Not a secret anymore, Cryptology at FAU!

It takes time, but our Department is well on its way to becoming a major center for the study of Cryptology and Information Security. The first steps in this direction were taken a few years ago when Professor Ron Mullin joined the Department on a part time basis in 1996. Professor Mullin was no stranger to our Department, having been briefly part of our faculty in the early days (1967-1969) and then as an organizer of and participant in most of the annual Southeastern Combinatorics, Graph Theory and Computing Conferences held on our campus. A full time professor until 1996 in the Department of Combinatorics and Optimization at the University of Waterloo in Canada, he has published over 200 research articles on topics such as finite fields, combinatorial design, coding theory and cryptology. He is one of the three founders of Certicom, a company providing security solutions, including cryptographical products, to the industry. Professor Mullin also happens to be the Ph.D. dissertation director of one of the other founders of Certicom.

Professor Spyros Magliveras

In 2000 we were fortunate enough to hire Professor Spyros Magliveras, who was then the Henson Distinguished Professor in Communication and Information Science at the University of Nebraska, Lincoln. Professor Magliveras is a world renowned expert in cryptology, combinatorics and applied algebra. He is a recipient of the Institute for Combinatorics and its Applications' 2001 Euler gold medal award for his lifelong research in combinatorics. He became the Department's director of applied mathematics programs and, since 2004, the chair of the Department. Under his leadership all programs, applied and pure, have prospered and cryptology has reached maturity, with two more faculty members, Professors Wandi Wei and Rainer Steinwandt, joining the program on a full time basis. In 2003 Professor Magliveras established the Center for Cryptology and Information Security, funded by federal funds, as a means to channel all the Department's efforts in cryptology. In addition, the Journal of Mathematical Cryptology has just been launched; its first issue will appear in 2007. Professor Magliveras, Professor Steinwandt and a close collaborator of Professor Magliveras, Professor Tran Van Trung of the University of Duisburg-Essen in Germany, are the managing editors. In addition, several other faculty members are also members of the Center and involved in cryptology.

Cryptology is without doubt an area that is extremely attractive to students with mathematical talent. It bridges the gap between very abstract and sophisticated mathematics and very down to earth applications. An added drawing point, which should not be totally disparaged, is that it deals with a very hot topic, information security. Experts in the area are in great demand today and can command excellent salaries. Of the several students that decided to work in the area of cryptology, two have already obtained their Ph.D. working under the supervision of Professor Magliveras.

Events and People

Regional AMS meeting. Conference in honor of Michael Cwikel

On April 1,2 of last year, Florida International University played host to one of the American Mathematical Society' regional meetings. While FIU provided the venue, FAU also participated strongly in the event. Most notably, Professor Mario Milman of our Department was invited to organize and cochair (with Professor Marius Mitrea of the University of Missouri) the session on Harmonic Analysis and Partial Differential Equations.

Professor Michael Cwikel
Believing that his friend, the notable Israeli mathematician Michael Cwikel, was about to celebrate his sixtieth birthday, Professor Milman decided to organize (with the help of Professor Laura DeCarli of FIU) a satellite conference in honor of Professor Cwikel. The Cwikel conference began on March 29 at the Coral Gables Holiday Inn and was sponsored by the Charles Schmidt College of Science and by the Florida Israel Institute. As it turned out, Professor Cwikel was still two years away from his 60th birthday; even so, the conference was a great success. Professor Cwikel is not only an outstanding mathematician, he is also one of the nicest people around. The conference attracted a good number of his many friends and admirers from around the world, producing a meeting that was both a social and a scientific event.

On April 1 the Cwikel conference morphed into an additional session on "Interpolation Theory and its Applications" at the FIU AMS conference. In addition to Professor Milman, the following Department people presented papers and/or gave talks at diverse sessions of the AMS meeting of April 1-2: Professors Ralph Karr, Lee Klingler, Markus Schmidmeier, Tomas Schonbek and Daniel Waterman; Students Jan Kalis, Eva Kasprikova, Carla Petroro.

Notes from the chair

Dear Friends,

I hope you enjoy our first bi-annual bulletin. As any other literary venture, the bulletin will be as much a product of its editors as of its readers, and I hope you let us know what you think of it. We want to entertain and inform you and, above all, to keep you in touch with the department. We are a growing department expanding into several areas of utmost importance in today's world, such as cryptology and biomathematics. At the same time we do not forget humans have been practicing mathematics for thousands, perhaps tens of thousands, of years and we have no intention of disregarding the traditional aspects of mathematics.

Please feel free to write to me, either by e-mail or by regular mail, about anything having to do with the department.

Best Wishes
Spyros Magliveras
spyros@fau.edu

In Memoriam

The Department mourns the loss two of its faculty members, who passed away last year. Professor Helmut Schaefer joined the Department in 1988. By then he already had had a distinguished career as one of the foremost analysts of his generation and a well earned reputation as an excellent lecturer. AT FAU he continued unabated his mathematical work and became the dissertation advisor to our first Ph.D. graduates. He retired from the Department in 1998.
J. Brewer
Professor James W. Brewer joined the Department in 1986 and was the Department's chair from 1987 to 1996. During his tenure the Department initiated its Ph.D. program and doubled the size of its faculty. Teaching was one of his passions; his last teaching activity was a graduate seminar that had to be held at his house because he was already too sick to travel. A few months before his death, while there was still hope that he might win the battle with the brain tumor that defeated him, some of his friends and colleagues held a mathematical conference in his honor, which brought people from all over the United States to our campus.

Fractal Connections

H.O. Peitgen
One of the signs of Spring at FAU is the presence of Professor Heinz-Otto Peitgen, a world leader in the field of chaos and fractals. In perhaps too simplistic terms, chaos studies non-linear systems where possibly a very small initial perturbation can have enormous, hard to predict, consequences. Fractals are objects that at first glance seem to have a complicated geometric structure, but where each microscopic part looks just like the whole object. Though the discovery of fractals can be traced back to the 19th century (or earlier), giving them a name and realizing their importance to mathematics and its applications, is the work of Professor Benoit Mandelbrot, currently at Yale University. Professor Peitgen saw early on the importance of Professor Mandelbrot's work and pioneered the use of fractals in medicine, as a way to enhance images produced by MRI machines. To this effect, he founded, and is still the director, of MeVis, a medical visualization institute associated with the University of Bremen that brings together mathematicians, computer scientists and physicians and has produced important advances in the early detection and treatment of certain cancers. In Boca Raton, Professor Peitgen, has been involved in similar efforts, though perhaps on a slightly smaller scale. Here he collaborates with Dr. Kathy Schilling, the director of the Center for Breast Care of the Boca Raton Community Hospital, and is aided in this effort by FAU professors Dr. Roger Goldwyn and Dr. Richard Voss. The Center for Development of Computational Clinical Imaging, under the direction of Professor Goldwyn, was established in the Charles E. Schmidt College of Science, as an institute in which this collaboration can most efficiently be carried out.

Professor Peitgen also has a deep interest in teaching and the formation of teachers, which motivated him to create the Math Science Partnership Institute, funded by a very substantial National Science Foundation grant. Working together with the Broward County School Board, the Institute provides additional training for mathematics teachers leading to a master's degree in middle school mathematics.

Professor Peitgen is the recipient of many prizes and awards during his very distinguished career. Here we only mention that last February he and Professor Mandelbrot of Yale were inducted into the Charles E. Smith College of Science Hall of Fame. More recently, Professor Peitgen was awarded the Deutscher Gründerpreis (German Start-up Prize) in the category "Visionary" at an awards ceremony in Berlin on September 12.

Combinatorial Communications

The Department of Mathematical Sciences is going to be the host of the 38th annual Southeastern International Conference on Combinatorics, Graph Theory and Computing (SICGTC), to be held on our campus March 5-9, 2007. Combinatorics and its sister Graph Theory are what may be called old-young areas of mathematics. Their origins go back at least to Leonhard Euler's celebrated solution of the Königsberg Bridges Problem in the eighteenth century, a century that saw a veritable quantum leap in mathematics and physics developments. However, the most impressive development of combinatorics and graph theory occurred from the 1950's onward, driven perhaps by the advent of the digital computer and the increasing importance of discrete mathematics. When you have machines that can process billions of numbers at the same time, knowing how to count well is of the utmost importance. Combinatorics is, when reduced to its simplest terms, sophisticated counting, counting as an art.
The origins of combinatorics at FAU are, of course, more recent, but only because FAU is still a very young institution. Thanks to the influence of Gian-Carlo Rota, the dissertation advisor of one of the department's early chairs, and the efforts of faculty members Ronald Mullin and Frederick Hoffman among others, our department had a strong combinatorics component almost from its inception. We have been hosting the annual SICGTC conferences at least two years out of every three (the remaining times it is hosted by Louisiana State Unversity). This conference brings together some of the foremost researchers in the area and it is a marvelous opportunity for our graduate students (and faculty) to interact with a large number of extremely active and gifted mathematicians. Of particular interest are the talks given by the invited speakers, who are selected for their eminence both as mathematicians and as expositors. In the past, we have had Paul Erdös, John Thompson, Daniel Gorenstein, Carl Pomerance and John Conway among many others; the invited speakers at the 2007 SICGTC Conference will include Professors Ralph Faudree, Aviezri Fraenkel, and Jonathan Jedwab. More information about the conference can be found at http://www.math.fau.edu/cgtc/cgtc38/.

News in Brief

A very successful Math Day 2006 was held on February 25, 2006. Close to one hundred high school students, accompanied by some of their math teachers, came to our campus to compete for prizes. In addition to the competitions, we had two excellent talks by Professors Heinz-Otto Peitgen and Dragan Radulovic of our department.

In January of 2006, the Department of Mathematics played host to the yearly regional Mu Alpha Theta Competition which brings together over a thousand high school students from the neighboring counties. Congratulations are due to Professor Markus Schmidmeier and his army of enthusiastic volunteers for the planning and flawless development of the event.

Jason Boynton, Hyungju Ban, Michal Sramka, and Daniel Socek successfully defended their Ph.D. dissertations and will be awarded Ph.D. degrees. Jason's dissertation, Integer-valued Polynomials and Pullbacks of Arithmetical Rings, under the direction of Professor Lee Klingler, was defended on June 28, 2006. Hyungju's director was Professor William Kalies and he defended his dissertation, Computing Global Decompositions of Dynamical SYstems on October 24, 2006. Michal, directed by Professor Spyros Magliveras, defended his dissertation, New results in group theoretic cryptology, on November 2, 2006. Daniel's Ph.D. is in computer science, but his area is also cryptology and Professor Magliveras acted as a co-supervisor.

Arie Israel graduated with a Master's degree this August becoming at age eighteen the youngest student to obtain such a degree at FAU. The secret to graduating young is to start young, and Arie began his university career with us at age 14. He will be continuing his education as a Ph.D. student at Princeton.

Alex Opritsa, a student in our Department, received the prestigious Wimberley award given every year to the student whose work is deemed as most outstanding. Alex is also the president of the FAU chapter of Pi Mu Epsilon, the National Honorary Mathematics Society. He will probably continue in our Department as a graduate student after receiving his BS degree.

Math Club. Thanks to the initiative of two of our graduate students, Jan Kalis and Eva Kasprikova, students are soon going to have a Math Club. Membership is open to all FAU students; for details please contact either Jan (jkalis1@fau.edu) or Eva (ekasprik@fau.edu).

Problems and Solutions

Please send your solutions to Professor Wandi Wei, Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431. Solutions may also be submitted electronically to newsletter@math.fau.edu
Solutions and the names of people sending in correct solutions will be published in the next issue.
  1. My calculator evaluates the following number as 2:

    (10+6√3)1/3 - 2(10+6√3)-1/3.

    Is this correct? Prove or disprove that the displayed number is exactly 2.


  2. The yellow circle is inscribed in the blue square and the red circle is tangent to the yellow circle and to the sides of the square. If the square has sides of length 2 units, determine the radius of the red circle.