Mathematics Newsletter 1996-1997

Contents:

Applied Math Colloquium

Kathleen Leick

On-line Seminar and Colloquia Info

Here are the speakers, their affiliations, and the titles of their talks.

  • Jennifer L. Sinclair, U of a, Modeling the Vertical Transport of Dense Gas-Particle Suspensions
  • Frank Hoppensteadt, Arizona State University, Saddle-Node Bifurcations in Brain Dynamics
  • Tony F. Chan, UCLA, Multilevel Elliptic Solvers on Unstructured Grids
  • John Sylvester, University of Washington, Linear and Nonlinear Aspects of 1-D Scattering
  • Carl Pixley, Motorola Microprocessor and Memory Technologies, Aspects of Mathematical Verification of Commercial Hardware Designs
  • Shui-Nee Chow, Georgia Institute of Technology, Traveling Waves in Lattice Dynamical Systems
  • Maciej Wojtkowski, U of a, Completely Integrable Versus Completely Hyperbolic Hamiltonian Systems: New Examples
  • Misha Vishik, University of Texas at Austin, Regularity in Hydrodynamics of an Ideal Incompressible Fluid
  • Brian Marcus, IBM Almaden Research Center, Symbolic Dynamics and Coding for Data Storage
  • David Poirier, U of a, Simulations of Convection and Segregation During Solidification of Dendritic Monocrystals
  • Satoshi Hamaguchi, IBM T.J. Watson Research Center, Simulation of Micro-Profile Evolution: A Shock-Tracking Algorithm for Etching and Deposition
  • Tim Minzoni, UNAM (Mexico), Evolution of Lump Solutions for the K P Equation
  • David Brydges, University of Virginia, Statistical Mechanics of the 2-Dimensional Focusing Nonlinear Schroedinger Equation
  • Robert Kohn, Courant Institute (NYU), Branching of Magnetic Domains and Folding of Thin Film Blisters
  • R.D. James, University of Minnesota, Simple Dynamic Models of Evolution on Wiggly Landscapes Arising in Phase Transformations and Friction
  • Yannis Kevrekidis, Princeton University, Catalysis on Microdesigned Surfaces
  • Igor Mezic, University of California, Nonlinear Dynamics of Jet Engines: Is Fear of Flying Rational?
  • C.K. Chu, Columbia University, Computational Fluid Dynamics -- a 25 Year Review
  • Thomas Spencer, Institute for Advanced Study, Princeton University, a Review of Some PDEs with Random Coefficients
  • David G.Schaeffer, Duke University, Stress Fluctuations in Sheared Granular Material
  • Jerry Bona, University of Texas, Austin, Decay of Nonlinear Waves
  • Michael Crandall, University of California, Santa Barbara, the Mysterious Infinity-Laplacian
  • Roger Brockett, Harvard University, Differential Equations on Lie Algebras and Coadjoint Orbits
  • You-sheng He, Shanghai Jiao-Tong University, High Speed Hydrodynamics with Free Surface
  • Bryan Travis, Los Alamos National Laboratory, Traveling Waves in Numerical Model of Subsurface Bioremediation with Microbial Ecology
  • Larry Shepp, Rutgers, ATT, Bell Labs, Tomography and Probability
  • Zhouping Xin, Courant Institute (NYU), Vortex Methods and Self-Similar Vortex Sheets for 2-D Incompressible Euler Equations
  • Harrison H. Barrett, U of a, Quantum Optics and Image Science: Some Points of Contact
  • Jean E. Taylor, Rutgers, Variational Approaches To Surface Motion for Crystals

The Co-Op Class of 1996-97

Elias Toubassi

This year the Co-Op program has eight participants, four from Tucson area high schools and middle schools, two from Phoenix area high schools and two from Pima Community College. The group includes Dan Benson, South Mountain High School, Phoenix; Paul Des Jarlais, La Cima Middle School; Paul Flasch, Pima Community College, West Campus; Virginia Johnson, Deer Valley High School, Phoenix; Jay Kirsch, Sabino High School; Paula Klein, Sunnyside High School; and William Martin, Pima Community College, East Campus.

Dan Benson graduated from Coconino High School in Flagstaff in 1969. He received his B.S. in Mathematics Education in 1973 from Northern Arizona University. In 1979 he earned a Master's Degree from ASU. He taught mathematics in Ash Fork, Globe, Prescott and has spent the last 13 years teaching at South Mountain High School in Phoenix. He is active in the mathematics reform movement, serving on several state committees, participating in the Phoenix Urban Systemic Initiative, and has been active in the implementation of the Interactive Mathematics Program. In 1990 Dan participated in the UofA's Image Processing Program for teachers which is run by the Lunar and Planetary Laboratory. He enjoys hunting with his bird dogs Tinker Belle and Buffy, spoiling his grandchildren, sailing San Francisco Bay and hopes to spend time this summer traveling to someplace cool.

Paul Flasch was born in North Dakota and received his B.S. in Physics from St. John's University in Minnesota and an M.S. in Mathematics from North Dakota State University. His teaching experiences range from middle school to adult education to college teaching. The latter includes North Dakota State University, Moorhead State University (Minnesota), Concordia College, Fergus Falls Community College (Minnesota), and currently at Pima Community College. His main teaching interests are calculus and differential equations. In addition, he has been active in encouraging Pima students to participate in the AMATYC Math Contests. Outside interests includes reading both fiction and non-fiction, hiking, and especially playing four wall handball.

Paul Des Jarlais was born and raised in Arizona. He attended the University of Arizona and in 1988 he received a B.S. degree in physics with a minor in mathematics. After working at several different jobs he returned to the U of A in Spring 1990 to become a certified physics and math teacher. He received his secondary teaching certificate in physics and mathematics in December 1991. He has been teaching at La Cima Middle School, in the Amphitheater School District since the Fall of 1992. At La Cima he has helped start a "student run" news program (Wake Up La Cima) whereby all the teacher announcements are read on the air (live television) by the news staff. His hobbies include computers and most anything related to Star Trek: The Next Generation. He has been married since December 1992 and on December 30, 1996 they became the proud parents of their first child Timothy, who is keeping them on their toes.

Virginia Johnson was born in California but as an army brat grew up in many places including Japan and Zaire. She did her undergraduate study at LeTourneau College in Texas and got her Bachelor's degrees from Houghton College in Houghton, New York. After college she taught school in Hamamatsu, Japan for two years, then in Kinshasa, Zaire for one year. Due to political unrest she and fellow missionaries were forced to leave Zaire after one year of a planned three year term. After working office support for several years she returned to teaching at Deer Valley High School in Glendale, Arizona, her current home school. While at Deer Valley she has sponsored the Renaissance and National Honor Society Programs which are aimed at honoring and encouraging academic excellence. This past Christmas she traveled to Port au Prince, Haiti to be with her sister's family. She hopes to go back there again next Christmas. She is in the process of buying her first home and she looks forward to setting up permanent residence.

Jay Kirch received his bachelor's degree from Concordia University in Irvine, California in 1991. He worked for two years teaching algebra, geometry, and computer programming at Lutheran High School in Denver, Colorado. In 1994, Jay and his wife Amy, moved to Tucson. After working as a substitute teacher, he eventually secured a permanent position at Sabino High School. He is currently working on a master's degree in Math Education at the University of Arizona. Jay has been involved in coaching at the high school level in a variety of sports including football, basketball and track.

Paula Klein has a B.S. in Theory and Composition with a minor in mathematics. In 1986 she earned an M.S. degree in Industrial Engineering from the University of Arizona. She taught instrumental music in grades 5-12 and is currently teaching math at Sunnyside High School. Her interests include playing in an orchestra which includes our own John Leonard. She is also interested in animals and in 4-H Clubs raising swine and pigeons. She is married with two sons ages 16 and 18.

William Martin grew up in Northern Minnesota and other parts of the midwest. Early on he acquired a love of water activities which was somewhat cured by serving in the U.S. Coast Guard. His academic training started at the University of Colorado. After his service in the Coast Guard he finished his Bachelor's and Master's degrees at Western Michigan University with the latter in Applied Mathematics. He has taught at Pima Community College since 1984 and with his wife and three daughters enjoys the varied activities available in the Tucson area.

Entry Level Mathematics Colloquium

Richard B. Thompson

On-line Seminar and Colloquia Info

The Entry Level Mathematics Colloquium is sponsored by the Entry Level Committee and is presented jointly with the Mathematics Instruction Colloquium. Its purpose is to present mathematical topics that are of interest to, and understandable by, those teaching our 100 and 200 level courses.

In 1996-97 the Entry Level Mathematics Colloquium presented a series of six talks by entry level faculty members, graduate students, and regular faculty members. The programs used mathematical tools including simple arithmetic, statistics, probability, simple multivariate calculus. A variety of presentation methods were used, ranging from computer animation to chalkboard writing. Speakers and topics included the following.

  • Richard Thompson, "Reform Calculus Meets Statistics: Discovering the Normal Distribution."
  • William Martin, "Distances on the Earth, Sunrise and Sunset Times; Using Dot Products."
  • Larry Wright, "Gambling: Using Probability and Statistics to Make Money."
  • Paul Flasch, "Random Numbers."
  • Amy Rabb-Liu and Richard Thompson, "Mathematics Arising in the Classroom: Two Analyses of the 'Teacher's Dilemma' Problem."
  • Daniel Madden, "Why is 'Who are you?' a Mathematical Question? An Introduction to Signature Verification.

The next-to-last colloquium was an experiment in broadening the base of participation in the program. "The Teacher's Dilemma" was circulated to all entry level faculty members and graduate students, along with a request for analyses of the mathematics involved in a scenario from a high school mathematics class.

Faculty News

Larry Grove

Congratulations are in order for several faculty members due to recent promotions. In 1996 Marta Civil was promoted to Associate Professor with tenure, and Bill McCallum and John Palmer became Full Professors. In 1997 Sam Evens, Jiang-hua Lu, Dinesh Thakur, Jan Wehr, and Jack Xin were all promoted to Associate Professor with tenure.

Tom Kennedy and Robert Maier accepted joint appointments in the Physics Department; Bob Beals a joint appointment in Computer Science. Conversely, Tim Secomb from Physiology, Adrian Patrascioiu from Physics, and Dan Stein from Physics have accepted joint appointments in Mathematics.

As always we have had an eclectic and engaging collection of visitors, including: Antonius Broumas, who is going on to MSRI in Berkeley; Aidan Egan, who is moving on to work for Intel in Dublin; Scott Glasgow; Alain Goriely of the Free University in Brussels; Jeff Haag from Humboldt State University; Shandelle Henson, an American Fellow of the American Association of University Women; John Kieffer of the University of Minnesota; Oliver Knill, Hanno Rund Visiting Assistant Professor; Sergey Kuksin of the Steklov Institute in Moscow; Reg Laursen of Luther College in Iowa; Jocelyn Lega; Cun-Zheng Ning, who is moving on to Ames Research in San Jose; Thierry Passot of the Observatoirede la Cote D'Azur; Jeff Sheats, moving on to an NSF Postdoc at MIT; Alexander Shoshitaishvili; and Olga Yiparaki of Agnes Scott College in Atlanta.

Bill Faris has spent the year as a Program Officer with the National Science Foundation.

Helmut Groemer is retiring from teaching after 33 years in the Department. To those of us who have known him for a few years, however, it is clear that his ever-active research program will continue unabated.

Donna Krawczyk was awarded a Leicester and Kathryn Sherril Creative Teaching Award, which includes a $1500 prize from the U of A Foundation. Donna is an Adjunct Lecturer who has been highly active in reform calculus projects.

Don Myers was named as a Distinguished Adviser by the College of Science, and Steve Willoughby was recognized with a Distinguished Achievement in Science Education Award.

We have two new regular faculty members. Thumbnail sketches follow.

Robert Beals grew up in an academic family; he was born in Chicago and lived there until 1976. A year in Paris followed, after which his father (mathematician Richard Beals) accepted a position ate Yale, and Bob continued growing up in Hamden, Connecticut. He earned a BS degree in mathematics at the University of Chicago, including a semester in Budapest, then a PhD in Computer Science at Chicago, under the direction of Laszlo Babai. There followed a year as an NSF Postdoc at the University of Oregon Computer Science Department, then two years with joint appointments at the Institute for Advanced Studies in Princeton and DIMACS at Rutgers. He spent the summer of 1995 at the University of St Andrews in Scotland and the summer of 1996 at the Institute for Defense Analysis - he has returned to St Andrews for the summer of 1997.

His research focuses on the theory of algorithms, particularly for computational group theory.

Bob is married to Diana Reid. They have two children - Colin was born in January 1993, and Olivia in January 1995.

Joseph Watkins was born in Raleigh, North Carolina, and grew up in Kingsport, Tennessee. He earned BS and MS degrees at the University of Tennessee, then a PhD at the University of Wisconsin in 1982. His research involved abstract limit theorems in probability theory, under the direction of Tom Kurtz. Then, under the auspices of the Canadian National Science and Engineering Research Council, he began a post-doctoral position, directed by Joe Walsh, at the University of British Columbia from 1982 until 1985. While in Vancouver he met and married Jean deJong.

Joe spent a term at IMA in Minnesota in the fall of 1985, then became an Assistant Professor at the University of Southern California in January 1986. Daughter Laura was born at USC.

In 1992 Joe became a Visiting Assistant Professor at the U of A, and daughter Emily was born shortly thereafter. Joe played a very active role in the SWRIMS program, particularly regarding the migration of killer bees into Arizona, and in 1996 he became a tenure-track Associate Professor. His research now involves probabilistic applications to concrete modeling problems in mathematical biology.

Financial Aid

Faye Villalobos

The Richard S. Pierce Undergraduate Scholarship - an endowment scholarship for undergraduate mathematics majors was established in 1992 in memory of Professor Richard S. Pierce. Scholarships of up to $500 each are awarded each year to outstanding undergraduate students in Mathematics. Recent recipients have gone on to or are planning to attend graduate school at the Universities of Arizona and Michigan in the fields of computer science, mathematics, and philosophy.

The James R. Clay Graduate Travel Fund - a fund for current Mathematics graduate students and recent Mathematics PhD students to provide support for travel expenses to attend and participateby presentation at mathematical conferences or meetings was established in 1995 in memory of Professor James R. Clay.

If you would like to contribute to either of these funds, complete the form at the end of this newsletter, make your check payable to THE UNIVERSITY OF ARIZONA FOUNDATION, and mail both to:

	Department of Mathematics
	The University of Arizona
	617 N. Santa Rita Ave.
	Attn: F. Villalobos, 
	Business Manager
	Tucson, Arizona 85721
	(email  villal@math.arizona.edu)

Graduate Life

Alexander Perlis

As for our social stunts, the math department's graduate students have an act that would be difficult (and dangerous to your health) to follow.

There were the evenings of salsa dancing, culminating in Joe Erker's and Francisco Bido's salsa party (both dance and dip); the limbo contest saw some good competition, with an energetic (albeit stumbling) performance by David Marshall. Marshall Mundt's halloween party saw some outrageous costumes: Karla Horsch's impression of Charlie Chaplin accidentally got taken for Adolf Hitler (go easy on the mustache, Karla!), and Susan Hammond's toilet-paper mummy made quite a mess. Kris Green was a tree, and Cecilia Fosser and Craig Hyde went with pots on their heads, whatever that was supposed to mean?!? Marshall's mortal combat dancing technique is always a welcome piece of eye candy. Speaking of dancing: our own David Ropp, disco-meister extraordinaire, never ceases to amaze us with his charm, moves, and suave looks; in fact, as this article goes to press, Dave was to be found winning the Saturday Night Fever dance contest at Gallagher Theater. Karl Bauer and Kris Green showed off their new abode by hosting a BBQ, which included some pretty darn good joke telling by our grad wannabe Melanie Bell. Now thinking that their first party wasn't good enough (believe us, it was!), or simply because it was good time for some good chile, Joe and Francisco had everyone over again for another keg, more dancing, and lots of chile. The department-wide party thrown by Professor Bill McCallum found most of the grad representation around the keg on the patio, and a few of us (no names shall be mentioned!) were caught sneaking back to the patio after the party to quietly finish what got started. Then there was the BBQ hosted by yours truly, which was benign at first but ended on a rather wild note -- ask wildboy Aaron Ekstrom for the details! Of course, these were merely the official descriptions of the official events. The real truths of the matter are hidden forever, as we are each sworn to secrecy.

Deciding that we were deeply in need of true culture, not to mention an evening of fun and relaxation away from mathematics, our own Kiwi graduate student in applied mathematics, David Marsden, invited all graduate students to the opera. The evening started with a wine and cheese party hosted by David, followed by the performance of La Boheme on campus, and finished with another wine, cheese, port, and pate party. The following weekend, Cecilia Fosser and Craig Hyde had the gang over for a potluck, followed by the Ballet Hispanico on campus. Nita Rado and Katy Rudin will always be remembered for stealing front row seats at the student rush price! The participants from our department were Orna Amir, Francisco Bido, Cecilia Fosser, Kris Green, Karla Horsch, Craig Hyde, Andre Lehovich, Scott Lietz, David Marsden, Brooke McGuire, Gema Mercado, Alexander Perlis, Nita Rado, Katy Rudin, and Olga Simek.

Sensing that the studies aren't physically demanding, Kris Green organized a departmental street hockey team to compete against other such teams on campus. The team, Random Chaos, has won three games so far and is preparing for a tournament. The members are Kevin Anderson, Scott Beaver, David Burnett, Dan Coombs, Brandon Gallas, Kris Green, Karl Haller, David Hochheiser, Craig Hyde, Matt Kruse, David Marsden, and Marshall Mundt.

Speaking of physically demanding (and even graceful) activities, Orna Amir has spiked interest in the Brazilian martial art and dance form known as Capoeira. Many of us watched the Capoeira performance at Downtown Saturday Night, a few feet from Bruce Bayly's weekly song and dance. Capoeristas from the math department are Orna Amir, Francisco Bido, Cecilia Fosser, Karla Horsch, and Nita Rado.

Graduate students Dan Coombs from England and Barbara Müller from Germany love rock climbing. Their interest must have rubbed off on the rest of us, for there have been sightings of math graduate students learning the ropes at an indoor climbing gym. Then Dan organized a trip to Mount Lemmon to try the real thing. There were some scrapes, a few scratches, but no falls. And the view from the top was unbelievable! The participants were Karl Bauer, Dan Coombs, Cecilia Fosser, Susan Hammond, John Larson, Brooke McGuire, Barbara Müller, Alexander Perlis, Angel Pineda, and Hung Quan.

Graduate Student News

Susan Hammond

The academic year 1996-1997 has been another successful one for graduate students. What follows is a summary of the progress and degrees earned during the past year. Congratulations to all for their hard work, and good luck in the future!

The following students received Ph.D. degrees in the Applied Mathematics program during the past year:

  • Richard Brazier, "Seismic Wave Propagation Stitching: Matching Local and Global Techniques" adviser T.C. Wallace.
  • Alexei Samsonovich, "Attractor Map Theory of the Hippocampal Representation of Space" - advisers Alwyn Scott and Bruce McNaughton.
  • Abbie Warrick, "Application of Wavelet and Radon Based Techniques to the Aperture Radar Images" - adviser Pamela Delaney. Abbie is currently working at Livermore Laboratories in California.
  • Tityik Wong, "Contributions to the Theory of Stochastic Orders" - adviser Moshe Shaked.

The following students received Ph.D. degrees in the Mathematics program during the past year:

  • Yu-Wen Cheng, "Endomorphisms of Modules over Discrete Valuation Domains" - adviser Warren May.
  • Son-Xuan Dang, "The C-function for Affine Kac-Moody Algebras" - adviser Doug Pickrell.
  • Cheryl DeLorme, "The Shafarevich-Tate Group of an Elliptic Curve" - adviser Bill McCallum. Cheryl has accepted a 10 month post-doc position for next year at MSRI in Berkeley.
  • Mohamed El Hadrami, "Poisson Algebras and Convexity" - adviser Hermann Flaschka.

The following students will be finishing Ph.D. degrees in Mathematics this summer:

  • Ed Alexander, "An Investigation of the Results of a Change in Calculus Instruction at the University of Arizona" - adviser Steve Willoughby.
  • Cynthia Kaus, "Topological and Geometrical Considerations for Maxwell's Equations on Unstructured Meshes" - adviser Richard Ziolkowski. Cindy has accepted a 2-year (renewable) Assistant Professor position at the University of Minnesota.
  • Amy Rabb-Liu, "Teaching Methods and Student Understanding in Calculus" - adviser Steve Willoughby. Amy has accepted a position as Assistant Professor at Montclair State University in New Jersey, where she will be helping to develop a new PhD program in mathematics education.
  • Stephen Shipman, "A Continuum Limit of a Finite Discrete Nonlinear Schrödinger System" - adviser Nick Ercolani. Stephen will teach for another year at the U of A, continuing his research.

The following students received Master's degrees in the Applied Mathematics program: Karl Bauer, Kris Green, Craig Hyde, David Marsden, Brooke McGuire, Regan Murray, Chad Neller, Angel Pineda, Jason Rose, and Gema Mercado Sanchez.

The following students received Master's degrees in the Mathematics program: Fahd Al-Shammari, M. Avila Godoy, Armando Bezies-Kindling, William Flack, Ewa Romanowska, Ryan Ruddy, Santiago Torres, and Hsi-Tsung Yang.

The following students passed the preliminary Ph.D. exams: Agustin Brau Rojas, Aaron Ekstrom, Li Liu, Slawomir Tomaszewski, Jung Min Woo, William Schuster, Kris Green, Gema Mercado Sanchez, and Regan Murray.

The following students passed the qualifying exams: Fahd Al-Shammari, Orna Amir, Susan Hammond, Seog-Young Kim, Christopher Lott, David Marsden, Angel Pineda, and Jason Rose.

Math Awareness Week 1997

David Lovelock

Some of my colleagues think the most important event that happened at the U of A on Tuesday, April 1, 1997, was the welcoming home of the NCAA Basketball champions. They were wrong. The most important event that happened at the U of A on Tuesday, April 1, 1997, was the publication of 150 web pages celebrating Math Awareness Week 1997.

Math Awareness Week is an annual nationwide event. The theme for 1997 was Math and the Internet. The Department of Mathematics celebrated MAW 97 in two complementary ways: locally, with events based in the Math Department over the period April 21 - April 30, and globally, with the opening of the UA MATH MAW 97 WEB site at http://www.math.arizona.edu/maw.html.

The local events were opened on Monday, April 21, by Congressman Jim Kolbe at a very successful reception in the Lobby of the Mathematics Building. The reception was attended by over 100 people representing a cross section of Tucson's population who also showed much interest in:

  • a live beehive on display drawing attention to the unveiling of WebBEEPOP, a bee population model accessed via the internet;
  • mathematical exhibits of student work for the National Science Fair, the Geometry Center, and Math 430, A Second Course in Geometry;
  • computers hooked to the Internet.V

Additional local activities over the next ten days included public lectures by William Velez and David Lovelock on The Code Breakers, which dealt with the Enigma machine; and Dan Madden on Why is "Who Are You?" a Mathematical Question? An Introduction to Signature Verification. Two special Math Movies were organized by John Leonard: Breaking the Code, about Alan Turing during WW2; and The KGB, the Computer, and Me, about Cliff Stoll breaking an international spy ring. Claire Macha set up three display cases in the Science Library emphasizing MAW 97.

Special bookmarks were made for each of the local MAW events, and they were given away to the first 40 people at each activity. These items proved very popular (someone even suggested that the originator be given the Nobel prize) and have become collectors' items. For example, the one for Madden's talk had eight signatures that needed identifying (G. Washington, B. Franklin, the four Beatles, and two 007's), while the Vélez/Lovelock bookmark contained a message that had to be deciphered. The first person to do so received $50. She was very pleased! Copies of all seven bookmarks can be seen at our MAW web site.

In setting up the web site we had three goals in mind: To establish links to further information related to the local activities, to make the site interesting and understandable to a wider audience than professional mathematicians, and to make it useful for people interested in mathematics education at all levels.

General topics covered are Ciphers, Teaching, Math Resources, and Technology Resources. Some areas with UA Math department contributions are:

  • WebBEEPOP, a bee population model accessed via the internet. A team effort of the U of A's Southwest Regional Institute for the Mathematical Sciences and the Carl Hayden Bee Research Center.
  • A series of Java Applets created by Chris Sinclair, including a simulation of the Enigma machine.
  • Photos of the Enigma Machine previously available from the Electronic Museum, University of Hamburg, Germany - now available at The U of A.
  • The ability to download Enigma, a DOS program designed to allow you to experiment with the Enigma coding and decoding machine and Cryptaid, a DOS program designed to aid in the decoding of simple substitution aristocratic ciphers.
  • Data sets for Precalculus, Calculus, and ODEs.
  • Pictures of geometrical models constructed by U of A mathematics major Jennifer Widmann as part of a final project for Math 430, A Second Course in Geometry, taught by David Gay. These pictures show maps on the surfaces of many-holed doughnuts which are colored with the minimum number of colors - they are featured on one of the bookmarks.
  • Useful links and information pertaining to the Texas Instruments TI-81, TI-82, TI-83, and TI-92 Graphing Calculators.
  • GIF Movies with Mathematica by Oliver Knill, covering topics from Dynamical Systems such as the Cubic Henon family, the game of Life, the Lorentz system, Julia sets, Caustics, the Double Pendulum, the Henon attractor, the Menger Sponge, and Barnsley's fern.

May I suggest that you visit the web site, if only to read the list of people who helped make MAW 97 the success it was. The main MAW site at Swarthmore selected our site as one not to be missed.

Math Center/Undergraduate Programs

Chris Mikel, Math Center Coordinator

Sixty-eight undergraduate students received bachelor degrees in Mathematics in the 1996-97 academic year. This was a particularly good group of students, academically, and many of them will be continuing their studies in graduate programs. Graduates who are going on to graduate school include:

  • Noah Goodman, University of Texas, Austin, PhD program in Mathematics.
  • Trevor Irwin, University of Indiana, PhD program in Mathematics
  • Todd Murphey, Cal Tech, PhD program in Control and Dynamical Systems.
  • Jonathan Pillow has been awarded a Fulbright Fellowship for a year of study in Morocco, concentrating on Maghrebian literature of French expression. After that, he will pursue a PhD in Cognitive Sciences at MIT.
  • Lyn Reid, University of Washington, PhD program in Applied Mathematics.
  • Keith Schon, Stanford University, PhD program in Mathematics.
  • Elena Shoshitaishvili, University of Arizona, PhD program in Geophysics.
  • Chris Sinclair, University of Texas, Austin, PhD program in Mathematics.
  • David Vakil, Cal Tech, PhD program in Astronomy.

Congratulations and good luck to all!

Departmental awards were given to the following outstanding undergraduate students this year:

  • Outstanding Senior Award - December 1996 - Andrew Klein
  • Outstanding Senior Award - May 1997 - Jonathan Pillow
  • Richard Pierce Memorial Scholarships - Evan Deaubl, Logan Trujillo
  • Richard Peet Memorial Scholarship - G. Weldon Gilcrease
  • Graesser Foundation Math Scholarships - Gary Gongwer, Carolyn Lanser, Patrick Shipman, David Staley, Sofiya Vasina

Three students spent a semester studying mathematics in Budapest, Hungary. Jonathan Pillow, Keith Schon, and Noah Goodman report having had an outstanding experience participating in the Budapest Semester in Mathematics Program , administered through St. Olaf College.

Undergraduate students who will be participating in summer research programs in the summer of 1997 include:

  • Noah Goodman and Chris Sinclair: Institute for Advanced Study, Park City, Utah Topic: Symplectic Geometry and Topology
  • G. Weldon Gilcrease: Northern Arizona University REU
  • Carolyn Lanser: Carleton College and St. Olaf College REU.

A new display case in the lobby of the Mathematics Building is gradually being filled with photographs of undergraduate math majors. There are currently about 245 officially declared math majors and while not all of their pictures are as yet on display, it is hoped that the photos will help students to get to know one another better.

Coffee Hour for undergraduates and faculty was held in the Common Room (Rm 203) on Wednesday afternoons this spring to provide an opportunity for students and faculty to meet and talk informally. The tradition will be continued into the next year.

New directions were taken with the undergraduate colloquia this year. Two talks were given by Chris Sinclair, an undergraduate math major. Fall semester Chris spoke on "The Invariant Manifold of Halo Orbits and Aperiodic Tilings: Construction Techniques", topics on which he began doing research while at the Geometry Center in Minnesota the previous summer and continued studying after returning here for his senior year. In the spring semester, Chris gave a colloquium entitled "From Quasicrystals to Aperiodic Tilings of the Plane", in which he described the results of his year-long investigations made under the tutelage of Professor Nicholas Ercolani.

The other innovation in the colloquium program was the series of four talks on "Space and Time" given by Professor Carl DeVito and PhD student Cindy Kaus in the spring semester. The topics in the series included "Fundamental Concepts of Space", "Abstract Spaces", "Mathematical Concepts of Time", and "The Geometry of Space and Time". In these fascinating lectures, Dr. DeVito and Ms. Kaus gave an overview of the historical development of the theory of space and time and described the direction that current research is taking to increase our understanding of these fundamental concepts.

The Math Center welcomed back its director, Professor William McCallum, from his one year leave spent at the Institute for Advanced Study in Princeton, NJ. On his return, Dr. McCallum assumed his new position as Associate Head of the Mathematics Department for Undergraduate Programs. A slight reshuffling of the rooms dedicated to the Math Center was done to provide Dr. McCallum with space to meet with undergraduate students and to promote improved coordination of the undergraduate programs. The main office of the Math Center is now in Rm 209 and Professor McCallum's office in Rm 207.

Mathematics Colloquium

Lucas Hsu
Minhyong Kim

On-line Seminar and Colloquia Info

The following is a list of speakers , their affiliations and the titles of their talks. Local hosts are given in parenthesis.

  • Doug Cardell and the staff of Sunnyside high school (Velez), "K-12 Multilevel Collaboration to Reform Mathematics Education."
  • Tom Sideris (Xin), University of California at Santa Barbara, "The null condition and global existence of non-linear elastic waves."
  • Irena Swanson (Grove/Yiparaki), New Mexico State University, "Tight closure and primary decompositions."
  • Rob Lazarsfeld (Kim), University of California at Los Angeles, "Higher-Dimensional Complex Geometry and Abelian Varieties."
  • Bernd Sturmfels (Kim), University of California at Berkeley, "Noncommutative Groebner Bases for commutative rings."
  • Aaron Bertram (Kim), University of Utah, Quantizing the Littlewood-Richardson rule.
  • Wayne Raskind (Kim), University of Southern California, Arithmetic and geometry of algebraic cycles.
  • Ralph Cohen (Kim), Stanford University, "Holomorphic Bundles and Bott periodicity."
  • Paul Wiegman (Kim), University of Chicago, "Discrete soliton equations and quantum mechanics."
  • Fang Hua Lin (Xin), University of Chicago, "Dynamics of vortices and filaments and geometric measure theory."
  • Spencer Bloch (Kim), University of Chicago, "The Riemann Zeta Function, Modular forms, and Lie Algebras."
  • Mark Goresky (Evens), Northeastern University, "Topology and Arthur's trace formula."
  • Richard Wentworth (Kim), U of California at Irvine, "Holomorphic Vector Bundles on Riemann Surfaces."
  • Dan Abramovich (Lu), Boston University, "Resolution of singularities (in characteristic zero)."
  • Jean-Paul Allouche (Thakur), CNRS, "Finite Automata and Number Theory."
  • Paul Vojta (Kim), University of California at Berkeley, "An update on Diophantine Approximation and Nevanlinna Theory."
  • Peter Sarnak (Thakur), Princeton University, "Zeroes of Zeta Functions, their Spacings and Spectral Nature."
  • Robert Kusner (Hsu), University of Massachusetts, "Geography of the Moduli Space of Embedded Constant Mean Curvature Surfaces."
  • Peter Olver (Hsu), University of Minnesota, "Moving Coframes and Computer Vision."
  • Ron Donagi (Ercolani), University of Pennsylvania, "Integrable Systems: From Algebraic Geometry to Strings."
  • Tom Spencer (Hsu), Institute for Advanced Study, "An approach to Critical Phenomena in Two Dimensions."
  • Sergiu Klainerman (Hsu and Levermore), Princeton University, "Harmonic Analysis and Non-Linear Wave Equations."
  • David Levermore, U of A, "The Complex Ginzburg-Landau Equation: A Damped-Driven Perturbation of a Hamiltonian System."
  • Niky Kamran (Hsu), McGill University, "Quasi-Exact Solvability."
  • Lenny Friedlander, U of A, "Direct and Indirect Methods in Spectral Analysis."
  • Raffe Mazzeo (Friedlander), Stanford University, "Local and Global Aspects of the Moduli Spaces of some Non-Compact Geometric Problems."
  • Lihe Wang (Hsu and Xin), University of California at Los Angeles, "Regularity for Harmonic and Bi-Harmonic Maps."
  • Yasha Eliashberg (Hsu), Stanford University, "Contact Homology and Legendrian Knots."
  • Serge Lang (Kim), Yale University, "Heat Kernels All Over the Place."
  • Richard Montgomery (Ercolani and Hsu), University of California at Santa Cruz, "Braids, Periodic Orbits, and the Planar N-body Problem."

Mathematics Instruction Colloquium

Fred Stevenson

On-line Seminar and Colloquia Info

The Mathematics Instruction Colloquium meets Tuesday afternoons in the Mathematics Building. Its topics are as varied as its speakers but, generally speaking, the conversation involves educational issues of the day. This was the eighth year for the Colloquium and it met 19 times over the course of the year.

There were several visitors who contributed presentations. They included: Jean McGehee from NAU: Interactive Technology in the Geometry Classroom; Jan Shroyer of Grand Valley State University: Mathematics Course for Future Elementary School Teachers; William Ramaley of Fort Lewis College: The History of Mathematical Induction; and Gelsa Knijnik of the Universidade do Vale Ril dos Sinos in Brazil: An Ethnomathematics Approach to Mathematics Education.

Several mathematics faculty gave presentations. Helmut Groemer spoke on the Symmetry of Frieze Patterns in Mayan Architecture, Olga Yiparaki on Students' Understanding of Quantifiers, Joe Watkins on The Research Mathematician as a Storyteller.

The CO-OP teachers each contributed two talks for the year. Topics included Critical Learning Periods and P.E.T Scans by Eric and Linda Langner; Image Processing by Dan Benson; Math Anxiety by Denise Meeks; An Interactive Math Program by Paul DesJarlais; Non-Euclidean Geometry for High School Students by Jay Kirch; and a presentation by students from Sunnyside High School on their project of designing a roller coaster, supervised by Paula Klein and Virginia Johnson.

Doctoral students in Mathematics Education also spoke: Math for Students with Visual Impairments by Scott Sakamoto; Thinking about the Classroom by Amy Rabb-Liu; and Assessing Calculus Reform by Ed Alexander.

All in all it was a broad, well rounded, thought provoking, and instructional year in the Mathematics Instruction Colloquium. We look forward to next year when Professor Steve Willoughby will be in charge of the lecture series.

Putnam Competition

John Leonard

On Saturday, 7 December (Pearl Harbor Day), 14 of our undergraduates devoted most of the day to pondering the 12 brain-teasers that constituted the Fifty-seventh Annual William Lowell Putnam Mathematical Competition. They were Shao-Chu Yu, Sofiya Vasina, Kirill Shokhirev, Elena Shoshitaishvili, Keith Schon, Lyn Reid, Robert Macomber, Cheryl Lacotta, Antonina Kolokolova, Pavlos Konstadinidis, Christine Keller, Noah Goodman, Gary Gongwer, and Brian David. Mssrs Goodman and Schon took the exam in Budapest (but in English, not in Hungarian).

The results were quite satisfying... the U of A team was ranked 51st out of 294 institutions which had teams competing. Three U of A students, Sofiya Vasina, Kirill Shokhirev, and Lyn Reid, were included in the prestigious list of "Top Participants", approximately the top 20% of those competing.

Appended below are three of the problems, on which you may whet your wits: solutions usually appear in the American Mathematical Monthly in October, so you have lots of time to work on them.

Problem A1. Find the least number A such that for any two squares of combined area 1, a rectangle of area A exists such that the two squares can be packed into that rectangle (without the interiors of the squares overlapping). You may assume that the sides of the squares are parallel to the sides of the rectangle.

Problem A3. Suppose that each of twenty students has made a choice of anywhere from zero to a total of six courses offered. Prove or disprove: There are five students and two courses such that all five have chosen both courses or all five have chosen neither.

Problem B5. Given a finite string S of symbols X and O, we write D(X) for the number of X's in the string minus the number of O's. For example D(XOOXOOX) = -1. We call a string S balanced if every substring T (of consecutive symbols) of S has D(T) between -2 and 2. Thus e.g. S = XOOXOOX is not balanced, since it contains the substring T = OOXOO (and D(T) = 1 - 4 = -3). Find, with proof, the number of balanced strings of length n for each n.

Send solutions to John Leonard - unbearably clever solutions will be published in the next issue.

Puzzler

Suppose that the positive integer k can be factored as k = mn. Arrange the k integers 1,2,...,k in an m by n array, m rows and n columns. Now rearrange the entries in each row so that they are in decreasing order; after that rearrange the entries in each column to be in decreasing order. Will some of the rows then need further rearranging? In fact they will not, each row remains in decreasing order. Do you believe it? Can you prove it?

SWIG

Anu Rao

The Software Interest Group(SWIG) is a perennially recurrent seminar, for and by graduate students and friends, that focusses on practical computing issues.

Throughout 1996-1997, the Graduate Student Software Interest Group seminars were well attended. The World Wide Web was a general focus of discussion...with talks on creating homepages (including ready-made templates), using animations and math equations in web pages, and running Netscape from the comfort of home. As always, many thanks to our volunteer and coerced speakers!

Here are some of the talks from the past academic year - more information is available if you check out the department's web page - http://www.math.arizona.edu

  • Making Your Own Homepage: Part 1 - Cindy Kaus and Anu Rao
  • Questions and Answers: Computing in Mathematics - Bob Condon
  • Making Your Own Homepage: Part 2, Incorporating LaTeX2e Documents - Cindy Kaus and Anu Rao
  • Does Animation Have You in Knots? - Mark Hays, Cindy Kaus, and Anu Rao
  • Gnuplot and Netscape: What They Can Do For You - Anu Rao
  • Matlab and IDL: An Introduction/Showcase - Anu Rao
  • Running Internet Applications from Home with Slirp - Ricardo Martinez
  • Mathematica Basics - Anu Rao
  • Using the Make Utility - Mark Hays
  • Latex2e Dissertation Style - Kevin Kremeyer
  • Using Tcl/Tk - Aaron King
  • Debuggers - David Ropp
  • How to Run Netscape from Home - Mark Hays, Ricardo Martinez, and Anu Rao

SWRIMS

William Yslas Vélez

The Southwest Regional Institute in the Mathematical Sciences (SWRIMS) was initially funded in 1994, with a grant from the National Science Foundation (NSF).

The aim of SWRIMS is the integration of research and education. During the first two years of the project, SWRIMS funded activities at Northern Arizona University, Utah State University, and the U of A. Each of these sites formed a Core Group, consisting of two or three faculty members, two or three high school teachers, a couple of graduate students, and some undergraduate students. Funds were provided to give the university faculty and graduate students release time from their teaching in order to carry out SWRIMS activities. The other Core Group members were provided with stipends. A survey of the activities during those first two years can be obtained from the article, "On the Integration of Research and Education", which appeared in the October 1996 issue of the Notices of the American Mathematical Society.

Beginning in January 1997, the scientific topic for the remainder of the grant period has been Cryptography/Security. Core Groups have been formed at Arizona State University, New Mexico State University, and the U of A. A small conference on this topic was held at the U of A in March 1997. This conference brought in researchers to give talks on their investigations. Non-specialists were also in attendance, so the presenters were given the challenge of presenting their research results to a general audience. This is a difficult task to accomplish, yet we can say that most of the attendees got a great deal from the conference.

The Core Groups at the three sites are hard at work. The group from Arizona State University is working with some of the mathematics faculty from Mountain Pointe High School. They are offering a course, which meets five days a week at Mountain Pointe, on topics in cryptography and combinatorics. They plan to offer the course again for the entire coming year.

The Core Group at the U of A is developing a short course for high school teachers on cryptography. This course will begin with elementary substitution ciphers, and will move on to more sophisticated mathematical techniques. It is hoped that we will be able to introduce some historical perspectives by discussing the German World War II enciphering machine, ENIGMA. A software version has been built at the University.

The Core Group at New Mexico State is also working with the local high schools, including Las Cruces High School. They have built a working model of a simplified ENIGMA machine, and are also integrating some of their work on cryptography with the Super Computer Projects that are on-going at the high schools.

During the 97-98 academic year, the three Core groups will work to develop further materials on cryptography for use in the high schools.

Staff Stuff

Carole Anderson
Jerrie Bieberstein

Well, another year is behind us and we are forging ahead towards the new millenium. Awesome, Dude!! Let's update the comings and goings of the staff. To begin: We had some internal job shifting. Robert Lanza accepted a new position in the Algebra Office as Administrative Secretary, and Julie Zehring changed desks and duties there while Jerrie Bieberstein had new duties added - all as a result of a vacancy in that office. We welcome Susan Dzik, Administrative Assistant, to the ACMS Office, Jennifer Roll to our Copy/Mail Room Office Assistant position, and Laurie Lefebvre to the Word Processing Specialist position. Welcome, Welcome, Welcome.

The winner of the Department of Mathematics, College of Science, Staff Award for Excellence for 1997 is Carole Anderson. The selection is made from reviewing nominations submitted by faculty and staff for staff employees. The criteria used to evaluate nominees includes their volunteer work on special projects, service on departmental or University committees, filling in when their unit is short staffed, exceptional cooperation and courteousness, their suggestions that save their units time and money, etc. So Congratulations Carole!

Congratulations also to nominees Jerrie Bieberstein, Robert Lanza, Laurie Lefebvre, Jennifer Roll, Sandy Sutton, Bernadette Thomas, Faye Villalobos and Brooke Zang. The department received over 30 nomination forms and more staff were nominated this year than in any other year. All College of Science staff will be recognized at a luncheon on 1 May 1997, in the Arizona Ballroom.

We are still the luckiest department on campus, boasting this exceptional group of staff: Rex Alison, Carole Anderson, Jerrie Bieberstein, Susan Dzik, Betty Fink, Deborah Gaines, Lois Gorski, Mark Hayes, Janet Lange, Robert Lanza, Laurie Lefebvre, Kathleen Leick, Ricardo Martinez, Bridget Mendibles, Zora Mlejnkova, Jennifer Roll, Sandy Sutton, Bernadette Thomas, Jose Torres, Faye Villalobos, Brooke Zang, and Julie Zehring.

'Til next time...

The Teaching Post-Doc Program

Elias Toubassi

During the past academic year the Entry Level Committee created three-year teaching post-doc positions. The positions are similar to research post-doctorate positions, but have an emphasis on teaching and scholarly activities pertaining to teaching. They are intended primarily for individuals with a career track in teaching in mind. They are meant to provide an excellent opportunity for those planning on a teaching career in a community college, four year college, or Master's degree institution.

Participants in the program will be offered opportunities to be involved in current and future curriculum and teacher enhancement projects. The starting salary for these positions for the 1997-98 academic year has been set at $30,000 with a teaching load of 9 to 10 units per semester. During their tenure participants will be exposed to the full spectrum of lower division courses as well as upper division courses in the candidate's specialty. They will also be provided with leadership opportunities such as supervising GTA's, serving as course coordinators, and participating in training workshops. In addition, they will be provided with a computer for their personal use and a small travel stipend to attend professional meetings.

View From The Headship

Hermann Flaschka

On July 17, 1996, at 10:30 AM, having just returned from a refreshing two months at universities in Belgium and France, I stepped into my new Department Head Office (we all make mistakes). Thanks to the exaltedness I acquired at that instant, I am now asked lots of questions, all the time. The two most frequent ones, by far, are: (1) why did you do it? (2) what has it been like?

To number (1), there is no good answer. I asked it of myself, when our computer system was stolen in mid-August 1996, and again when, a few days later, lightning hit the tide-us-over replacement version cobbled together by Bob Condon and his staff. Anyway, I believe my decision to declare candidacy came during an unguarded moment, when sentiments lsuch as "I owe the department" and "I could help make us even better" actually seemed logical.

The answer to number (2): it has been interesting, even educational. There are headaches, of course. But mostly, there are pleasant discoveries -- how incredibly creative and helpful and energetic my colleagues are. And by "colleague", I mean (in alphabetical order) Adjuncts, Co-ops, Faculty, Graduate TA's, and Staff.

Only now, after ten months, can I claim to have even a bird's-eye view of our department's mission and contributions. The variety and magnitude of our activities is sometimes overwhelming. We teach 24,000 student credit hours every fall-more than any other department in the University. Different strands, such as College Algebra, Business Math, and Calculus, each serve thousands of students and require detailed planning and coordination. Descriptions of our outreach programs fill a 25-page catalog (now available on our Web page). The Math Center is consolidating and extending resources for our majors; increased undergraduate research opportunities will be a focus next year. The graduate program must balance four distinct emphases: Math, Applied Math, Math Education, and now Statistics. Along with all this, our faculty members continue to make time for their own scholarly activities. But the demands keep growing, while the resources shrink.

Unfortunately, the mathematics profession as a whole has not yet been successful in conveying the excitement and relevance of its vocation to the general public. This will be our biggest, and perhaps most critical, challenge during the next few years.

We must continue learning and discovering. We must, at the same time, explain modern mathematics to the non-academic public (our tax-paying sponsors, our students' parents, our students, and all those peoples' elected representatives), and convince them of the value of the results. There is a gap caused by the public's lack of appreciation of the purpose of a Research University and academia's lack of understanding of demands for accountability and social responsibility. The gap has grown large very quickly, and it threatens to curtail all universities' opportunity for fundamental inquiry, at a time when science and rational thinking will be needed to deal with national and global problems.

My hope, for however long I survive in this job, is to enhance our opportunity to develop our science, by explaining our contributions to as wide an audience as possible, while supporting even broader participation of the Math Department in activities within the University as well as outside.

Most of my message has been about "I think". To finish: "I thank". I would be more of a wreck than I already am, were it not for Janet Lange and Bernadette Thomas (who tell me what to do, every day), and Faye Villalobos (who reports on how many cents are left in our bank account). Marty Greenlee does everything I don't know how to do yet. Dan Madden controls thousands of calculus students (sort of). Bill McCallum organizes the undergraduate major. Elias Toubassi runs the huge entry-level program. And then there is all the help I've gotten from Doug,Carl, Chris, Marlene, Warren, Bob, Nick, Moysey, Dave, Dave, David, Donna, ... and many more. My first year has been a group effort, and I am happy to have had the opportunity to contribute.

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