London, and
Vinsonhaler (if not actually Bird, McHale, and Parrish) move on, a complete restructuring of the
actuarial faculty group will need to occur. Preliminary planning for that eventuality is currently
under way.
C. Curriculum Changes
Effective in 2005, the SOA and CAS are instituting some small, but significant, changes in their
recommended curricula. For the first time ever, new entrants into the actuarial profession will be
required to show that they have had appropriate academic coursework in certain topics. Universities
will need to submit certain basic information about their course offerings in these topics in order to
be on the list of schools offering approved courses. The first three topics to be included on the list
of required courses are (1) micro- and macro-economics, (2) quantitative corporate finance, and (3)
time series and forecasting. We do not anticipate any difficulty in getting the relevant UConn
courses placed on the approved list.
These changes in the professional qualification requirements will not affect our curriculum design,
since our students have tended to take such courses in any case. It may alter the order in which
students take certain courses, but not the overall set of courses taken.
D. Accreditation of Actuarial Programs
The Society of Actuaries Board of Governors is currently debating a proposal that SOA undertake a
project of accreditation of academic Actuarial Science programs. The fundamental purpose of
professional program accreditation is to serve as additional motivation for schools to build
excellence into their programs. Accrediting of schools by a professional society is also a service to
the public, which views it as a strong statement that institutions on the accredited list are schools of
high quality for the study of the discipline. Depending on what standards of accreditation are
ultimately selected, we might need to do some amount of faculty and/or curriculum upgrading at
UConn in order to be among the chosen few.
It is too early to speculate on what the ultimate benefits of accredited status may entail, if, indeed,
this program of accreditation is undertaken at all. The Society Board is expected to decide on the
accreditation question later this year at its annual meeting in October.
Stay tuned for further details.
[Editor’s note: Richard L. London is a vice-president of the Society of Actuaries, with special
responsibilities in actuarial education.]
MATHEMATICS COLLOQUIUM SERIES 2003-04
by Vadim Olshevsky
We had a busy year, with 13 speakers in the fall semester and 27 speakers in the spring. (The
schedule and abstracts of the talks can be found on our Web site.) In addition to the regular
colloquium series and several presentations from job candidates, the Department launched three
new special colloquium series.
1) Speakers in the “Major Prize Recipient” series: Alan Edelman (MIT, Householder Prize
1990), Madhu Sudan (MIT, Nevannlinna Prize 2003), Nassif Ghoussun (UBC&PIMS, CoxeterJames Prize 1990), Avi Wigderson (Princeton, Nevannlinna Prize 1994). It is worth mentioning
that two of our speakers are recipients of the highly prestigious Rolf Nevanlinna award (and a
third will be coming in Fall 2004). It is well-known that there is no Nobel Prize in mathematics
and that the two top international awards are the Fields medal and the Nevanlinna Prize.
2) We had six “cross-disciplinary colloquia,” jointly sponsored with the department of
Computer Science and Engineering. These drew much larger audiences than usual, with many
graduate students from both departments in attendance. Included were mini-colloquia by Ion
Mandoiu and Aggelos Kiayias (UConn CSE).
3) William Stein (Harvard) spoke on “The Birch and Swinnerton-Dyer Conjecture.” This was
the first in the “Clay Millennium Problems” series. (The Clay Mathematics Institute has
designated a $7 million fund for the solution of this and six other open problems.)
The talks in 2003-04 covered a number of topics in diverse fundamental and applied areas,
ranging from Abstract Algebra and Topology to Bioinformatics and Financial Mathematics.
Despite a rather limited budget, the colloquium had an international flavor, and our speakers were
not only from the US (including our own Yung-Sze Choi and Richard Bass), but also from
Canada, France, New Zealand, Poland, and Russia. All in all, it was an enjoyable colloquium
year for our faculty, visitors, post-docs and graduate students. Finally, the colloquium committee
received substantial help and advice from a large number of faculty members, and this is a good
opportunity to thank everybody for their feedback.
ALUMNI NEWS
Robert Makuch (UConn Math BA, 1972) has gone on to have a distinguished career. He received
a Master’s from the University of Washington (1974), earned two advanced degrees in Biostatistics
from Yale University (M. Phil. 1976, PhD 1977), and worked in biometric research at the National
Cancer Institute (1977-1986). Dr. Makuch, who is the author or co-author of close to 200 research
articles and is a Professor and head of the Biostatistics Division at Yale, was elected a fellow of the
American Statistical Association in 2003.
James Walsh (UConn Math Bachelor’s, 1980) served in Africa in the Peace Corps. Jim later
earned his PhD in dynamical systems from Boston University and has been on the faculty of
Oberlin College for over a dozen years.
UCONN ACTUARIAL CENTER
by Jeyaraj Vadiveloo, Center Director
The UConn Center for Actuarial Studies and Risk Management, which is substantially funded by
Deloitte-Touche, had a very busy year and is actively engaged in a variety of projects. Here are
some of these projects:
1. Mortality study for Phoenix Life Insurance Company on an acquired block of universal life
policies. This project partially supported one actuarial graduate student, Nikolai Kovtunenko, for
the Spring semester, 2004, and helped Phoenix Life make some key strategic decisions on how to
manage the deteriorating mortality experience on this block of business.
2. Integrated pricing model for excess-of-loss short-term liabilities for Best Re, a Property &
Casualty reinsurance company domiciled in Tunisia. This project partially supported two actuarial
graduate students, Hui Shan and Jaya Trivedi for Spring 2004, and was managed by a former
actuarial graduate student, Anita Sathe, who currently is a P&C actuary at Deloitte. This pricing
model will be used by Best Re for all its branch offices in Asia and Africa and Anita and I will be
doing a workshop on this pricing model for Best Re in Tunisia and all its client companies in the
Far East this summer.
3. Life Settlements project spearheaded by Mass Mutual and supported by several other major
insurance companies. This project will provide partial summer support to five graduate students (4
from actuarial and 1 from the School of Business) and three faculty members (1 MATH and 2
SBA). The project will be supervised by a team of professionals from Deloitte, several of whom are
former UConn graduate students in actuarial science. This is a highly visible project and the
research paper we will be doing should become the authoritative actuarial analysis on the Life
Settlements industry.
4. Education and training project with the Insurance Supervisory Department (ISD) of Tanzania.
The UConn Actuarial Center hosted a high-ranking delegation from Tanzania in Fall 2003, and they
want to enlist our help to set up an Institute of Risk Management at the University of Dar Es
Salaam. This project will be funded by the ISD and besides providing financial support for students
and faculty in the Mathematics Department, it will establish a relationship between UConn and the
University of Dar Es Salaam. The Institute is expected to be in place in late 2004.
5. Professional training center at Wuhan University in China. Based on a visit to China in Spring
2004 by the Director of the UConn Actuarial Center, Deloitte is interested in enlisting the help of
the Center in setting up a professional training center in actuarial science and risk management at
Wuhan University. This training center will be geared towards the insurance industry in China and
will also incorporate applied research projects involving actuarial science students in China and
UConn and supervised by Deloitte professionals.
PROFESSIONAL MASTER’S IN APPLIED FINANCIAL MATHEMATICS
by James Bridgeman
2003-04 marked the first full year of the department’s new financial mathematics graduate
program. In November of 2002, the Connecticut Board of Higher Education approved the
department’s proposal to begin conferring a Professional Master’s Degree in Applied Financial
Mathematics. A pioneering group of 5 students started in the new program in the spring semester
of 2003 and 12 were enrolled by the fall semester, 9 of whom stayed the course through spring
2004. The first degrees are anticipated next winter.
The program is one of three practically oriented professional master’s degree programs recently
initiated at UConn under the auspices of a Sloan Foundation grant, the two sister programs being in
Applied Genomics and in Microbial Systems. The purpose of the Applied Financial Mathematics
degree is to take students who come with a base of core knowledge and skills in mathematics and
prepare them to apply those skills in a professional career based around financial analysis. The
program director, Jim Bridgeman, says that the idea is to produce graduates who “look like finance
MBA’s, but ones who can be relied upon for precise answers and reliable models from the start ...
akin to the way insurance companies look at the best actuarial students.”
To get them there, the program design, coordinated and shepherded through seemingly endless
approval processes by Chuck Vinsonhaler, requires students to complete an interdisciplinary menu
of coursework in the Mathematics, Statistics, and Finance departments. Some of those courses
were already in place in the MATH department’s actuarial science, probability and PDE groups and
the Finance department’s MBA sequence. Others were newly developed by Yazhen Wang of
Statistics (statistical computing for financial models and simulations) and by our own Rich Bass
(advanced financial mathematics concepts using stochastic models), a course also taught by Evarist
Giné-Masdeu. In addition, the program includes a varying series of ad-hoc one-credit courses with
a professional practice focus (the first few have included professional writing, financial computing,
and a series of visiting lecturers from industry on professional roles in finance), a requirement to
perform a professional internship, and an exit exam or project tailored to each student’s specific
program and plans.
The program benefits from validation, advice and support from an advisory group of financial
professionals from local industry including Aetna, Bradley Foster & Sargent, Citigroup,
Deloitte&Touche, GE-ERC, Hartford Life, ING, and the State of Connecticut’s Financial Services
Cluster. Our first few internship opportunities have come from this group.
So far, the students enrolling in the program have had diverse backgrounds. The biggest practical
challenges facing these students seems to be how to pay for their degrees (the university expects
this program to run a financial surplus for the long run so financial aid will be almost nil) and how
to find good internship opportunities, given a tough job market and a new program that’s just
starting to create its track record. But there’s little doubt of its popularity. We received 22 new
applications for Fall 2004 and admitted 10.
CHANGES IN COMPUTING: A BOLD NEW DIRECTION
by Kevin Marinelli, Systems Manager
This past year has seen some of the most dramatic changes in our computing environment since the
Mathematics Department first started using computers.
The last large-scale computing change in the department was in 1998/1999 when we changed our
computing infrastructure from Sun/SGI UNIX computers to Dell computers running Linux. This
change was a major cost effective choice for the department at a time when we had limited funding
from the State for addressing Y2K computing issues. New Dell computers cost 1/5 of what a new
Sun or SGI workstation would cost, which meant that it was possible to put new computers in
every faculty and graduate student office.
Five years is a lifetime for a computer, and our Dell computers had started to show their age. Disk
drives, video cards, RAM and other components were failing by the spring of 2003. That was the
least of our problems, however. RedHat, the distributor of the version of Linux we use, sent out
two announcements with serious negative implications for us. RedHat’s first announcement was
that they would support a distribution of their operating system for a period of 12 months only. Any
version older than 12 months would no longer receive support. It is exceptionally difficult to plan
for a complete operating system overhaul and user retraining every 12 months in a University. It is
an inefficient use of people’s time and a serious inconvenience to their work, and the transition time
for RedHat operating system changes came at the worst possible time of the year for us,
immediately before final exams.
The second announcement by RedHat was the termination of the distribution of the free version of
their operating system. Their new payment schedule is $150 per computer per year. With
approximately 120 Dell computers in the department using Linux, this was an enormous
detrimental blow to our departmental budget.
Approximately 6 months was spent doing analysis and testing to work out a plan to upgrade our
aging Dell computers and deal with all of the associated issues. Much care and time was put into
determining the deficiencies, strengths and opportunities that we have encountered with our Dell/
Linux systems. The planning showed that we had serious deficiencies in dealing with PeopleSoft
(student academic records, class rosters, etc.) and sharing Microsoft documents with others in the
University.
We knew that we could not continue with RedHat Linux. A number of other distributions of Linux
(Suse, Mandrake, Debian) were tested in the late spring and early summer of 2003. Each had a
deficiency that caused one of our critical applications or tasks to fail. We have a commitment to
stay with UNIX/Linux as an operating system and decided to look into Apple computers more
seriously because Apple adopted FreeBSD UNIX as the core of their operating system technology
in 2000.
The plan was submitted to the CLAS Dean’s office and was reviewed carefully, especially the
funding section of the proposal. The Dean knew that we needed to have our computers replaced
because they were getting old and that we had serious operating system viability issues. After his
careful consideration, we received $250,000 to fund the purchase of 75 new Apple G5 computers
with flat panel displays. It is expected that the new computers will be sufficient for Department use
until about 2008.
The Apple computers also have a number of apparent deficiencies. They lack a 3-button mouse that
makes using a computer more efficient. Matlab, one of our critical applications, is distributed from
MathWorks with an unsuitable user interface environment. The investment of funds and time to
learn system management of Apple computers is quite significant. After more careful examination,
we were able to overcome each of these stumbling blocks. Logitech makes an affordable and
excellent 3-button mouse that is Macintosh compatible. We worked out how to install and use
Matlab under Apple’s more efficient X-window graphics interface system. And finally, we made an
arrangement with the UConn Department of Molecular and Cellular Biology to pay for training in
exchange for helping them manage their Apple servers for a year.
All of the software we have used to do research and teaching under Linux is available and works
well on Apple Macintosh computers. Several programs and utilities work better under the new
environment, such as LaTeX, compilers, and access to the PeopleSoft system. The user interface
and tasks associated with using Macintosh computers are substantially different from Linux. To
help make the transition, I offered a special section of Math 300 to incoming graduate students.
Faculty members and senior graduate students also attended the class and assisted in sharing their
new knowledge of Apple computers.
The transition is rocky for us at times as we overcome new and challenging technical problems. In
general, now that we are almost a year into the transition, our computer environment works better,
with fewer complaints about basic computer problems than any other time in the last 10 years. We
still have a long way to go with learning, integrating and leveraging Apple’s computer technology
for our needs, but we have made excellent progress beyond what many thought would be possible
with our choices.
Graduate Computer Lab, 11 Apple G5 computers, 1 Dell Precision Workstation
FACULTY NEWS
Bill Abikoff was a speaker at the convocation ceremony for the recently formed Honors College at
the Polytechnic University (Brooklyn, NY) in January 2004. (See http://honors2.poly.edu/Alumni.htm)
Yung-Sze Choi received the Chancellor's Excellence in Research award for 2003-2004 and was
recognized for this achievement at the Graduate Commencement in May 2004.
Evarist Giné will give a Medallion Lecture at the joint 67th Annual Meeting of the Institute of
Mathematical Statistics and 6th World Congress of the Bernoulli Society, in Barcelona, Catalonia,
on July 26-31, 2004. The IMS selects eight Medallion Lecturers every year, and the one-hour
lectures are delivered at the IMS meetings held during that year. Another researcher with ties to our
Department, Vladimir Koltchinskii of the University of New Mexico, will give a Medallion
Lecture at the same meeting. Evarist was also the President of the Program Committee for the IX
Congreso Latinoamericano de Probabilidad y Estadistica Matematica, held in Punta del Este,
Uruguay, in March 2004. In addition, Evarist was awarded a 2-year grant from the National
Security Agency to work on his project, “Limit Theorems in Probability Theory and Applications,”
through February 2006.
Sarah Glaz received the 2004 UConn AAUP Excellence Award for Teaching Innovation.
(See the article by Jim Hurley elsewhere in this issue.) The award was presented at a ceremony at
the Legislative Office Building in Hartford on April 14.
Joe McKenna received the Distinguished College or University Teaching Award of the
Northeastern Section of the Mathematical Association of America for 2004.
Reed Solomon was awarded a 3-year NSF grant for his proposal “Computability Theory, Reverse
Mathematics and Countable Algebraic Structures”.
Ed Tomastik (emeritus) has revised and greatly expanded his highly successful book Calculus:
Applications and Technology. The third edition (with a 2005 copyright) has recently been published
by Thomson Learning (Brooks/Cole).
A First Graduate Course in Abstract Algebra by Bill Wickless (emeritus) has recently been
published by Marcel Dekker, Inc., as number 266 in their series Pure and Applied Mathematics.
VISITORS
Lev Sakhnovich, an author of three monographs and over 170 papers, spent the academic year
2003-2004 at UConn as a guest of Vadim Olshevsky. Vadim and Lev obtained new results on
matrix and operator Bezoutians, robust control, and filtering. They also worked with graduate
student Tom Bella and obtained a new result in coding theory. Kevin C. O’Meara, of the
University of Canterbury (New Zealand) visited us again for the fall semester of 2003. Kevin gave
two talks at the Algebra seminar on “Diagonalization Complexity,” and on December 4, he also
gave an expository lecture entitled “Gromov Translation Algebras” in the colloquium series. (One
can read Kevin’s recent publication on translation algebras in the year 2002 issue of Advances in
Mathematics.) Prof. Huaiyu Jian of Tsinghua University (P. R. China), a specialist in Partial
Differential Equations with interests in variational calculus and geometric analysis, visited
Changfeng Gui for the spring semester. Yuli Eidelman (Tel Aviv) spent September/October 2003
here as a guest of Vadim Olshevsky. They (together with I.Gohberg) obtained new results on
semiseparable matrices, with applications to the semiseparable QR algorithm for solving general
eigenvalue problems. Profs. S-G Lee and Kwak (Sung Kyun Univ., Seoul, Korea) visited to learn
about our actuarial program.
SARAH GLAZ RECEIVES AAUP TEACHING INNOVATION AWARD
by James F. Hurley
On April 14, the 2004 AAUP Excellence Awards were presented at the Legislative Office
Building in Hartford, and the award for Excellence in Teaching Innovation went to Sarah Glaz.
The award recognized her development and teaching of the groundbreaking new course Math
108V, Mathematical Modeling in the Environment. That general-education course focuses on the
mathematics relevant to environmental issues. Sarah skillfully leads her students from data
analysis through modeling short- and long-term environmental effects to finding appropriate
policies for combating pollution and preserving the integrity of the environment in which they
live. Matters of current importance discussed in the course include groundwater contamination,
air pollution and (mis)handling of hazardous materials. Its interdisciplinary approach includes
relevant scientific background and ethical, legal and political considerations in addition to
mathematical models and their predictions. In its short life, Math 108 has stimulated inquiries
from colleagues near (Connecticut College) and far (a university in Romania).
In preparing Sarah's nomination, your correspondent had the pleasure of experiencing a complete
week of Math 108V during February, and quickly saw just how well founded have been the
positive articles about the course in the UConn Advance (2001), the UConn Alumni magazine
Traditions (2002) and the CLAS Newsletter (2003). As a Storrs resident on the University's
mailing list to those with homes within the area of concern for UConn's former toxic waste
disposal site, he found the week's topic — propagation of groundwater contamination — of keen
interest. He and the students participated in an interactive analysis of how pollutants contaminate
ground water and flow from their source to befoul, among other things, water wells of residences.
This involves ideas whose complete examination of course requires knowledge of the calculus of
contour plotting, but Sarah gave the students a very understandable and intuitively appealing
exposition of the key ideas at their level of mathematical preparedness, and then provided in-class
and homework exercises to solidify their understanding. Space allows for just one example of her
providing (quite literally) hands-on experience with such sophisticated mathematics: when the
need arose to estimate distances on contour maps, she handed out strips of dental floss for her
students to use in conjunction with the scale printed on the map! Soon the students were plotting
paths and flow rates for the contaminants and determining which houses downstream from the
source were likely to be affected. Can you think of a better way to capture student interest, show
the relevance of mathematics to key issues about which the students will have to vote in the
future, and teach them to analyze such matters rather than simply react to political rhetoric?
Sarah integrates computer methods (including Excel and a HazMat software package) and
scientific calculators to optimize calculations that the students first experience in the classroom
via such plotting and hand-calculation exercises as the one described above. A computer
laboratory period immediately after that dental-floss and hand-calculation session elicited oohs
and ahs as students saw how quickly automated analysis tied to the underlying mathematical
model can proceed.
How do the students react to the course? Enthusiastic letters from former students played a major
part in Sarah's selection for the Award. Perhaps the following incident underscores just how
much the students enjoy the course and Sarah's teaching of it. At the end of my week of visiting
Math 108V, a student asked whether I was a faculty member. When I said I was, he smiled
broadly and said “Isn't she just great?” To experience more of what evokes such student
enthusiasm, please visit http://www.math.uconn.edu/~glaz/Math108, which also has links to two
articles about the course.
REGINA SPEICHER RECEIVES UNIVERSITY'S OUTSTANDING TEACHING
ASSISTANT AWARD
The Mathematics Department is fortunate to have many graduate students with distinguished
teaching records. The university has recognized the teaching contributions of one of these students,
Regina Speicher, selecting her as the recipient of its 2004 Outstanding Teaching Assistant Award.
Regina had previously received the department's Louis J. DeLuca Memorial Award in recognition
of her exemplary teaching. She has also made important service contributions to the department
during her graduate career, and is this year's recipient of the department's Connie Strange Graduate
Community Award in recognition of such contributions.
Regina Speicher grew up as one of five children on a lake in Brackney, PA near Binghamton, NY.
Being part of an active family, her interests as a child (outside of schoolwork) included many
different sports, such as basketball, tennis, and softball, as well as playing the piano and reading.
As the daughter of a mechanical engineer and high school math teacher, Regina especially enjoyed
her math and science courses in high school, where she graduated as valedictorian. She began her
undergraduate years at Villanova University as a mathematics and biology major, with thoughts of
becoming a physician. While in college, Regina played softball for the university on an athletic
scholarship and attained distinction as both a Villanova University and Big East Scholar Athlete.
Intrigued by a talk given at Villanova demonstrating the connections and applications of
mathematical research to biology, Regina eventually decided against medicine and received a BS
degree in Mathematics. Although she spent two summers working as an actuarial
intern in Washington, D.C., Regina decided to attend graduate school with the goal of becoming a
mathematics professor.
Regina is in her fourth year at UConn. Currently, she is working in the area of nonlinear elliptic
partial differential equations with her advisor, Dr. P.J. McKenna. Regina finds teaching
undergraduate courses to be an enjoyable and rewarding experience. She shares her teaching
expertise with others as part of the department's TA Network, of which she is a founding member,
and serves as a mentor for new graduate students. She has also been elected by her peers as one of
the two graduate student representatives to the department's Graduate Program Committee, and her
service as liaison between the committee and the students has been invaluable. Congratulations,
Regina!!!
Regina Speicher & Manny Lerman
THE UCONN MATHEMATICS CLUB
by Keith Conrad, faculty advisor
This spring, after a 10-year hiatus, the UConn Math Club was revived. [Web address:
http://www.math.uconn.edu/~kconrad/mathclub.] The officers of the Math Club were: President Scott D'Alessandri; Vice-President-Chris Collin; Treasurer-Cheng Yu. The primary purpose of the
club is to provide a forum for undergraduate students to hear about topics that are not met in the
basic mathematics courses. Talks in the Math Club have generally attracted between 12 and 14
students a week, presumably not just because of the free pizza and soda! There were noticeably
larger turnouts for the talks by our own Professors Wickless and McKenna.
Equally encouraging is that, just as research seminars within the department have outside speakers,
so too did the Math Club. There were four talks by mathematicians not affiliated with UConn (see
the schedule below), and the club hopes that USG funds will allow this trend to continue.
Meetings at the start of the semester were in a small room, but moved to the department's
colloquium room to better accomodate the audience. When plans for an undergraduate lounge are
realized, we hope that the Math Club can make regular use of the new room.
Schedule of Math Club talks for Spring 2004
Feb. 11
K. Conrad
Relativistic Addition and Real Addition
Feb. 25
W. Wickless The Impossibility of Trisecting Angles
Mar. 3
D. Pollack (Wesleyan) An Introduction to Elliptic Curves
Mar. 17
A. Russell
Coin-flipping Over the Phone: an Introduction
to Provably Secure Two Party Communication
Mar. 24
P.J. McKenna Why Suspension Bridges Sometimes Fall Down
Mar. 30
R. Kaufmann (OK State) An Introduction to Topology
Mar. 31
A. Rej
The Geometry of Quaternions
Apr. 7
D.R. Solomon Orders of Infinity
Apr. 15
D. Khoshnevisan (U. Utah) Random Thoughts (In Two Acts)
Apr. 21
T. Weston (Amherst) The Banach--Tarski Paradox
Math club meeting on March 31st.
UNDERGRADUATE COMPETITIONS
Results in our two undergraduate problem-solving competitions -- the national William Lowell
Putnam Mathematical Competition in December and our in-house Calculus Competition in the
spring -- were especially gratifying this year, leading to our awarding unusually many prizes at the
department's annual awards ceremony in April 2004.
3615 students from 479 colleges and universities in the United States and Canada participated in the
Putnam competition, which was administered in the form of a brutal examination given in two
three-hour portions on Saturday, December 6, 2003. The median score nationally was 1 point out
of 120. Twelve UConn students participated, and five of them received substantial scores. Brian
D'Astous and Michael Nehring placed in the top 13 percent, Cheng Yu in the top 15 percent,
Andrew Polonsky in the top 22 percent, and Zachary Chaves in the top 30 percent. As far as we
can determine, never before have so many of our students placed so well. All five were honored at
the awards ceremony, and all are expected back next year, so with additional emerging talent, the
future looks bright indeed.
The department's annual Calculus Competition was held on March 31, 2004. Twenty-one students
participated, and every single one of them submitted a paper of substance, an unprecedented
occurrence. For the second year in a row, Gregory Magoon was the top finisher over-all; he was
followed by Heeseop Shin and John Haga. Shin also led in the intermediate category, followed by
Yik-Sian James Seow. Seow in turn won in the beginner category, followed by Laura Mariano and
Aparna Boddapati (tie) and then Matthew Boland. A number of honorable mentions were also
awarded.
The presence of such a large group of bright and interested problem-solvers has induced the
department to resurrect its one-hour-per-week undergraduate problem seminar (not given in many
years) this fall.
For recognition of our majors by the University as a whole, please direct your attention to the
article "Undergraduate Student News," where you will learn, among other things, of the
extraordinary success of this year's junior mathematics majors in achieving invitations to the
national academic honor society, Phi Beta Kappa.
ALUMNI NEWS
Niel Infante (UConn Math MS, 1996) is senior systems programmer in the Plant Sciences
Department at The University of Arizona. After leaving us, Niel earned Master's degrees in
Computer Science from Wesleyan and The University of Pennsylvania. He is continuing his
research studies, begun at Wesleyan, on the fundamental structure of rice, sorghum, and maize.
(E-mail: [email protected])
Peter Johnson (UConn Math/Stat BS, 1985; MS in Math, 1987) did actuarial work for the
Hartford, taught at Colby-Sawyer College (New London, NH) for seven years, and earned a
doctorate in Curriculum and Instruction (Math Education) at Penn State. He has been on the faculty
of Eastern Connecticut State University since 2001. Pete and his wife Kathleen have two young
sons and reside in Eastford, Connecticut.
Robert T. Leo, Jr. (UConn Math BA, 1967) received his Master's in Mathematics from the
University of Oregon in the summer of 1968. Bob resides in Manchester, Connecticut and is a
Project Manager at IBM Global Services.
UNDERGRADUATE STUDENT NEWS
Among the students nominated in 2004 to join the University’s chapter of Phi Beta Kappa,
the national liberal arts and sciences honor society, which dates from 1776, were a significant
number of mathematics students. By concentration, the initiates included one Applied
Mathematical Sciences major: Rebecca Schuetz; six Mathematics/Actuarial Science majors:
Christie Dietrich, Stanislav Gotchev, Brian Jawin, Monica Johnson Noel, Surekha Patel, Thomas
Wilk Jr; and eight Mathematics majors: Jonathan Axtell, Brian D'Astous, Amie Howell, Geri
Izbicki, Kelly McCabe, Michael Nehring, Valerie Pare, Melissa Prokop. The criteria for
nomination are a high overall grade point average and a program rich in liberal studies. This spring
only ten juniors were chosen, from all fields of study; so the fact that four of our juniors (Brian
D'Astous, Christie, Stanislav, and Michael) were selected is something in which we take great
pride.
Geri Izbicki, Peter Fagan, Jonathan Lynn, and Melissa Prokop graduated with honors.
David Gross, Undergraduate Studies Chair, has an update [lightly rewritten by your editors]
on a family of recently graduated students: Let me take a moment here to let you know about the
accomplishments of some of our graduates. Michael Wininger graduated in December 2003 with a
dual degree (BA in Math/BS in Physics). He is now working in the engineering department of
Adidas in Oregon. Michael has been accepted to three graduate schools and is leaning toward going
to graduate school in Scotland to study rehabilitation engineering, concentrating on prosthetic
engineering. Many of you may remember his brother Matthew (BA in Mathematics-Actuarial
Science with Cum Laude honors, May 2000). Matthew is a Senior Actuarial Associate at the
Hartford and is closing in on Fellowship in the Society of Actuaries, having completed the course
work and nearly all of the professional development requirements. Congratulations are also due on
his upcoming marriage. To round this out, the third Wininger brother, William, graduated in May
2004 with a BA degree in Political Science and a minor in History. (Of course, he took calculus.)
He was just accepted to the Harvard Divinity School where he will continue his studies in political
science with a specialization in mid-eastern studies. He feels that to really understand all the
political influences in the countries of that region, one must understand the religious influences as
well. Quite a trio of brothers!
MATHEMATICS POSTDOCTORAL PROGRAM 2003-04
Three post-doctoral fellows decided to leave us after one or two years at UConn: Ines
Armendariz is a member of the Statistical Laboratory at the University of Cambridge, Great Britain
([email protected]); Kyle Kneisl has taken a position with the National Security Agency;
and Alex Stokolos is an assistant professor in the Department of Mathematics of De Paul University
([email protected]). Continuing post-docs were Yasar Sozen (third year), Fabiana
Cardetti, Zhixiong Chen, Jennifer Hill, Moritz Kassmann, Dahae You, and Zhenbu Zhang (second
year). New to the program were Edlira Shteto (Ph.D. Scoula Normale Superiore, Pisa, 2003), Bjorn
Kjos-Hanssen (Ph.D. University of California, Berkeley, 2002) and Martynas Manstavicius (Ph.D.
Tufts University, 2003).
Some of the post-docs gave seminar talks, including
Dahae: A Fatou Theorem for alpha-harmonic Functions
Martynas: On the p-variation of Markov Processes
Moritz: (1) Nonlocal Operators of Variable Order and Harmonic Functions
(2) Harmonicity, Mixed Boundaries, and Mixed Feelings
Fabiana: Local Controllability on Lie Groups
Bjorn: Reverse mathematics and diagonally non-recursive functions.
(Bjorn spoke at the Connecticut Logic Seminar, which has been held weekly at Wesleyan
University for many years.)
MATH DAY 2004
The Department’s annual Awards Day Ceremony was held on Thursday April 29 in conjunction
with national Mathematics Awareness Month. After cookies and punch and opening remarks by Dean
Ross Mackinnon, various students were recognized for their achievements.
Freshman Calculus Achievement Award, presented by Jim Hurley
• Abigail Hidalgo
The CIGNA Awardees in Actuarial Science, presented by Jim Bridgeman
• Peter Fagan Monica Johnson
Beibei Li
Katie McCarthy
Surekha Patel
The University of Connecticut Calculus Competition winners,
presented by Stu Sidney
Gregory Magoon - First over-all (for the second year)
Laura Mariano - Second Beginner (tie)
Heeseop Shin
- Second over-all & First Intermediate
Aparna Boddapati - Second Beginner
John Haga
- Third over-all
Matthew Boland - Fourth Beginner
Yik-Sian James Seow – Second Intermediate & First Beginner
Andrew Polonsky - Honorable mention over-all
Five additional students received honorable mention in the Beginner category:
James W. Chernesky Jr, James Cornacchio, Michael Carrison, Nicole Gonzalez, and Kelly Michaelis.
•
•
•
•
•
Superior or Noteworthy Performance on the William Lowell Putnam
International Mathematics Competition
• Superior performance Brian D’Astous
• Noteworthy performance - Zachary Chaves
Michael Nehring
Andrew Polonsky
Cheng Yu
Pi Mu Epsilon honor society initiates, presented by Jerry Leibowitz
• Gina Cavallo
Geri Izbicki
Carly Williams
Presentations by Manny Lerman
The Louis J. DeLuca Memorial Award for Outstanding Teaching Assistant
• Minerva Catral
The Connie Strange Graduate Community Service Award
• Regina Speicher
Dean Ross Mackinnon
Speaking the Praises of Mathematics
Awards Day Audience
April 29, 2004
This year’s Awards Day colloquium speaker was Roland J. Minton of Roanoke
College, who spoke on The Mathematics of Sports. Here is Professor Minton’s
abstract:
Alan Shepard hit a golf ball "miles and miles" on the moon. Would golf actually be
easier on the moon? The New York Yankees had trouble hitting Boston pitcher Tim
Wakefield's knuckleball. Why is this pitch so unpredictable and why don't more
pitchers use it? How much margin of error does Andy Roddick have on his 140 mph
tennis serve? Why does it help to put spin on the serve? These and other sports
questions can be analyzed using basic algebra and calculus. The focus in this talk is on
what information mathematics can contribute on a variety of sports issues. By the end
of the talk, you will know answers to the above questions as well as why it was so hard
as a youngster to keep your eye on the ball.
Guest speaker Roland Minton being
congratulated by Jim Hurley
after his stimulating lecture/demonstration
Stu Sidney and Putnam Stalwarts
Brian, Cheng, and Andy
Jerry Leibowitz and Miki Neumann
with Geri & Gina, new Pi Mu members
STU's PUZZLE CORNER
by Stuart Sidney
Powers of sums and sums of powers
Way back when you first learned about the notion of definite integral, you may have
a
evaluated a few directly from the definition. Typically, the first few integrals were of monomials x
with a a positive integer, say 1, 2 or 3, and to actually evaluate such an integral you needed to find a
a
formula for Sa(n) = ∑{k : k = 1, …, n}. If you did the cases a = 1 and a = 3,
2
you couldn't help noticing that (S1(n)) = S3(n) is true for every positive integer n. Perhaps you
wondered whether there were any other equalities of this type. Precisely, always assuming that a, b
and c are positive numbers and b > 1, are there any triples (a, b, c) for which
b
(*) (Sa(n)) = Sc(n) for all n
other than the triple (a, b, c) = (1, 2, 3)? Our three problems study this question in increasing
generality. The first is well known, and not too hard; the second is somewhat harder; and as for the
third, as of this writing, your diligent columnist has yet to settle the matter.
Problem 1. Prove that if a, b and c are positive integers with b > 1,
then (*) holds only if (a, b, c) = (1, 2, 3).
Problem 2. Prove that if a, b and c are positive rational numbers with b > 1,
then (*) holds only if (a, b, c) = (1, 2, 3).
Problem 3. Determine whether it is true that the only triple of positive real numbers (a, b, c) with b
> 1 for which (*) holds is (a, b, c) = (1, 2, 3).
Alas, Problem 3 is not a famous problem with a big cash reward attached to it (recall the
$100,000 Beal conjecture from last year's column), so the best I can offer is publication of the first
correct solution. Along those lines, last year’s puzzle column did elicit some response. I invited
solutions to the following problem:
2
2
4
4
4
2
2
3
4
2003 Problem 2. Do the equations a + b = c , a + b = c , and a + b = c have solutions in
natural numbers?
2
2
4
Tom Leibowitz provided the solution 7 + 24 = 5 to the first equation, which is a cousin
2
2
4
2
2
2
2
2
to my solution 15 + 20 = 5 . Mine arose by starting with 3 + 4 = 5 and deducing (3·5) + (4·5)
2
2
2
2
2
2
2
= (5·5) ; more generally, x + y = z leads to (x·z) + (y·z) = (z·z) .
The second equation has no solution (in natural numbers), while one solution to the third is given
2
3
4
2
3
2
by 6000 + 400 = 100 . To arrive at this last equation, start with 6 + 4 = 10 and look for natural
k 2
l 3
m
number exponents k and l for which (6·10 ) + (4·10 ) = 10 where m is a multiple of 4; thus m =
2k+2 = 3l+2, and the choice k = 3, l = 2 does the job.
Let's keep alumni input pouring (or at least trickling) in. Please send me your suggestions or
solutions, by e-mail to: [email protected] or via surface mail to: Stuart Sidney,
Department of Mathematics, Unit 3009, The University of Connecticut, Storrs, CT 06269-3009.
LET US HEAR FROM YOU
The editors of Math CONNections welcome comments from our readers. Please send them to one
us by E-Mail or fill out this form and return it by mail or by FAX.
(See the back page of this issue for the addresses.)
Name:
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GIFTS
State appropriations to the University and tuition and fees paid by students are the ultimate
source of the bulk of the operating budget of the Department and are supplemented by grants and
contracts from agencies such as the National Science Foundation. We are also grateful for the
continuing support of the actuarial science program in the form of scholarships underwritten by
corporate friends of the University. Contributions from current and former faculty members and
their families have endowed the prizes and awards mentioned in the Awards Day article: for
outstanding performance by undergraduates on the Department's Calculus Competition and the
Mathematical Association of America's Putnam Mathematics Competition, and the Louis J. De
Luca and Constance Strange awards for outstanding teaching and service by our graduate students.
We hope that the readers of Math CONNections will be inspired by such examples to
participate as contributors on behalf of these or other departmental activities. If you wish to make a
gift to the Department, please contact our chairman, Miki Neumann, about the details. He can be
reached by EMail at [email protected]; by mail at Prof. Michael Neumann, Department of
Mathematics, The University of Connecticut, Storrs CT 06269-3009; or by telephone at (860) 4863918.
Math CONNections 2004
EDITORIAL STAFF
Jerry Leibowitz
Wally Madych
Stu Sidney
[email protected]
[email protected]
[email protected]
STAFF PHOTOGRAPHER
Kevin Marinelli
[email protected]
∆ABC
≤≤≤≤≤
√√√
∑∑
∏∏
≥≥≥≥≥
√√√
∫∫∫∫∫∫
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