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Mathematics Newsletter 1994-1995

Contents

Applied Math Colloquium

Michael Tabor

On-line Seminar and Colloquia Info

Speakers, affiliations and their titles:

  • Charles R.Doering (Los Alamos National Laboratory), "Randomly Rattled Ratchets"
  • Vernon Smith (University of Arizona), "Experimental Methods in Economics: Auctions and Miscellaneous Other Topics"
  • Robert E. Dickinson (University of Arizona), "What is Computed in Climate Models?"
  • Alain Goriely (University of Arizona), "Nonlinear Fronts Selection for Reaction-Diffusion Equations"
  • Vangelos Coutsias (University of New Mexico), "Cornuspirals"
  • James Powell (Utah State University), "Mountain Pine Beetles And Lodgepole Pine: A Mathematical Model Of Mass Attack"
  • Harvey Segur (University of Colorado), "Periodic Waves in Shallow Water"
  • Robert Behringer (Duke University), "The Scientist In The Sandbox: Complexity And Dynamics In Granular Flow"
  • Barbara Lee Keyfitz (University of Houston), "A Geometric Theory Of Conservation Laws Which Change Type"
  • George Papanicolaou (Stanford University), "Wavelet Based Methods For Nonstationary Processes With Applications To Seismology"
  • Harry L. Swinney (University of Texas), "Hexagons, Stripes And Self-Replicating Spots In a Reaction-Diffusion System"
  • Henry S. Greenside (Duke University), "Extensive Chaos"
  • Chuck Newman (Courant Institute), "Disordered Systems And Percolation - A Survey Of Selected Results"
  • Samuel I. Vainshtein (University of Chicago), "Sign-Singular Measure And Its Association With The Scaling Of Random Processes And Multifractal Structure"
  • Gene Myers (University of Arizona, Computer Science), "Advances In The Computational Aspects Of DNA Sequencing "
  • David M. Stuart (UC Davis), "The Gradient Flow Of The Superconducting Ginzburg Landau Functional"
  • Maria Schonbek (UC Santa Cruz), "Decay Of High Sobolev Norms For Solutions To The Navier-Stokes Equations"
  • Pierre Meystre (University of Arizona, Optical Sciences), "Nonlinear Atom Optics"
  • Mahadevan (University Of Illinois, Urbana), "Constrained Dynamical Systems: Atypical Examples"
  • Bjorn Birnir (UC Santa Barbara), "Are Solutions To Completely Integrable Nonlinear PDE's Physically Relevant?"
  • David Arnett (University of Arizona-Steward Observatory), "Cosmic Simulations"
  • Mark Millonas (Los Alamos NL), "Using Colored Noise To Explore The Kinetics Of Ion Channels"
  • Emily Stone (Utah State), "Extracting Structure and Dynamics from Complicated Spatio-temporal Data"
  • Vaughan Jones (UC Berkeley), "Combinatorial Structures In Subfactors"

Our Computing Environment

Bob Condon

It has been an expansion year for computing in Mathematics. Among other things, a new computer classroom and an open access undergraduate lab facility were completed. As usual, much of the work was locally performed -- check out Math 102 and Math 224/226 to see what has been accomplished. In an especially hectic year, I'd like everyone to know what a great job our graduate/undergraduate student crew of Mario Encinas, Rosario Garcia, Cindy Kaus, Gloria Martinez, Armando Mendoza, Steve Uurtamo, and Yu-Wen Cheng have done. With their extra help, we were able to beat some tough situations and get the new facilities on-line.

In the graduate area, we installed some much faster workstations -- yes, we still need more new equipment -- and increased the amount of disk space available for all. Thanks to Anu Rao, we were able to schedule some brown bag specials. Mark Hays gave a talk on making movies while anonymous Steve and Ricardo Adams spoke on brewing beer ... "one of the best ever," said an amazed Bill Dunn. Cindy Teasely gave weekly talks on the use of Sun and Unix systems and provided desperately needed system support and user help. Cindy Kaus and Yu-Wen Cheng, our grad student contingent, staffed the new M226/M228 lab. They helped our undergraduates both by answering questions about mathematics and about the use of our educational software.

For undergraduate use we now operate two 30-unit PC-classrooms and one 25-unit open access work/study lab. During the year, we have added 60 new PC computers to support these facilities, all having Intel 486/66 and Pentium-90 class processors. Thanks to the efforts of Ricardo Martinez, Doc Hays, and Cindy Teasley, we've been able to provide Unix accounts to our undergraduate mathematics majors by configuring nine of the new M226/M228 machines as dual purpose DOS/Linux systems. Approximately 60 undergraduate majors are now computing with Unix on these hybrid systems. At weekly UCAN help sessions, Cindy Teasley has been explaining use of email, X11 windows, Pascal, C, and LaTex software to these students. In addition to the Arizona Mathematical Software and Linux/Unix, M226/M228 students have the use of the mathematics-biology modeling programs provided by Bill Schaffer's (of EEB and Applied Mathematics), and PVM (Parallel Virtual Machine - getting 7 Pentium machines to compute as one in parallel).

To support this considerable growth, the Department has upgraded its older network and computer server hardware. Over the past year, the old Turquoise, Amethyst, Sahuarita, and Yecora systems have been retired, and faster server machines have taken their place. Ricardo Martinez has been busy rebuilding and rewiring the departmental networks which provide access to these central systems. New network configurations that better support clusters of common usage have been installed. With the new infrastructure, the Department can hope to adequately support its 400+ users and 200+ machines while allowing for future growth and usage in the second and third floor building areas.

As always, many people are due thanks. Every Mathematics computer user should realize that (at least in Arizona) resources do not simply drop from the sky. Our facilities exist due to careful and longstanding effort. Faye Villalobos has done marvelous work with the budgets - making dollars stretch and grow. Thanks to the work of David Lovelock, David Lomen, et al, we were able to build and equip the original M101/M103/M105 complex. Based on this success, we've been able to add on the M102 and M226/M228 facilties. Michael Tabor, Zhen Su She, Bruce Bayley, David Levermore, Alan Newell, et al, have provided considerable support for better computing hardware (both servers and workstations), necesssary software (such as Mathematica, Maple, and IDL), and specialized resources (such as movie making, color printing, and, hopefully soon, parallel processing). Bill Velez has done a tremendous job recruiting and helping finance superior undergraduate help. Those serving on the Computer Committee over the years -- Jim Cushing, Larry Grove, Marek Rychlik, Moysey Brio, et al -- have quietly labored on everyone's behalf by writing reports and proposals, lobbying for greater departmental and institutional support, and providing numerous auxiliary services (table saws, computers, transport, books, counsel). We owe thanks to our administration; the Science Dean(s) (Ed McCullough and Eugene Levy) and Vice President for Research (Michael Cusanovich) have always pulled for our success. To all that I haven't mentioned, I'm running out of space ... next year. To our past help -- Myriam, Dutch, Hannah, Bassam, Cathy, Matt, Jose, James, and Ann -- I owe/miss you ... do well!

Next year: more disk space, more rooms wired, faster machines, and department information on-line!

The Co-Op Class of 1994-95

Elias Toubassi

The Co-Op Program continues to develop close bonds between the University and teachers from the middle schools and high schools in our area. This year we have six fine teachers: Virginia Crook, Utterback Middle School; Kay Groll, Canyon Del Oro High School; Gene Hendricks, Sunnyside High School; Ron Hopley, Tucson High School; Dennis Mobley; Palo Verde High School; and Chris Yetman, Canyon Del Oro High School.

Virginia Crook is well traveled due mainly to her husband's career in the military service. She has lived in 41 different places, including six countries. Her education includes a BA from Florida State University in 1961 in Spanish with a minor in mathematics education and a Master's in mathematics education in 1985 from the University of Nevada at Las Vegas. Virginia has taught a variety of subjects including Mathematics, English, Spanish, and Computer Literacy at levels ranging from sixth grade to adult education classes. Her interest in mathematics education took off in 1981 when she accepted a position at Southern Nevada Vocational Technical Center. This interest continued when she moved to Tucson and a teaching position at Utterback Middle School in 1988. She continually strives to grow professionally as shown by her participation in programs such as PRISM and Making Math Count. Virginia has three grown up daughters - Debbie, Sheryl, and Linda.

Kay Groll comes to us with two passions, revising the curriculum at Amphi High School and introducing technology, particularly graphing calculators, in the algebra courses. She has taught all levels of mathematicsand computer programming, including Pascal, but her focus is how to teach mathematics with a real-life, problem solving approach. Her strong advocacy for the use of graphing calculators in algebra prompted us to assign her to teach a pilot section of Math 117 with calculators in cooperation with Chris Yetman. She moved to Tucson from Decatur, Illinois in 1983 where she taught high school for three years. She earned a Bachelor's degree in 1979 and a Master's degree in 1980 from Eastern Illinois University. Her outside interests revolve around her family. She has two children Karen (9) and Karl (8). She keeps in touch with her children's education and sports activities by volunteering in their classes and by coaching their soccer teams. Her own current consuming passion is competing on USTA tennis team which hopes to capture the national title this October in Orlando!

Gene Hendricks' participation in the Co-op Program is a milestone. When the program started in 1987 Gene was hired by the University as our representative to Sunnyside High School to cover Paul Dye's classes while Paul was a Co-op teacher. At the end of the year Gene was given a permanent position at Sunnyside. With Gene's participation this year the Co-op program has come full circle. Prior to earning his teaching certificate in 1985 Gene had worked for Ralston Purina for nine years as a training supervisor. His academic achievements include a BS in Systems Engineering from Arizona in 1972 and a Master's degree in 1994. His hobbies include walking, hiking, and playing bridge - which he takes very seriously as he is a life Master in the American Contract Bridge League.

When I think of Ron Hopley, I think of his many contributions in the areas of geometry. Three years ago, after his participation in the PRISM Program, he set out, with the help of members of the computer club at Tucson High, to bundle the 3-D graphing program Acrospin with over 90 geometric data files. He subsequently wrote an article on this which appeared in the Mathematics Teacher in May 1994. He has worked with David Gay on the Mathematical Gem and Mineral Show, and more recently assisted in Math 330. Ron enjoys problem solving and had a great time in Fred Stevenson's Math 507 course last Fall. He earned both his degrees from the U of A, the Bachelor's in 1974 and Master's in 1987. Ron's wife Sally is a librarian in the Catalina Foothills School District. They have a two year old son and are expecting their second child this summer.

Dennis Mobley was born and raised in Tucson. He attended the U of A and earned a Bachelor's degree in 1974 and a Master's degree in 1985. He taught eight years at Wakefield Junior High and the last eight years at Palo Verde High School. None of what I just wrote would surprise anyone but read on! Dennis' great grandfather settled in Prescott, Arizona in the 1880's from Leeds, England. Dennis has coached water polo for 20 years, 12 of these at the club-level at the University of Arizona. His women's team won the Intercollegiate National Championship in 1977. Dennis was the crew chief on a hot air balloon team for one and a half years. He has done some traveling. His water polo team toured Australia and New Zealand for two months in 1979-80 and he spent a year in Edinburgh, Scotland, as a Fulbright Exchange Teacher in 1981-82. Dennis has done a lot to revive the interest of Palo Verde students in mathematics. He has developed a mathematics elective for seniors in the spirit of For All Practical Purposes. He is also responsible for tripling the number of students taking advanced courses including calculus. Dennis and his wife Rosetta have two children.

Chris Yetman is a most enthusiastic teacher. He will try to teach anyone who will stop and listen. He was born in Tucson and is a graduate of Amphi High School. He earned a Bachelor's degree from Carleton College in 1986 with a double major of Mathematics and English. He earned his teaching certificate in 1988 from the U of A and took a position at Canyon Del Oro High School that year. He, like Kay, is an avid spokesperson for the use of graphing calculators in the algebra curriculum. He is very hopeful that their pilot section of Math 117 will become the standard course. His goals for the near future are to earn a Master's degree, climb a few more 14,000 foot peaks, and write software for the high school curriculum. Chris enjoys outdoor activities, especially hiking, technical rock climbing. and growing vegetables and rose bushes. Last June he was married to Elethia Viñas, a Spanish teacher at Mountain View High School.

Entry Level Colloquium

Richard Thompson

On-line Seminar and Colloquia Info

Music teachers at all levels get together and play music for their own enjoyment. Almost all teachers of English read good literature and discuss it with their colleagues. In the same fashion, mathematics teachers should find opportunities to get together and have fun doing mathematics. To provide a forum for this type of mathematical activity, Professor Richard B. Thompson initiated an Entry Level Mathematics Colloquium (ELMC), starting in the Fall Semester of 1994.

The ELMC is sponsored by the Entry Level Committee, and is presented jointly with the Mathematics Instruction Colloquium. Many beautiful and useful mathematical topics are relevant to, or arise from, the material in our entry level mathematics curriculum. These can be explored by any mathematician with the experience and background needed to teach Freshman and Sophomore courses. The ELMC presentations have been of particular interest to those who are teaching 100 and 200 level courses. This includes Adjunct Lecturers, Co-of Teachers, Teaching Assistants, and regular faculty members. Attendance by any member of the mathematical community has been welcomed and encouraged.

The following nine talks were scheduled during the 1994-1995 academic year.

  • Richard B. Thompson, "Spheres: Approximations, limits, and reality."
  • Charles T. Naffziger, "Does That Always Work? A 'shortcut' for solving a particular type of equation."
  • Ed Kingham, "Getting To The Root Of The Matter: Finding complex roots of polynomials."
  • William G. Faris, "The Mathematics Of Coin Tossing."
  • Mary Sibayan, "Simpson's Rule - On Trial."
  • Richard B. Thompson, "Roots Of Polynomials: Where are they, why are they there, and how can we find them?"
  • John L. Leonard, "What Surface Area Isn't." (This talk was cancelled, due to illness of the speaker.)
  • Bruce C. Hartman,"Calculus And Consumers."
  • Charles T. Naffziger, "Mathematics And Juggling. An introduction to site-swaps: a mathematics-juggling link."

Based upon good responses from both speakers and listeners, it is expected that the Colloquium will continue during 1995-1996 year.

Faculty News

Larry Grove

Probably our main news-event is that we must soon have a new Department Head. Alan Newell will return from sabbatical leave as Head for 1995-96, but he has announced that he has accepted a position at Warwick University in Britain. The Department has already put in place measures to ensure (we hope ) a peaceful and fruitful transition, including electing the Department's contingent of a Search Committee. We wish Alan the best of luck in his new endeavors, and of course we wish ourselves the same for continued inspired leadership.

The Department was honored to receive a Certificate of Excellence, one of five nation-wide in 1995, from TIAA-CREF, as part of the Hesburgh Award Program. To quote a portion of the citation - "The mathematics department has fundamentally transformed how math is taught and learned at the university. Alternative teaching methods such as cooperative learning, group work, and team teaching have expanded the impact of this transformation far beyond the individual faculty member. The program has revitalized the department, encouraging many of its ... faculty members to consider and emphasize teaching more seriously."

Bill McCallum has been awarded one of three AMS Centennial Fellowships for 1995-96. The other two recipients are Kent Orr of Indiana U and Rafael de la Llave of the U of Texas (Austin). McCallum earned his PhD at Harvard in 1984 under Barry Mazur. He spent two years at UC Berkeley, then a year at the Mathematical Sciences Research Institute (MSRI), also in Berkeley, after which he joined the faculty at the U of A. He spent the 1993-94 academic year on sabbatical leave in Paris at the Institut des Haut Étude Scientifiques (IHES). Bill's research, in arithmetical algebraic geometry, has been focused recently on bounding the orders of rational points on curves by means of Galois cohomological descent and p-adic analysis. Bill also plays a central role in our undergraduate program - he heads the Math Center and is one of the co-authors of the developing Consortium Calculus text on multivariable calculus.

Steve Willoughby has been awarded the Lifetime Achievement Medal for Leadership by the National Council of Teachers of Mathematics (NCTM). The medal acknowledges a lifetime of achievement in leadership, teaching, and service.

On the debit side Lai-Sang Young has recently resigned from the U of A. She will continue as a Professor of Mathematics at UCLA; we wish her the best of luck - our loss is clearly UCLA's gain.

Tom Kennedy has been promoted to Full Professor, and Doug Ulmer to Associate Professor with tenure. Earlier promotions not yet announced in this column include David Gay and David Levermore to Professor, and Lennie Friedlander and Robert Maier to Associate Profesor with tenure

New members of the faculty include Jiang-Hua Lu, Assistant Professor;,and Shandelle Henson, H. Rund Visiting Assistant Professor. Gregory Eyink has served in a visiting position this year and will be an Assistant Professor in Fall 1995. Also in the Fall we will be joined by Minhyong Kim, Assistant Professor, and Jeffrey Sheats as R. Pierce Visiting Assistant Professor.

Other visiting faculty for the past year have included Greg Anderson, Alecsander Dyachenko, Quanyuan Feng, Randy Flesch, Wladek Forysiak, Joceline Lega, Emmanuel Leveque, Simon Malham, Pat Morton, Sergey Nazarenko, Cun-Zheng Ning, Ted Petrie, Andrei Puchkarev, Samarendra Sinha, Joe Watkins, and Charles Zhang.

Family Math

David Gay

The room is filled with old and young alike. Everybody is intent. Moms, dads, and kids are doing mathematics. They are confronting tasks together. Different mathematical adventures await as they move around the room. Then they sit together and play a mathematical game of Taxman, gather data for the Birthday Problem, solve a Blocks-in-a-Box puzzle, or ... . A dad shouts with success, a mom laughs at her mistake, a child shows her dad how to "do it right". They are having a good time, finding out how each other learns, and respecting each other's capabilities. Families learn and use strategies for solving problems -- looking for clues, gathering data, making guesses, using models and pictures, and working together. Families hear about the connection between mathematics and careers and success in high school. Families learn that girls and minorities can (and should) do mathematics.

This scene has been repeated around the State several times as part of Family Math in Arizona, a program funded by Eisenhower Higher Education Funds for the period 1994-96. The project is administered jointly by the U of A Mathematics Department, the Southwest Institute for Research on Women (SIROW), and New Frontiers, a local educational agency.

Each year the project involves 30 middle school mathematics teachers - participants in the NSF Teacher Enhancement Program, Making Everybody Count - who organize, promote and present these workshops. Annually these teachers reach approximately 2400 parents and children throughout Arizona, including rural and isolated areas. The goal is to make parents, school board members, and other members of the community partners in the school reform of mathematics education.

Mathematics acts as a 'critical filter' in educational and career entry and in advancement. Lack of skill and confidence in mathematics prevents individuals from taking advantage of many educational programs and job opportunities. This is particularly so for those traditionally under represented in mathematically related fields, namely, women and minorities. As a foil to this the Lawrence Hall of Science at the University of California, Berkeley, developed Family Math in order to get parents and their children to understand, value and enjoy mathematics. Family Math achieves this through workshops of 'hands-on', cooperative and problem-solving activities that are stimulating and engaging.

Family Math provides opportunities for families to learn and enjoy mathematics together. Family Math also give parents a direct experience of what goes on in the classroom; it gets them involved as learners (not just as passive observers of what their children learn). From a Douglas principal at whose school a series of Family Math in Arizona workshops took place: "Parental involvement does make a difference in the overall success of the student. This has been one program that has successfully involved parents in the education of students. We could use more programs of this nature." From a teacher-presenter in Sierra Vista: "For the first time, I am in a non-adversarial relationship with parents."

Some anticipated consequences of the direct learning experience provided to parents by Family Math in Arizona include the following: the parents feel as though they belong in the educational process; they get to know mathematics as something human, something that everybody does, something they can believe their children (grandchildren, next door neighbors, kinfolk) can and should do, something they will therefore encourage future citizens to do; they will support school efforts to improve mathematics education; it sends a message to the community that we care to inform them about what is going on.

Making Everybody Count is a program reaching middle school mathematics teachers and their principals with mathematical ideas and effective pedagogical techniques for getting students actively involved in mathematics. To achieve real, long-term systemic change in the teaching and learning of mathematics, the community at large must also be reached. This is what Family Math in Arizona sets out to do.

Involvement of the teacher-presenters in Family Math in Arizona extends their formal association with Making Everybody Count, thus reinforcing the uses of innovative classroom approaches acquired during its summer institutes and keeping a network of supportive colleagues thriving. Making Everybody Count is jointly administered by the Mathematics Department and SIROW and co-directed by David Gay and Debbie Yoklic.

Graduate News

Cynthia Kaus

Many graduate students in both the Mathematics Department and Applied Mathematics Committee programs continued to achieve success in the 1994-1995 school year. Those students deserving congratulations for receiving Ph.D.'s in mathematics are Barbara Shipman, Will Dunn, Greg Holmberg, Hsin-Min Sun, Steven Olson, Haijun Li, and Chun-Woo Yang.

Barbara has accepted a position as Assistant Professor of Mathematics at the U of Rochester in New York; Steve has a position at the U of A as an adjunct lecturer; Haijun has a position as Assistant Professor at Washington State U; and Chun-Woo is currently an instructor at Pima Community College.

In applied mathematics the recent recipients of Ph.D.'s are Haiyan Cui, Mark Hays, James Sehnert, Bing Xu, Ramon Durazo, Michael Elfendahl, John Geddes, Aric Hagberg, Elizabeth Hunke, Andrew Long, Dan McGee, Peter Miller, Justine Ritchie, Ed Soares, Georgios Sochos, Gustavo Cruz-Pacheco, Michael Wolfson, and Edward Bevan.

Since earning their degrees, the following grads have accepted Postdoc positions: Aric Hagberg (LANL), Elizabeth Hunke (Los Alamos), Andrew Long (U of Wisconsin), Peter Miller (Australia National U), Justine Ritchie (U of Michigan), Ed Soares (U of Massachusetts), and Georgios Sochos (U of A, ECE). Haiyan Cui has a research position at the U of A Cancer Center, Ramon Durazo has a position as Professor at the U of Mexico, Dan McGee has a position at the U of Puerto Rico, and Edward Bevan has a position at Naval Weapons Research.

Congratulations are also extended to those students receiving Master's degrees during '94-'95. Master's recipients in mathematics are Armando Bezies-Kindling, Henry Jensen, John Keisling, Warren Staley, Glen Wiggy, Aamer Rizvi, Ed Alexander, Sally Duvall, Hortensia Soto-Johnson, and Steven Wexler. Those in the applied program are Natalie Komarova, Jeff Nelson, Anita Rado, Lance Smith, Matt Wagner, Ahmad Alkhatib, Brandon Gallas, and Kebenesh Wondimagegnehu. Many of the Master's recipients are continuing at the U of A in doctoral programs and others are seeking opportunities at other Universities and in industry. Good luck to them all in their future endeavors.

Many of our students have successfully hurdled other obstacles in their paths such as the oral preliminary exam and the written qualifying exams for the PhD. Those passing the oral exam are Chris Bowman, Cheryl Delorme, and Utith Inprasit in mathematics; and Marshal Mundt, Alexie Samsonovich, and Martin Garcia n applied mathematics.

After a long gruelling summer and/or winter vacation studying for the written qualifying exams, the following mathematics students have successfully passed the qualifiers: Sang Yook An, Agustin Brau Rojas, Jeff Cunningham, Aaron Ekstrom, Bill Flack, Greg Gillis, Cynthia Kaus, Weiye Li, Tony Thomas, Agnieszka Walsh, Eileen Murray, Melanie Ayers, and Dave Hrencecin. Applied mathematics students passing the quals are Cecilia Fosser, Brandon Gallas, Craig Hyde, Aaron King, Natalie Komarova, Li Liu, Jeff Nelson, Mario Parra, Anita Rado, Eric Veum, Rodrigo Gonzales, Lance Smith, Matt Wagner, and Anastasia Ruzmaikina. Congratulations to all of them.

This year, the graduate students in the mathematics department had a strong voice on their side. Melanie Ayers spent the past year representing uson the Graduate Professional Student Council (GPSC). Melanie was busy accomplishing many of her (and our) goals. Thanks to her and the GPSC, the U of A is now offering dental insurance to graduate students. The GPSC is also pushing for a child-care plan. They bought a stove for the child-care center at Christopher City and are sponsoring a monththly Grad Nite at Gentle Ben's. The proceeds from Grad-Nite will hopefully help to provide child-care to graduate students university wide. Melanie also represented the mathematics grad students at a graduate committee meeting. One of the positive outcomes of that meeting will be a graduate student representative on the graduate committee. The elected student will serve as the liaison between the faculty and graduate students. Many thanks to Melanie for all of the hard work and effort she has put forth this year.

After all the hard work, one might think there has been no time for anything else. The following students prove that grad life is not all work and no play. Cecilia Fosser and Craig Hyde announced their engagement this spring and are planning an 11 August wedding in Florida. Reva Chopra and Gopal Mohapatra, a graduate student in GeoSciences, are also planning for their wedding on 26 May in Kharagpur, India. A couple of new additions were also welcomed into the mathematics department. Amy Rabb- Liu and Charles welcomed a beautiful baby girl named Hannah into their family and Eileen Murray added an adorable puppy named Cody to her family this spring!

Congratulations to all of the graduate students in the department for making this a successful year and good luck to all as we continue on our ever-challenging paths in the future.

Graduate Seminar

Stephen Shipman

The Graduate Student Seminar was started in the Fall of 1992 as a means for graduate students to share their research problems or any related or unrelated problems of interest. In particular, it allows beginning graduate students to hear about areas of current research from a perspective and at a level which is understandable to them. It was felt that, in addition to learning the core material in a systematic way, students should also begin to see how the concepts they are learning arise naturally in applied or pure mathematical research problems.

The seminar consists of a one-hour informal talk each week by a graduate student, and the topics vary widely. The speakers and the audience come from both the Mathematics and Applied Mathematics Programs.

Some of the topics presented in the 1994-1995 academic year included the following: Barbara Shipman spoke about Grassmannian manifolds, Steven Olson presented topics on homomorphisms of near-rings from his Ph.D. dissertation, and Mohammed El Hadrami spoke on complex line bundles. Bill Dunn, in a three-talk series, presented his work on algorithms for computing Groebner bases for polynomial ideals, and Margie Lyscas presented her work on inherently ambiguous languages. More on the applied side, George Fennemore discussed PDE models for ground water dynamics, Stephen Shipman talked about discretized ODEs and their relation to Jacobi matrices, Francisco Bido presented an overview of some aspects of evolution equations and inverse scattering techniques, and Chris Bowman presented his work on patterns and the phase diffusion equation.

Anybody who would like to share his/her knowledge on a subject is welcome to speak, and anyone is welcome to attend. Contact Stephen Shipman at the U of A Mathematics Department, e-mail address: ships@math.arizona.edu.

Late-In-The-Day Courses

David Gay

In the fall of 1995, the Department of Mathematics at the University of Arizona will offer two courses at times convenient for local teachers. One course will be for elementary and middle school teachers; the other for high school mathematics teachers.

Geometry for Elementary School, the course for K-8 - teachers, will emphasize hands-on activities and group work. Topics will include measurements in the plane (perimeter, scale drawings, coordinates, area, the Pythagorean Theorem), computer investigations (polygons, angles, circles, tessellations, symmetry), and three-dimensional geometry (volume, surface area). Manipulatives - Geoboards, pattern blocks, Mira, three-dimensional solids -- and the computer program Logowriter will be used to study these topics. Class and student work will involve exploration, discussion, oral and written communication, and the completion of projects. Professor Marta Civil will be the instructor.

The course for high school mathematics teachers - Analysis of Functions: A New Look at Precalulus Mathematics - will examine traditional topics in a non-traditional way. The topics will include linear, exponential, polynomial, rational, and trigonometric functions. Emphasis will be placed on modeling, real-world applications, understanding concepts, and communicating this understanding. Group projects aimed at enriching teachers' knowledge will be part of the course. Graphing calculators will be used throughout. Professor Elias Toubassi will be the instructor.

The course for high school teachers is the first of a two-course sequence. The second course, Analysis of Functions: A New Look at Calculus, will be taught in the spring semester of 1996. It will take a look at the teaching and learning of calculus in light of the current calculus reform movement and of the recent development of technological aids for the classroom.

Mathematics Colloquium

Sam Evens

On-line Seminar and Colloquia Info

This year (as every year) we had a number of interesting colloquia. There were several memorable experiences. Sasha Bobenko brought the colloquium closer to Hollywood by showing us a movie showing time evolution of something reputed to be the solution of a differential equation. Reviews were generally positive, although the lack of popcorn upset some people in the audience. Arkady Vaintrob showed how super geometry can be used to show that cohomology exists, but unfortunately this does not seem to have helped any graduate students with their krypton-laced qualifying exams. Bert Kostant may have involved the most star systems in his talk, and impressed the audience by drawing a truncated icosahedron on the blackboard.

As usual, there were a number of memorable hikes. Somewhat surpisingly, no speakers were lost during the hikes although several finished well after dark. One of those hikes was started later than expected by an impromptu but entirely necessary discussion of stacks.

The dinners after the talks were generally a success, largely due to the efforts of J.H. Lu, vice-chairperson in charge of dinners. We managed to avoid going to any one restaurant more than twice and even succeeded in ordering in Russian once and in Chinese several times. Efforts to order in Polish at a Chinese restaurant were unsuccessful.

Here is a partial list of speakers with affiliation and titles.

  • Nolan Wallach (UCSD), "Invariant Differential Operators"
  • Hans Wenzl(UCSD),"Quantum groups and 3-manifolds"
  • Lai-Sang Young (UA and UCLA),"Ergodic Theory of Strange Attractors"
  • Taka Shiota (Kyoto), "The Symmetries of the KP Hierarchy"
  • Sasha Bobenko (Berlin), "From Discrete Surfaces to the Discrete Quantum Pendulum"
  • Arkady Vaintrob (Las Cruces), "Homological Vector Fields and their Normal Forms"
  • Gordan Savin (Utah), "A Deformation of the Regular Representation of sl(2)"
  • Michel Talagrand (OSU, Paris) "A New Look at Probabilistic Independence"
  • Mikhael Gekhtman (Weizmann Institute), "Stuctured Matrices and their Applications"
  • Krystyna Kuperberg (Auburn and MSRI), "Counterexamples to the Seifert Conjecture"
  • Estelle Basor (Cal Poly, San Luis Obispo), "Random Matrices and the Strong Szego Limit Theorem"
  • Dan Burghelea (OSU), "Introduction to L2-topology"
  • Reyer Sjamaar (IAS), "Symplectic Cross-sections and Multiplicity Free Actions of Lie Groups''
  • Jacek Graczyk (Cal Tech and Warsaw U), "Dynamics of Quadratic Polynomials"
  • Eric Friedlander (Northwestern U), "Topology of Algebraic Cycles"
  • Dan Barbasch (Cornell-IAS) "The Role of Hecke Algebras in Representation Theory"
  • Felipe Voloch (Texas), "Manin Maps"
  • Ted Petrie (Rutgers), "A Topologist's Intrusion into Equivariant Algebraic Geometry"
  • Ivan Mirkovic (U Mass, Amherst), "Finite Dimensional Representations and the Geometry of the Loop Grassmannians"
  • Jeremy Teitelbaum (UI, Chicago ), "Geometry of p-adic Symmetric Spaces"
  • Bertram Kostant (MIT), "Structure of the Truncated Icosahedron (e.g. Fullerene, Viral Coatings) and a 60-element Conjugacy Class in PSL(2,11)"
  • Robert Coleman (UC Berkeley) "p-adic Banach Spaces and Families of Modular Forms"
  • Kate Okikiolu (Princeton U) "The Multiplicative Anomaly for Determinants of Elliptic Operators and the Campbell-Hausdorff Formula"
  • Tom Liggett (UCLA), "Coexistence of Types in Infinite Interacting Systems"
  • Serge Kuksin (IAS and Moscow),"On Weak Turbulence in Nonlinear Wave Equations"
  • Peter Kuchment, (Wichita State U), "Photonic Crystals: Elements 0f Theory"
  • Allen Moy (Michigan and IAS), "Bruhat-Tits Buildings and the Representation Theory of p-adic Groups"
  • Valery Lunts (Indiana), "Cohomology of Toric Varieties"
  • David Geiseker (UCLA), "Stable Bundles on Algebraic Surfaces"
  • Tzong-Yow Lee, (U of Maryland), "Wave Front Propagation in some Reaction-Diffusion Equations"
  • Piotr Podles (visiting UC, Berkeley), "Quantum Geometry"

Mathematics Instruction Colloquium

David Gay

Late every Tuesday afternoon a group of local mathematics teachers gathers to discuss, listen to presentations on, and to argue about the learning and teaching of mathematics. It's a mixed crowd of thirty-odd math ed graduate students, co-op teachers, and mathematics faculty involved in teacher preparation and outreach, College of Ed faculty, mathematics instructors from Pima College, adjunct faculty, local public school mathematics teachers, and assorted others.

This is the Mathematics Instruction Colloquium, begun seven years ago as a forum for issues in mathematics education for present and future educators in elementary, middle, and high schools; junior colleges,and universities.

Presenters are typically faithful attenders but also include visiting mathematicians (e.g. Peter Hilton, Hassler Whitney) and nationally known mathematics educators (e.g. Bruce Meserve, past president of the NCTM; Deborah Schifter, Education Development Center in Newton, MA). Topics have ranged from what to do in the classroom (Patty Paper Geometry; Using Graphing Calculators in College Algebra) to mathematics education research proposals (Evaluation of a Calculus Curriculum using Concept Mapping), recreational mathematics (Mathman Tells All), and just plain mathematics ( ____ ).

All persons in the community who are interested in and concerned about the teaching and learning of mathematics are welcome to attend and participate. The Colloquium meets every Tuesday, 4:15-5:15 pm, during fall and spring semesters.

Math Movies

John L. Leonard

Each semester this past year, MATH MOVIES enlivened four Wednesday afternoons with mathematics in a visual form. (Actually, there were no movies, for videos have replaced movies, by an application Gresham's Law, but there's no alliteration in Math Videos.) Perhaps, we should bill the series as MTV -- Math Tele Vision.

Fall featured Transition to Chaos, by Robert Devaney; Let Us Teach Guessing, featuring George Polya; The Story of Pi and The Theorem of Pythagoras, from Cal Tech's Project Mathematics!; and Crystals and Shortest Paths, by Frank Morgan. In the Spring we saw N is a Number, a portrait of Paul Erdös; Not Knot and Real Estate Opportunities in Hyperbolic Space; The Shape of Space, by Jeff Weeks; and The Best Mind Since Einstein, a Nova production about Richard Feynman.

All these videos are either in the Media Center of the U of A Main Library or belong to members of the Math Department, so they are all relatively easily available for personal viewing.

New Teaching Option

David Gay

This spring (1995) the Graduate Committee of the U of A Mathematics Department has created a new option for its Master of Arts degree. Called the "Teaching Option", it will be of interest to local high school mathematics teachers. Up to 50% of the course requirements for this new version of the MA degree can be satisfied by completing late-in-the-day mathematics courses of the kind the Department has been offering for the last four years or so.

Late-in-the-day courses which presently qualify are: History of Mathematics (Math 504), Exploratory Problem Solving (Math 507), Number Theory and Modern Algebra (Math 512), A Second Course in Geometry (Math 530), Probability and Statistics (Math 561), and Calculators and Computers in the Secondary Classroom (Math 571). This list may be enlarged in the future. A total of twenty four units of approved course work are required for the Teaching Option of the MA degree. Nine to twelve of these units should be chosen from among the courses just listed and from appropriate courses in the College of Education. At least 12 units of mathematics must not be from this list and should include a year long course sequence which is not dual-numbered.

The degree also requires the completion of a thesis which could incorporate educational themes with mathematical themes.

The Department of Teaching and Teacher Education (TTE) in the College of Education also offers a degree appropriate for high school mathematics teachers. The mathematics content option for the Master of Arts in TTE requires 15 units of graduate courses in mathematics (which may include courses from the list above) plus 18 units of suitable courses in the College of Education.

Patterns

Michael Tabor

A one day workshop on Pattern Formation In Biology was organized in March 1995 by the U of A Program in Applied Mathematics (supported by the Flinn Foundation) and the Program in Mathematics and Molecular Biology at UC Berkeley (sponsored by the NSF).

Patterns are ubiquitous in nature and there are often tantalizing and sometimes misleading similarities with pattern formation problems in applied mathematics and physics. The aim of this workshop was to focus on laboratory based, biological pattern formation processes and explore the role of mathematics in quantifying and predicting them. Invited speakers included: H. Berg (Harvard) E. Budrene (Harvard) L. Davidson (U.C. Berkeley) J. Keener (U of Utah) J. Kessler (U of A) N. Mendelson (U of A) A. Newell (U of A) G. Oster (U.C. Berkeley) Y. Pomeau (U of A/ Ecole Normale)

Pi Mu Epsilon

John Leonard

Pi Mu Epsilon, the national mathematics honorary fraternity, has thirteen new members drawn from the U of A student body. They are: David Ainsworth, Lynn Curtis, Brian David, Kristine Davidsen, Trevor Irwin, Paige Jacobson, Andrew Klein, Alaina Levine, Hung Mac, Howard Nachtigal, Allison Pohlman, James Reynolds and David Staley. The local chapter, Arizona Alpha, promotes scholarship in undergraduate mathematics and co-sponsors the Department's series of Math Movies. Persons interested in furthering these goals are welcome to apply for membership, in Room 108 of the Mathematics Building.

Putnam Exam

John Leonard

Last December 3rd, nine of our undergraduates devoted six hours of a perfectly good Saturday to wrestling with 12 challenging mathematics problems that constituted the 55th Annual William Lowell Putnam Mathematical Competition. Those nine: Pavlos Constadinidis, Randy Ho, Trevor Irwin, Antonina Kolokolova, Keith Schon, David Staley, Steve Uurtamo, Chris Vera, and Jon Wilkening, had their efforts well rewarded. Randy Ho placed 49.5th out of the 2314 contestants participating, and earned an Honorable Mention. Jon Wilkening was included in the prestigious list of Top Participants - approximately 20% of the best mathematics students of the U.S. and Canada. The U of A team placed 46th out of the 284 schools fielding teams.

Should you care to whet your witte, here are two of the twelve problems. Should you desire the complete exam, please contact John Leonard at the Mathematics Department. Solutions are published in the American Mathematical Monthly, typically about October or so. Problem A2

Let A be the area of the region in the first quadrant bounded by the line y = x / 2, the x-axis, and the ellipse x2 + 9y2 = 9. Find the positive number m such that A is equal to the area of the region in the first quadrant bounded by the line y = mx, the y-axis, and the ellipse x2 + 9y2 = 9. Problem A3

Show that if the points of an isosceles right triangle of side length 1 are each colored with one of four colors, then there must be two points of the same color which are at least a distance 2 - (2 apart.

Staff Stuff

Carole Anderson and Jerrie Bieberstein

The revolving door of the Math Department Staff spins on. Who went out? Debbie Rodriquez (Word Processing), Stephanie Snyder (Algebra Computer Lab), Mary Bollschweiller (Administrative Assistant), Roxanne Batiste (Copy Room Queen), Myriam Oviedo (Office Automation Specialist). Tidbits on these ex-employees: Debbie moved on in her career pursuit, Stephanie went to (of all places) CLEVELAND, Mary B "moved on up" to the Provost's Office (ADMIN), Roxann eventually traveled to Louisiana and by means of minimal communications (a real switch for her!) tells us she is still planning to open Roxy's Fashions. Last but not least Myriam is pursuing her degree studies. We wish them all the best.

On the flip side, here's who came in. We have some bright shiny new faces, starting with Robert Lanza (Office Assistant - not quite yet Copy Room King, Roxann's a tough act to follow!), Earleen McGrew (Word Processing), Zora Mlejnkova (Office Automation Specialist, part-time at ACMS).

We have some reassignments - Janet Lange moving into Mary B's position as Administrative Assistant in the Department Head's office and Bernadette Thomas moving from ACMS to Senior Office Assistant with Janet. In Computerland we welcomed Cindy Granado Teasley (Support Systems Analyst). The staff members still with us include Carole Anderson, Jerrie Bieberstein, Betty Fink, Deborah Gaines, Lois Gorski, Kathleen Leick, Ricardo Martinez, Bridget Mendibles, Sandra Sutton, Brooke Valmont, Faye Villalobos, Carie Wells, and Julie Zehring.

So, we end another academic year basically intact, smoother around the edges, sharper in our wit, and looking forward to whatever the next year will bring.

SW RIMS

Cathy Yslas

The Southwest Regional Institute of Mathematical Sciences (RIMS), funded by the NSF and established in 1994, is currently sponsoring projects at The University of Arizona, Northern Arizona University, and Utah State University. Together, the mathematics departments at these universities share a common belief that the distance that has developed between teaching and research is artificial, and with the right leadership itcan be successfully closed.

Director William Yslas Velez has stated that the most important project of Southwest RIMS is the establishment of better working relations between university faculty and high school teachers. As a consequence, Southwest RIMS hopes to expose students of all ages to mathematics as practiced by professionals and to empower them with a feeling that useful information can be gleaned from the simplest of models. For the next few weeks, University of Arizona mathematicians will be working with students and teachers at Sunnyside High School.

Southwest RIMS has chosen mathematical modeling as its main objective. For the next three semesters, Summer '95 - Spring '96, Southwest RIMS will be supporting activities dealing with population biology at each of the three universities. Three core groups consisting of two faculty members, one graduate student, two undergraduates, and two high school teachers will be working together to develop material for use in the high school classroom.

"The Research Mathematician as an Educator" RIMS conference was held 17-18 February 1995 at The U of A.. Keynote speakers were Professor C. Herbert Clemens (U of Utah); Professor Anthony Phillips (SUNY Stony Brook); and Doug Cardell, Paul Dye, and Jeff Uecker (Sunnyside High School, Tucson). They presented a few of their own experiences using innovative methods to communicate mathematics to the precollege population. Workshops for high school, middle school, and elementary school teachers were also given as part of the conference. Participants were faculty, graduate students, and undergraduate students from twelve universities and community colleges; as well as local high school teachers, elementary school teachers, and Dr Lloyd Douglas from the NSF.

The next Southwest RIMS conference, "Mathematical Modeling in Population Biology", will be held at Utah State U, 17-19August 1995. Main speakers include Alan Hastings (U C Davis), Hal Smith (Arizona State U), and Mark Lewis (U of Utah). There will be 20 contributing speakers on a variety of topics in population dynamics and related fields. For further information about the conference, contact Professor J.M. Cushing, Department of Mathematics, U of A, Tucson, AZ 85721; phone: (520) 621-6863; email: cushing@math.arizona.edu; or Professor Jim Powell, Department of Mathematics, Utah State U, Logan, UT 84322; email: powell@sunfs.math.usu.edu.

A catalog detailing the efforts and programs of participating mathematics departments encouraging students to study mathematics has been produced. The entries specify efforts made that go beyond usual teaching duties. Currently, the section, "A Tour of Outreach Activities in the Department of Mathematics at The University of Arizona", is available upon request. For a copy contact: Professor William Yslas Velez, U of A, Department of Mathematics, Tucson, AZ 85721; phone (520) 621-2259; email: velez@math.arizona.edu. Sections about the outreach activities of Utah State and NAU should be available at the August Conference.

Wiener Prize

The following article appeared in the April 1995 edition of the Notices of the American Mathematical Society. It was written by Allyn Jackson, and is reprinted here with permission of H. Rossi, editor of the Notices.

The Norbert Wiener Prize in Applied Mathematics was established in 1967 in honor of Professor Norbert Wiener (1894 - 1964) and was endowed by a fund from the Department of Mathematics of the Massachusetts Institute of Technology. Since 1970, the prize has normally been awardedevery 5 years jointly by the AMS and the Society for Industrial and Applied Mathematics (SIAM). The $4000 prize honors outstanding contributions to applied mathematics in the highest and broadest sense. Previous recipients of the Wiener Prize are Richard E. Bellman (1970), Peter D. Lax (1975), Tosio Kato (1980), Gerald B. Whitman (1980), Clifford S. Gardner (1985), Michael Aizenman (1990), and Jerrold E. Marsden (1990).

The 1995 Wiener Prize is awarded to HERMANN FLASCHKA of the University of Arizona and to CIPRIAN FOIAS of Indiana University. The prize was presented at the 101st Annual Meeting of the AMS in San Francisco in January 1995. The prize is awarded by action of the Councils of the AMS and of SIAM on recommendation ofa selection committee consisting of Thomas Kailath, Peter D. Lax, and Jerrold E. Marsden.

The following text contains the committee's citation for the prize, the (first) recipient's response upon receiving the prize, and a brief biographical sketch of the recipient.

Hermann Flaschka

Citation Hermann Flaschka has made deep and original contributions to our understanding of completely integrable systems. Starting with his discovery of the complete integrability of the Toda chain, Flaschka furnished an explanation for the appearance of a critical shock speed, discovered earlier by Holian through numerical calculation. He helped show how to derive averaged equations for multiphase oscillations for solutions of the KdV equation.. His recent work brings the methods of modern differential geometry and algebra to bear on the study of completely integrable systems, as in his infinite dimensional extension of the Schur-Horn-Kostant convexity theorem.

Response This award came as a great surprise. I thank the Societies for complimenting my work -- but the prize really recognizes a rich area more than anything I mighthave added to it. It is difficult to ask a question about the Toda lattice that has a boring answer. Professor Morikazu Toda has made a wonderful contribution to mathematics. His "Toda chain" reaches back to the great classic studies of Jacobi and Stieltjes, while constantly making contact with the newest ideas. It led me to think about such diverse topics as discrete shock waves, modulation equation equations, Riemann surfaces, theta divisors, toric varieties, momentum maps, semisimple and affine Lie algebras, Szegö's theorem, and measurable rearrangements; as an interested spectator, I have seen the Toda chain appear in many more mathematical settings too numerous to try to list. I have enjoyed using integrable systems as the vehicle to learn a little about interesting fields with which I was not familiar.

It was by pure chance that I drifted into this area and then my good fortune to have been able to work with so many creative colleagues. I can't mention them all, but at least I want to thank the ones with whom I have collaborated over periods of many years: Tony Bloch, Nick Ercolani, Luc Haine, Dave McLaughlin, Alan Newell, and Tudor Ratiu. Thank you for up to 20 years of fun with mathematics, and again, thank you, AMS and SIAM, for the honor.

Biographical Sketch

Hermann Flaschka was born on March 25, 1945, in Oeblarn, Austria. He received his Ph.D. from the Massechusetts Institute of Technology (1970) under the direction of Gilbert Strang. He was a cofounder of and now is co-coordinating editor of Physica D: Nonlinear Phenomena (1980 - ). He was a visiting professor at the Research Institute for Mathematical Sciences, Kyoto (1980 - 1981).