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Mathematics Newsletter 1995-1996

Contents:

Applied Math Colloquium

Michael Tabor

On-line Seminar and Colloquia Info
Speakers, affiliations and their titles:

  • Joseph A. Zehnder, Department of Atmospheric Sciences, U of A, Barotropic Vortex Motion Near Large Scale Topography
  • Herbert Levine, Department of Physics, UCSD, Biological Implications Of Excitable Media Theory
  • Bernard Zeigler, Electrical and Computer Engineering, U of A, Modelling And Simulation On A Grand Challenge Scale
  • Deborah Sulsky, Department of Mathematics and Statistics, U of New Mexico, New Applications for Particle-in-Cell Methods
  • Boris Malomed, Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Israel, Stable Pulses in Ginzburg-Landau Equations
  • George Haller, Division of Applied Mathematics, Brown University, Fast Diffusion and Universality in Hamiltonian Systems
  • Stanley Osher, Department of Mathematics, UCLA, The Scope of the Level Set Method
  • A.M. Anile, Department of Mathematics, University of Catania, Italy, Mathematical Modeling Of Microelectronic Devices and Integrated Sensors and Actuators: A General Thermodynamical Framework
  • Kenneth M. Golden, Department of Mathematics, University of Utah, The Interaction Of Microwaves With Antarctic Sea Ice
  • Gary Walter, Hydro Geo Chem, Inc., Does Chaos Exist in Environmental Remediation Process?
  • Percy Deift, Courant Institute of Mathematical Sciences, Asymptotics for Some Problems Arising in The Theory of Random Matrices
  • Alain Goriely, Program in Applied Mathematics, U of A, Nonlinear Dynamics of Filaments
  • Jerrold E. Marsden, Control and Dynamical Systems, Caltech, Geometry and Motion Control
  • John Strain, Department of Mathematics, UC Berkeley, A New Approach To 2-D Vortex Methods
  • A.C. Scott, Department of Mathematics and Program in Applied Mathematics, U of A, The Problem of Consciousness
  • David Ferry, Department of Electrical Engineering, ASU, Transport in Ballistic Quantum Dots: Regularity, Chaos, Scares, and All That Stuff!
  • Juan Mario Restrepo, Mathematics Department, UCLA, Sandbars on the Continental Shelf
  • Andrew Odlyzko, ATandT Bell Laboratories, The Future of Research: Decline or Transformation ?
  • John K. Hunter, Mathematics Department and Institute of Theoretical Dynamics, UC Davis, Singularities and Oscillations in a Nonlinear Wave Equation
  • Hans Frauenfelder, Center for Nonlinear Studies, Los Alamos National Laboratory, Proteins - Paradigms of Complex Systems
  • David Rand, Mathematics Institute, University of Warrick, UK, Fluctuation-Driven Dynamics and the Evolution of Infection and Sex
  • Randolph Nelson, OTA Limited Partnership, New York, Mathematical Modeling in Finance
  • Tai-Ping Liu, Department of Mathematics, Stanford University, Construction and Nonlinear Stability of Shock Waves
  • Jennifer Tour Chayes, Department of Mathematics, UCLA, Length Scales in Magnetic Systems
  • Hon-Wai Wong, Department of Mathematics, Rutgers University, Dolbeault Cohomologies, Zuckerman Modules, And The Maximal Globalization Conjecture
  • Allen Newell, Department of Mathematics and Program in Applied Mathematics, U of A, Patterns: Their Origin and their Description

The Co-Op Class of 1995-96

Elias Toubassi

This year the Co-Op program has seven participants, five from Tucson area high schools and two from Pima Community College East Campus. The group consists of Jeanne Deloria, Tucson High School; Careylyn Hill, Canyon Del Oro High School; Ira Lackow, Cholla High School; Linda Malapanes, Mountain View High School; Brenda Ugalde, Pueblo High School; and Ellen Caldwell and Debbie Yoklic from Pima Community College.

Ellen Caldwell received her bachelor's degree from Randolph-Macon Women's College in Lynchburg, VA in 1976. After a brief stint at Westinghouse, she attended graduate school at the University of Wyoming, where she earned a master's degree in 1980. She taught for three years at Wenatchee Valley College and then took a position at Pima in 1983. Before she started a family she camped and hiked in all the states except North Dakota. Most of her leisure time these days is spent with her two daughters, ages 5 and 6. Ellen is also involved with her church, playing the piano for the youth choir and teaching Sunday School .

Jeanne Deloria received her bachelor's degree from the U of A in 1985 and her Secondary Mathematics Education certification in January 1990. She has been teaching at Tucson High School since that time. She is a member of a team of Tucson High teachers working on a curriculum for freshmen students. She participated in the Rainbow Program in the Summer of 1993 and is currently working on a master's degree in TTE. She has a busy summer ahead of her. She will be working on the Tucson High curriculum and organizing the material from several courses taken this year as a Co-Op to use with her students. On the leisure side she will be travelling with her mother to Iowa and Illinois to visit her birth place and collect genealogy information. Her hobbies include collecting puzzles, roller blading and bicycling. On May 20th she will be celebrating her first wedding anniversary to Doug Brooks. For those who are interested in unusual information Jeanne and Doug have the same birthday. This presents us with Jeanne's birthday problem: How many couples would you need to have in order for the probability of having a couple with the same birthday to be greater than 50%?

Careylyn Hill was born in Tucson but her family left shortly thereafter to live in Montana. After completing high school there she returned to Tucson in 1985. She went to Pima and then the U of A where she got her teaching degree in 1990. After a one semester teaching position at Blue Ridge High School in Pinetop she moved to Tucson and took a position at Canyon Del Oro. She is currently working on a master's degree in math education. She is very much interested in the reform movement in mathematics education and would like to learn as much as possible in order to provide a rich learning environment for her students. She has been involved in various sports activities, including coaching a summer league swim team and girls' volleyball. She is also a certified high school basketball official. She and her husband enjoy the outdoors and taking their two dogs hiking in the Catalinas.

Ira Lackow was born and raised in the Bronx, New York. He earned his teaching degree in 1976 and a master's degree in 1980, both from the U of A. He is married to Kathy Lackow who is also a math teacher and a 1993 Co-Op participant. They have two boys Seth and Jacob, ages 12 and 8. Ira's passion is baseball and he spends much of his free time coaching his sons' little league baseball teams. The Lackows enjoy the beaches of San Diego in the summer and skiing in winter.

Linda Malapanes started college at the U of A and completed her teaching degree at ASU in 1973. After living abroad for a few years in the Philippines and Italy she taught in Missouri and Illinois. In 1980 she returned to Tucson and took a teaching position in the Marana School District, first at Marana High School and currently at Mountain View. She has continued her professional growth by earning a master's degree in 1983 and participating in the PRISM Program in 1992. She loves teaching and her district has recognized her contributions by selecting her as Marana's Secondary Teacher of the Year in 1986-87 and nominating her for the Arizona Teacher of the Year Award. Linda and her husband Pete keep busy with a grandson, two sons, and a daughter who attends the U of A.

Brenda Ugalde earned her secondary education degree from the U of A in 1990. She did her student teaching at her Alma Mater, Pueblo High School, where she is currently teaching. She was a participant in Project BEAM, Bilingual Education Accessing Mathematics. This has led to a number of rewarding experiences, including a trip to Costa Rica to study Spanish. This was a wonderful opportunity for her to practice her Spanish and gain a better understanding of the culture, while living with a local family. The BEAM Program was also instrumental in her obtaining a master's degree in bilingual education this past December. She has traveled to Washington D.C. twice, once as a student and the other time as a participant in a program sponsored by the Quality Education for Minorities Network. She and her husband of four years spent their honeymoon in St. Thomas, Virgin Islands, and this Fall they plan to purchase a home and start a family.

Debbie Yoklic is no stranger to the Mathematics Department. In the '70s she held numerous positions - including secretary, business manager, and graduate student - earning a master's degree in 1978. Prior to coming to Arizona she grew up in Philadelphia and earned a bachelor's degree from Brandeis University in 1972. In 1983 she moved to her current teaching position at Pima. During her year as Co-Op she has spent time investigating issues related to technology in mathematics education. She continually tries to stay abreast of curriculum reform in order to maximize her effectiveness in the classroom. During the last eight years she and David Gay co-directed two NSF teacher enhancement projects for middle school teachers in Arizona. She, her husband, and two boys, ages 4 and 7, enjoy hiking and backpacking. She has recently set an Arizona State record in the 200 yard breaststroke in her age category.

Dynamical Systems Workshop

Nick Ercolani

The Mathematics Department hosted the first Southwest Regional Dynamical Systems Workshop from March 22--24. A total of 50 faculty, postdocs, and graduate students attended from the following institutions in the Southwest: University of Sonora (Hermosillo), University of Texas (Austin), University of North Texas, Arizona State, Northern Arizona, University of New Mexico, New Mexico State University, Center for Nonlinear Studies (Los Alamos), University of Colorado (Boulder), University of Utah, Brigham Young University, Caltech, UC Irvine, USC, UCLA, and UCSB.

There were 4 plenary speakers: Chris Jones (Brown University) who spoke on ``Mixing by Lagrangian Transport in the Ocean'', Sergey Kuksin (Steklov Institute) who spoke on ``Phase Portrait for the NLS Equation and Applications'', David Rand (University of Warwick) who spoke on ``Fluctuation-Driven Dynamics and the Evolution of Infection and Sex'', and David Ruelle (IHES) who spoke on ``Transfer Operators and Dynamical Zeta Functions''. In addition there were 1/2-hour talks given by 21 of the participants. The topics covered a range of fields representing the breadth of application of modern dynamical systems theory.

Due to the success of this meeting in promoting interactions between mathematicians at neighboring institutions, a Scientific Advisory Committee was formed to help plan the locations and themes of future regional meetings. The plan is to have the location of these meetings rotate from year to year among the southwest campuses. This will help to insure fully regional participation in these meetings. Also themes may vary from year to year such as between Dynamical Systems, Mathematical Physics, PDE, etc. The members of the advisory committee represent a broad cross-section of southwest regional institutions as well as mathematical interests: Alejandro Aceves (UNM), Dieter Armbruster (ASU), Peter Bates (Brigham Young U), Reuben Flores-Espinoza (Hermosillo), Daryl Holm (Los Alamos), Abel Klein (Irvine), Rafael de la Llave (Austin), Jim Meiss (Colorado), Maciej Wojtkowski (Arizona), Lai-Sang Young (UCLA).

A second regional meeting is being planned for next March to be held at the University of North Texas. The local organizers for this meeting were the PI's on the proposal: Nick Ercolani, Tom Kennedy, Jan Wehr, and Maciej Wojtkowski. Travel and accomodation costs for the southwest participants were covered by a grant from the Special Projects Division of the National Science Foundation.

Entry Level Mathematics Colloquium

Richard B. Thompson

As they say in show business, "We have now finished our second successful season." We even have press clippings from the first season. The April issue of FOCUS, the Newsletter of the American Mathematical Association, carried a report by Richard Thompson entitled, "Teachers Doing Mathematics: A Lower Division Mathematics Colloquium."

The Entry Level Mathematics Colloquium presented a series of eight talks showing that much useful and beautiful mathematics can be done with simple tools. The programs featured everything from computer animation to traditional chalkboard lectures. Speakers and topics included the following.

  • Richard Thompson, Global Positioning System: The mathematics of satellite navigation
  • John Leonard, What surface area ISN'T
  • Bill Mueller and Richard Thompson, Mathcad software: One package does it all (or at least a lot of it)
  • Bill Mueller, Centers of triangles of a fixed center: Adventures in undergraduate research
  • Donna Krawczyk, A look at spherical trigonometry
  • Richard Thompson, Lunar distances: "Reform mathematics" and "templates" in a navigational method used for 400 years
  • Carl DeVito, A little piece of time
  • John Brillhart, Sturm without Drang

The last talk, which presented the work of C. Sturm on polynomial sequences, must come close to holding a record for the most creative title of a mathematics lecture.

Faculty News

Larry Grove

Again the main faculty news item is that we are in transition. Alan Newell is off to Warwick. A Head Search Committee, comprised of Cheryl DeLorme, Nick Ercolani, Larry Grove, Jiang-hua Lu, Dan Madden, Richard Powell (Optical Sciences), Michael Tabor (chair), and Faye Villalobos, fairly quickly came up with exactly one candidate, Hermann Flaschka. Hermann went through a grueling series of meetings and interviews with practically everyone on the campus. He will be leading us into the future effective 1 July.

David Lomen has been named as a Distinguished University Professor. This is a newly created distinction, akin to the Regents' Research Professorships, but emphasizing excellence in teaching of undergraduates.

Visitors to the department this year included Richard Blecksmith (Southern Illinois U), Antonius Broumas (U of Texas (Austin)), Jean Marie De Koninck (U Laval), Aidan Egan, Quan Yuang Feng, Scott Glasgow, Alain Goriely, Sergey Kuksin, Jocelyn Lega, Simon Malham, Sergey Nazarenko, Cun-zheng Ning, Andrey Pouchkarov, Mikael Shapiro (CUNY), Alexander Shoshitaishvili, Ewan Wright, Chuck Vinsonhaler (U of Connecticut), and Mao-rong Zou (U of Texas (Austin)).

Bill Faris, Tom Kennedy, David Lovelock, and Marek Rychlik were on sabbatical leave for part or all of the year: Bill F in Moscow and Marek at the U of Maryland. Sam Evens, Deborah Hughes-Hallet, Bill McCallum, Zhen-su She, and Vladimir Zakharov were on leave-of-absence: Sam at Cornell, Deborah at Harvard, Zhen-su at UCLA, and Bill McC and Vladimir at the IAS in Princeton.

Late breaking news - after years of campaigning Nick Ercolani has been elected Derelict-of-the-Year, apparently due to a convincing nomination by Alan Newell (the only phrase from the nomination that is suitable for a family-oriented newsletter such as this one is "Italian stallion"). However, Nick forgot to appear at the awards ceremony, and now may possibly be the first Derelict-of-the-Year to suffer the indignities of impeachment proceedings. We'll keep you informed.

We welcomed three new tenure-track faculty members in the fall semester of 1995. Here is a thumb-nail sketch of each.

Greg Eyink

Greg was born in Coldwater, Ohio (originally known as Buzzard's Glory), and grew up on a farm in western Ohio. He graduated from Ohio State University in mathematics, then with a PhD in physics in 1987, under advisor K.D. Lane. A bewildering display of peripateticism followed - Universite Libre de Bruxelles (Belgium, '87 - '88), Rutgers Post-docs ('88 - '92), Post-doctoral Research (Munich/Rutgers, '90-'91), consultant at Los Alamos ('92), andVisiting Research Assistant Professor at Illinois (Urbana) in Mathematics and Physics ('92 - '94). He first came to the U of A as a visitor in 1994. His research areas are statistical mechanics, fluid mechanics and turbulence, dynamical systems, and PDE's.

Lucas Hsu

Lucas was born in Maylaysia and moved to Victoria, Canada with his family at the age of 13. He was an undergraduate at the University of Waterloo, and earned a PhD from Duke University in 1991. His research, in geometric analysis, was guided by Robert Bryant. He spent the academic year 1991 - '92 at Stanford and at MSRI in Berkeley, then went to the Institute for Advanced Study in Princeton from 1992 - '95. He was appointed Assistant Professor at the U of A in 1995.

Minhyong Kim

Minhyong was born in Seoul, Korea, and grew up there. He graduated in mathematics from Seoul National University, and went on to graduate studies at Yale. He specialized in Arithmetic Intersection Theory, under the direction of Serge Lang (and Barry Mazur, Harvard), and earned a PhD degree in 1990. He was a Moore Instructor at MIT from 1990 - '93, and an Assistant Professor at Columbia University from 1993 - '95.

Financial Aid

Faye Villalobos

Richard S. Pierce Undergraduate Scholarship

An endowment scholarship for undergraduate mathematics majors was established in 1992 in memory of Professor Richard S. Pierce. Dr. Pierce's interests included Ring Theory, Abelian Groups, and Boolean Algebras. Among the work for which he is best known is that of his basic results on homomorphisms of torsion abelian groups, the Pierce representation theorem for commutative rings, and his book on associative algebras, which has been translated into Russian. Scholarships of up to $500 each are awarded each year to outstanding undergraduate students in Mathematics.

James R. Clay Graduate Travel Fund

A fund for current Mathematics graduate students and recent Mathematics PhD students to provide support for travel and subsistence to attend and participate by presentation at mathematical conferences or meetings was established this year after the sudden loss of Prof. James R. Clay. Throughout his career, Professor Clay was noted for his work encouraging young mathematicians to join the international community of mathematics.

If you would like to contribute to either of these funds, please make your check payable to THE UNIVERSITY OF ARIZONA FOUNDATION and send to:

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

Grad Seminar

Stephen Shipman

The Graduate Student Seminar is a student-managed weekly mathematics seminar which began four years ago. The speakers are graduate students who present various topics of special interest to them, including dissertation research.

The Seminar serves several purposes. First, it gives beginning graduate students the opportunity to hear about various topics in mathematics, in particular current topics in mathematical research, at a level which is more accessible to them than the other mathematics seminars and colloquia. This helps students to obtain a broader and more versatile and integrated understanding of the world of mathematics at an early stage: indeed, concepts which are studied routinely in the core courses are seen in practice, and additional concepts are encountered.

An equally important role of the seminar is to supply the opportunity for graduate students to present mathematics to their colleagues. Sometimes a student will use the hour to give a trial presentation of paper which is to be presented in an oral examination. Students who are working on a masters or Ph.D. dissertation use the seminar to practice presenting their work and to motivate themselves to pull something together. Others present papers or projects from their coursework or simply talk about an area of special interest.

This year's speakers were:

  • Alexei Samsonovich: Spacial Maps and Path Integration in Rats' Hippocampus
  • David Hrencecin: Representations of Complex Semisimple Lie Algebras
  • Alexander Perlis: The Platonic Solids: Uniqueness and Construction
  • Eileen Murray: Aggregation Phenomena
  • Matt Kruse: Resonance Cascades
  • Olga Simek: Irreducibility of Eigenspaces of the Laplacian on a Manifold
  • Stephan Schaub: A Music-Theoretical Application of Polya-Redfield Enumeration
  • Mark Torgerson: Solving Systems of Multivariate Polynomial Equations
  • Stephan Schaub: "The Mathematics of Musical Scales"
  • Stephen Shipman: "A Finite Discrete Nonlinear Schroedinger Chain, Geometrically"
  • Alexander Perlis: "Continued Fractions"
  • Chris Bowman: "Wavelets and Pattern Analysis"
  • Mary Sibayan: "Fibonacci Numbers and the Golden Ratio"
  • David Marshall: "Ovals, Arcs, Curves, and...Codes?"
  • John Keisling: "An N-Particle Exclusion Process: Parts I and II"

Any graduate student who would like to present something at the seminar is welcome to contact me, either in person or via email: ships@math.arizona.edu

Graduate Student News

Alexander Perlis

Here follows a summary of the official progress of the graduate students in the applied and pure mathematics programs during the 1995-1996 academic year; to learn of the unofficial progress, not to mention most of the fun, you'll have to observe the nightly seemingly endless hours of collaborative effort taking place in our offices, in the department lounge/library, and in the aquarium (the latter is, of course, no place other than the computer room on the ground floor).

The following students received the Ph.D. degree:

  • Kebenesh Belayneh, "A hierarchical size structured population model".
  • Gustavo Cruz-Pacheco, "The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation", already at the University of New Mexico, soon to be at Mexico University.
  • Javier Diaz-Vargas, "On zeros of characteristic p zeta functions".
  • George Fennemore, "Wetting fronts in one-dimensional periodically layered soils", continuing at Los Alamos.
  • James Gartside, "Nonlinear interaction of two oblique waves in a compressible, inviscid free shear layer", continuing at the University of Utah.
  • Utith Inprasit, "Equilibria in structured population models".
  • John Keisling, "Invariant measures for an n-particle exclusion process", continuing here as an adjunct instructor.
  • Yixia Lu, "Discrete nonlinear Schroedinger equation", continuing at the University of Georgia.
  • Marcel Oliver, "A mathematical investigation of models of shallow water with a varying bottom", continuing at the University of California at Irvine.
  • Donald Stark, "Structure and turbulence in the complex Ginzburg-Landau equation with a nonlinearity of arbitrary order", soon to be at a national research lab in Mississippi.
  • Tityik Wong, "Preservation of stochastic orders under shock models".
  • Bing Xu, "A discrete nonlinear model of age structured population".

The following students received Master's degrees: Melanie Ayers, Karl Bauer, Geoffrey Cunningham, Kris Green, Wayne Hacker, David Hrencecin, Wei-ye Li, Eileen Murray, Chad Neller, Hyunju Oh, Mary Sibayan, Stephan Schaub, and Agnieszka Walsh.

The following students passed the preliminary PhD oral exam: Kevin Anderson, Geoffrey Cunningham, Joseph Erker, Cecilia Fosser, Brandon Gallas, Gregory Gillis, Wayne Hacker, Karl Haller, David Hochheiser, Craig Hyde, Cynthia Kaus, Aaron King, Matthew Kruse, Amy Rabb-Liu, Anita Rado, Anu Rao, Olga Simek, and Mark Torgerson.

The following students passed the qualifying exams: Karl Bauer, John Friese, Kris Green, Li Liu, David Marshall, Gema Mercado, Regan Murray, Alexander Perlis, Scott Sakamoto, Chunnan Wang, and Jung Woo.

Employment news regarding two recent grads: Constance Schober and Annelise Calini have received offers of tenure-track positions at the College of Charleston in South Carolina.

Congratulations to all!

International Science Fair

David Gay

Ten faculty members from the Department of Mathematics and seven graduate students in Mathematics and Applied Mathematics were judges in the 47th International Science and Engineering Fair held during the week of 5 May 1996 at the Tucson Convention Center. Close to 1000 exhibits were on display, the outcomes of projects completed by high school students from around the USA and 24 foreign countries.

Faculty members Bruce Bayly, Marty Greenlee, Marek Rychlik, Maciej Wojtkowski, and Joe Watkins, together with graduate students Ed Alexander, Reva Chopra, Matt Kruse, David Marshall, Marcel Oliver, Alex Perlis, and Anu Rao selected the Fair's Grand Prize awards in mathematics. The Fair contained 47 projects in the mathematics category.

Professors Don Myers, Moshe Shaked, and Larry Wright roamed the entire exhibit looking for winners of prizes to be given out by the professional statistics societies. Faculty members John Brillhart and David Gay joined five out-of-town mathematicians in determining the winners of the American Mathematical Society (AMS) prizes.

As examples of top exhibits in mathematics, here is a list of the award-winning titles for the AMS:

first prize --"Polynomial Automorphism of Splitting Fields";

two second prizes --"Elementary Proofs of Apiery Number Congruences"

and "Computational Model of Quantum Dot Diatomic Molecule";

four third prizes --"Utilizing a Cancellation Algorithm to Improve the Bounds of R(5,5)", "Expansions in a Special Family of Irrational Base Systems", "Sequences of Continued Fractions and its Relation with Egyptian Fractions", and "Enumerating N-Step Up-Side Self-Avoiding Walks";

five honorable mention prizes -- "A Hypothesis of Selfridge and the Equation n! = x2 + y2" ; "Finite Orthogonal Binary Wavelet Set for Multiresolution Analysis and Data Compression"; "Pick's Theorem in Three Dimensions and Beyond"; "Coordinates, Equations, and Area in Non-Perpendicular Coordinate Systems"; and "Do Cardiac Arrhythmias Have Chaotic Tendencies?" More details on these prizes will appear in a forthcoming issue of the Notices of the AMS.

Making Everybody Count: The Last Summer

David Gay

From Monday June 3 through Friday June 14, thirty middle school mathematics teachers from around the state will be in the mathematics building as part of Making Everybody Count. This will be the last of four summers for this NSF-funded project. The teachers coming to campus this year are returning from participation in the project last summer. During their two weeks here, they will take courses in Discrete Math from Bruce Bayly and Visual Math from Bill Velez and Maria Fernandez (College of Education). Each participant will report on implementing the previous summer's techniques and ideas into their own middle school classrooms. They will take part in a variety of workshops during the two week period, including leadership training, grant writing, and advanced Family Math training. Joyce House (Rincon High School) will oversee the latter activities.

Last summer, the teachers took courses in mathematics, computers, and techniques for getting students actively involved in doing mathematics --- especially women and minorities. During the intervening year, participants were involved in a number of "follow-up" activities: implementing the new material into their own classrooms, giving workshops on the ideas and techniques of the grant to teachers at their own schools, writing articles for the project newsletter, attending regional meetings of participants, presenting Family Math nights for parents and students, and observing another participant's classroom.

Many participants in the project have become leaders in their schools and districts outside of the classroom. One is a mathematics coordinator for an urban district, another is a presidential award winning teacher. Other examples of leadership roles taken on by former participants are Family Math trainer, director of rural district's grade 4-8 math curriculum revision, urban systemic initiative collaborative peer teacher, and collaborating peer teacher with the U of A's PRIME program.

This is the eighth summer during which institutes for middle school math teachers from around the state have taken place on campus. Making Everybody Count, 1993-1996, is the successor to Making Math Count, 1989-1992, also funded by the National Science Foundation. The latter was the successor to a third program funded by the Arizona Board of Regents during the summer of 1984. All these projects have been jointly administered by the Department of Mathematics and Women Studies at the University and co-directed by David Gay (Math Department) and Deborah Yoklic (Women's Studies). It is unlikely that a continuation of these programs will occur on campus in the near future. The National Science Foundation appears not to be funding these "leadership/renewal" programs. Rather, NSF gives preference to programs which are more systemic, i.e., those which work with all teachers in a district or in a city. Moreover, the associated schools must agree to adopt curriculum packages from among those recently developed by NSF curriculum development projects.

A notable feature of Making Everybody Count and Making Math Count is the representation on their staffs by persons from a broad range of educational constituencies: Bruce Bayly, David Gay, David Lovelock, Amy Rabb-Liu, and Bill Velez from the U of A Mathematics Department; Maria Fernandez and Virginia Horak from the U of A College of Education; Louise Pate and Debbie Yoklic from Pima College; Lisa Garcia, Linda Griffin, Brink Harrison, Joyce House, Bob Koenig, and Barb Paisecki from Tucson middle and high schools; Rich Blegen from Page High School (Page, AZ), Wendy Diskin from Meyer Elementary School (Meyer, AZ), and Michele Wright from Somerton Middle School (Yuma, AZ).

Math Center/Undergraduate Programs

Chris Mikel

The Math Center sponsored numerous talks and activities for undergraduate math majors and other interested persons during the past year. There were six Undergraduate Colloquia on such interesting topics as Chaos and Beetles, by Jim Cushing, and Medieval Islamic Mathematics: The Missing Epoch, by Dan Madden, just to name a couple. Talks were held on applying to graduate school, careers in mathematics,and how to conduct your job search.

Initial efforts were made by students, with the help of the Math Center, to create a Math Club. The highlight was a tour by Dr. Tabor and his applied math graduate students of the Applied Math Laboratory, an innovative lab in which research on math problems can be done with hands-on activities. We hope to see participation in the club grow next year.

Department scholarships and awards were given to the following undergraduate students:

  • Outstanding Senior Award - December 1995 - Brad Traweek
  • Outstanding Senior Award - May 1996 - Roger Levy
  • Richard Pierce Memorial Scholarship - Takekatsu Konno
  • Richard Peet Memorial Scholarship - Jonathan Pillow
  • Graesser Foundation Math Scholarships - Andrew Klein, Todd Murphey, Howard Nachtigal, Lyn Reid, David Staley, and Sofiya Vasina

Other Awards: Justin Bein received second place and a monetary prize in the Mathematics division of the 1995 Student Showcase.

Undergraduate students who will be involved in summer research opportunities in the summer of 1996 include:

  • Chris Chavez, Northern Arizona University, Math REU in Dynamical Systems
  • Andrew Klein, Institute for Advanced Study, Princeton, Probability Institute
  • Paul Mayfield, University of Tennessee, Math/Ecology REU
  • Todd Murphey, Goddard Space Flight Center, Summer Institute in Atmospheric and Hydrospheric Sciences
  • Jonathan Pillow, Michigan Technical University, Math REU in Probabilistic Methods in Graph Theory, Combinatorics, and Number Theory.

Graduate school plans for graduating students:

  • Brad Traweek (Aug95) is in the Master of Computer Science program at the U of A.
  • David Ainsworth will attend the University of Wisconsin to pursue a PhD in English Literature. (he has a double major)
  • Ryugi Arai will attend Stanford in a Mechanical Engineering program.
  • John Duchnowski will pursue a PhD in Mathematics at the U of A
  • Yun Hsu will attend Caltech in Bio-Engineering.
  • Sean Kiilehua will pursue a Master of Statistics at Texas A and M.
  • Matt Trinacty will pursue a PhD in Physics at Boston University.

Congratulations to all students who received undergraduate degrees in Mathematics during the 1995-96 academic year!

Mathematicians and Education Reform (MER)

Alexander Perlis

Conceived in 1985, and funded by the NSF starting in 1988, the goal of the original MER project was to involve mathematicians in precollege education. Annual meetings of thirteen research mathematics departments, including our own, have been organized and partially funded by MER starting in 1994; this so-called MER Department Network has the noble goal of establishing communications links between these departments at all levels and concerning all relevant matters; to this end, both faculty and graduate students attend the meetings, which consist mostly of small-group sessions devoted to specific topics, such as calculus reform, properly preparing graduate students for the shrinking job market, and identifying the future role of mathematics departments in the university. More information may be found online at MER.

The March meeting was held at the University of Maryland in College Park; the attendees from our department were Ed Alexander, Hermann Flaschka, Greg Gillis, Cindy Kaus, Alexander Perlis, and Elias Toubassi.

The Mathematics Colloquium

Jiang-hua Lu

On-line Seminar and Colloquia Info

The following topics were covered in the Mathematics Colloquium this year (you need to decide for yourself which is a subset of which): Riemannian geometry; combinatorics; real analysis; dynamical systems; control theory; quantum field theory; integrable systems; number theory; geometrical methods in mechanical systems; Lie theory; complex geometry; chaos; Euclid's "Elements of geometry"; partial differential equations, and non-commutative differential geometry. Lennie Friedlander (happily) took care of the colloquium for the month of February, and speakers were in general greatly entertained by their local hosts.

Here is the complete list of the talks with the names of the speakers, their affiliations, their titles, and their local hosts (in parenthesis):

  • Lucas Hsu (Lu), U of A, "Sub-Riemannian geometry"
  • Paul Pederson (Ercolani), UCLA, "Polynomial equations, real roots, and polytopes"
  • Charles Swartz (Myers), New Mexico State University, "The Uniform boundedness principle without completeness"
  • Viktor Ginzburg (Lu), UC Berkeley, "Hamitonian flows without periodic trajectories"
  • Stephanie Singer (Lu and Ercolani), Haverford College, "An application of Kostant's cascade of orthogonal roots"
  • Robert Bryant (Hsu), Duke University, "On the differential geometry of control systems"
  • John Baez (Kim), UC Riverside, "Higher-dimensional algebra and topological quantum field theory"
  • Luc Haine (Flaschka), University of Louvain-Neuve, "A new life to orthogonal polynomials and other special functions"
  • Michael Chertkov (Ercolani), Weitzman Institute, "Normal and anomalous scaling in a passive scalar problem".
  • Alan Weinstein (Lu), UC Berkeley, "Groupoids: unifying internal with external symmetry"
  • Alex Buium (Thakur and Ulmer), University of New Mexico, "Derivatives of integer numbers"
  • Kai Behrend (Kim and Lu), University of British Columbia, "Gromov-Witten invariants"
  • Jerry Marsden (Lu), Caltech, "Pattern evocation and geometric phases in mechanical systems".
  • Ian Grojnowski (Evens), UC Berkeley, "Instantons and affine algebras"
  • Noam Elkies (Thakur), Harvard University, "Lattices and their shadows"
  • Michael Weinstein (Xin), University of Michigan, "Nonlinear bound states in conservative systems"
  • Alexander Varchenko (Friedlander), University of North Carolina, "Geometry of q-hypergeometric functions"
  • Bruce Driver (Pickrell), UC San Diego, "Logarithmic Sobolev inequalities on loop groups"
  • Phillip Griffiths (Hsu), IAS, "Conservation laws in differential geometry"
  • Tudor Ratiu (Flaschka), UC Santa Cruz, "Geometric methods in the analysis of the stability of relative equilibria"
  • Simon Gindikin (Friedlander), Rutgers University, "Complex cohomology in real analysis"
  • Alexander Kirillov (Friedlander), University of Pennsylvania, "The orbit method for the Virasoro-Bott group"
  • David Ruelle (Wehr), IHES, "Applications of chaos"
  • Wilbur Knorr (Gay and Madden), Stanford University, "The wrong text of Euclid: mathematical differences"
  • Olga Yiparaki (Grove), Agnes Scott College, "Partitions and ultrafilters"
  • Vladimir Zakharov, U of A., "Classification of n-orthogonal coordinate systems"
  • Boris Tsygan (Lu), Penn State University, "Deformations, index theorems and non-commutative differential geometry"
  • Louis Nirenberg (Xin), New York University, "Symmetries of solutions of elliptic equations (expository)"

Mathematics Instruction Colloquium

David Gay

On-line Seminar and Colloquia Info

The Mathematics Instruction Colloquium has been meeting weekly, during the school year, since 1987. It is a forum for issues in mathematics education for present and future educators in elementary, middle, and high schools; junior colleges; and universities. Below is a list of the speakers and their topics for the 1995-1996 academic year.

  • Fred Stevenson (U of A Math), "Number Sequences with a Decimal Point".
  • Andee Rubin (TERC, Cambridge, MA), "Approaches to Geometry in the Investigations Curriculum Project".
  • Virginia Horak and Sue Adams (TUSD), "What's Happening in Mathematics at TUSD, Grades 6 - 12".
  • Nora Ramirez (Maricopa Community College District), "What's Happening in Mathematics with Phoenix Urban Systemic Initiative".
  • Carol Larson (U of A Dept. of Teaching and Teacher Education), "Novels and Mathematics".
  • Brenda Ugalde* (Pueblo H.S., Tucson), "Activities of the Southwest Regional Institute of the Mathematical Sciences (SWRIMS)" and Jeanne Deloria* (Tucson H.S.), "Computer Activities for the General Math Student".
  • Careylyn Hill* (Canyon del Oro H.S.) and Ira Lackow* (Cholla H.S.), "Functions Across the High School Curriculum".
  • Marilyn Carlson (ASU Mathematics Department), "A Longitudinal Investigation of the Development of the Function Concept".
  • Ed Alexander (U of A Math), "Teaching Undergraduate Statistics", and Linda Malapanes* (Mountain View H.S., Marana), "H.S. Math Preparation and University Placement".
  • Steve Willoughby (U of A Math), "Mathematics Education: Past, Present, and Future".
  • Karen Brighton (Program Coordinator, Arizona Tribal Coalition, Mathematics Department, ASU), "The Arizona Tribal Coalition and the Utah-Colorado-Arizona-New Mexico Rural Systemic Initiative (UCAN-RSI)".
  • Norman Lott Webb (Wisconsin Science Center, University of Wisconsin), "Probing the Depth and Breadth of Mathematical Knowledge Through Performance Assessment".
  • Ed Alexander, Tina Garn, and Donna Krawczyk (U of A Math), "TI-92: A New Teaching Tool".
  • Marjorie Senechal (Smith College), "Fun and Games with Penrose Tiles".
  • Ira Lackow* (Cholla H.S.), "Modelling Real Data with Trig Functions", and Jeanne Deloria* (Tucson H.S.), "Multicultural Mathematical Explorations".
  • Brenda Ugalde* (Pueblo H.S.) and Careylyn Hill* (Canyon del Oro H.S.), "Algebra II and the Real World".
  • Ellen Caldwell* (Pima Community College), "Projects in a Differential Equations Course", and Debbie Yoklic* (Pima Community College), "Helping Math Students Use Technology".
  • Jim Middleton (Department of Elementary Mathematics Education, ASU), "Math in Context: A New Middle School Curriculum".
  • Amy Rabb-Liu (U of A Math), "Student Misconceptions in Calculus".
  • Linda Malapanes* (U of A Math and Marana H.S.), "How Can a Public School Teacher Get a Grant?", and Greg Gillis (U of A Math), "Hex and other board-game models of percolation theory".

Speakers whose names are followeded by an "*" are teachers who were in residence during the academic year as part of the Department's Co-operative Program with the public schools and Pima Community College.

Mathematics In Industry

Robert Maier

This year's Applied Mathematics Modelling Seminar had "industrially useful mathematics" as its theme. Setting up ties to industry, high-technology industry in particular, is increasingly seen as a necessity for the mathematics community. The seminar, which was designed to appeal to graduate students as well as faculty, allowed us to conduct a sort of inventory of applied and industrial mathematics on the UA and ASU campuses.

Local speakers included Art Witulski of the ECE Department, Saumya Debray of the Computer Science Department, Janny Leung of the MIS Department, and Cholik Chan of the AME Department. Speakers from ASU included Gerald Farin of their Computer Science Department, who spoke on industrial applications of splines and approximation theory; and Christian Ringhofer and Matthias Goebbert of their Mathematics Department, who spoke on the fabrication of semiconductors. In addition, Karen West, who obtained her Ph.D. from the U of A Applied Mathematics program in 1985 and who now works for Science Applications in Tucson, spoke about mathematics in the defense and government contracting industry.

Two of the speakers in this year's Applied Mathematics Colloquium were also from industry. Andrew Odlyzko, a major figure in mathematical research at AT and T Bell Labs (now Lucent Technologies), spoke on ``The Future of Research: Decline or Transformation,'' and also gave a seminar talk on his own research. Randolph Nelson, an applied probabilist who used to work at IBM's Yorktown Heights Research Center and who now works for OTA Associates (an options trading firm in New York), spoke on ``The Mathematics of Finance.'' Many of the attendees at these colloquia by industry speakers had never set foot in the mathematics building before.

Next year we plan to continue our efforts in the direction of industrial mathematics by scheduling additional talks.

Mathematics On-Line

Bob Condon

The Mathematics Department currently operates two public access network information systems, i.e., a world-wide web server and an Internet ftp-site. Web users can find our departmental infoserver at URL "http://www.math.arizona.edu" (Home Page) , our ftp-site is located on "math.arizona.edu" at Internet address 128.196.224.2. A host computer with Internet connectivity and application software such as ftp, Netscape, or lynx is necessary to access our on-line information systems.

The Mathematics/Applied Mathematics web server provides interactive access to a variety of departmental information. For example, the schedules and abstracts for Mathematics and Applied Mathematics colloquia, SWIG and UCAN computing talks, and graduate student seminars can be found on our "Talks and Seminars" web pages. Information about our undergraduate and graduate degree programs, mathematics classes, and the University of Arizona at-large is available in our "Student Information" area. Descriptions of our various academic outreach activities and summer programs are available on the "Educational Programs" pages. Instructions for obtaining and installing the Arizona Mathematical Software are located in our "World Wide Web" area. Issues of our departmental "Weekly News" can be found in the "Announcements" section; links to other on-line news services are also provided.

The Mathematics Department intends to maintain up-to-date information about ongoing Mathematics and Applied Mathematics activities on its web pages. Comments and suggestions are welcome and easily delivered using the on-line "mail-to" forms that are provided.

The "math.arizona.edu" ftp-site provides network users with Internet file transfer capabilities. Our ftp and world wide web servers work in conjunction to provide flexible access to stored data. Our ftp-site can be accessed independently of the web; files can be retrieved and sent via the "ftp" network software program. Those interested in the University of Arizona Mathematical Software collection should note that "math.arizona.edu:/AZ-MATH" is the distribution base for this material, i.e, up-to-date versions of the various programs can always be found at this location.

Putnam Competition Results

John Leonard

In the 56th annual William Lowell Putnam Mathematical Competition, held in December 1995, the U of A team did quite well, and was ranked 89th out of 306 teams participating. One member, Jon Wilkening, was included in the prestigious "Top Participants List", as a result of earning a ranking of 245.5th out of 2,468 competitors. All eleven of the U of A entrants placed in the top half - like the children of Lake Wobegon, they're all above average. Our thanks to those undergraduates who represented us: Pavlos Constadinidis, Noah Goodman, Andrew Klein, Antonina Kolokolova,Roger Levy, Todd Murphey, Jonathan Pillow, Lyn Reid, Keith Schon, Sofia Vasina, and Jon Wilkening.

If you are feeling competitive, here are 3 of the puzzlers to chew on. Solutions will be published in the American Mathematical Monthly, probably in October.

Problem A4. Suppose we have a necklace of n beads. Each bead is labeled with an integer and the sum of all these labels is n - 1. Prove that we can cut the necklace to form a string whose consecutive labels x1, x2, ..., xn satisfy SUM 1k xi less than or = k - 1 for k = 1,2, ..., n.

Problem B2. An ellipse, whose semi-axes have lengths a and b, rolls without slipping on the curve y = c sin(x/a). How are a, b, c related, given that the ellipse completes one revolution when it traverses one period of the curve?

Problem B5. A game starts with four heaps of beans, containing 3, 4, 5,and 6 beans. The two players move alternately. A move consists of taking either
a. one bean from a heap, provided at least two beans are left behind in that heap, or
b. a complete heap of two or three beans.

The player who takes the last heap wins. To win the game do you want to move first or second? Give a winning strategy.

The Residency Program

Elias Toubassi

During the past academic year the Entry Level Committee proposed a revised role for adjunct faculty. It is based on the premise that future faculty in the program would be part of a multi-year residency of professional training. The concept is similar to that of a research post-doctorate position, but with an emphasis on teaching and scholarly activities pertaining to teaching. These positions are intended primarily for individuals with a career track in teaching and not research. At the conclusion of their residency these faculty would be prepared to take on positions at community colleges, four year colleges, or high schools.

Participants in the program will be offered an opportunity to be involved in current and future curriculum and teacher enhancement projects. The starting salary for the positions has been set at $30,000, with a teaching load of 9 to 10 units per semester. During their residency participants will be exposed to a wide range of courses in the 100 to 200 level. They will also be provided with leadership opportunities such as supervising GTA's, serving as course coordinators, and participating in training workshops. The Dean of the Faculty of Science and the Provost have endorsed this proposal.

Staff Stuff

Carole Anderson and Jerie Bieberstein

We thought we would be opening our Staff Stuff column with the same old same-old . But this year has been a banner year for our staff. Awards, anniversaries, new part-time (questionable) careers ... the Singing Soul Sisters(??) ... more on that later.

First - off to Jolly Old England went Kate Forysiak (ACMS), and up-up-and-away to Atmospheric Sciences went Earleen McGrew (Word Processing). Most recently we are losing Carie Wells (Algebra Office) to the Mexican restaurant business (vaya con Dios, Carie - muchos exitos!), and Cindy Teasley, who is off to San Diego.

On to the awards. Deborah Gaines received a College of Science Staff Award for Excellence, and Faye Villalobos was selected as one of the 1996 University Staff Award of Excellence recipients. She was presented with the honor during an "interrupted" mathematics faculty meeting in March. Her many prizes included a check for $1000. Congratulations ladies!

Alan and Tish Newell were bade a fond farewell at a party hosted by Nancy and Marty Greenlee on 19 April. And now comes the part about the SSS. The majority of the staff attending the festivities felt the urge to sing our departing department head off to England, over and over again. Alan dubbed us the Singing Soul Sisters (he was being kind). We have no future bookings.

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

One last thing - happy 10th anniversary to Julie, 25th to Deborah, and 30th to Faye. Later ...

Unix Computing Talks and Workshops

Bob Condon and Staff

During the past year, the Mathematics Department sponsored a pair of regularly scheduled computing talks for its undergraduate and graduate student Unix computer users. The "Unix and Utilities" workshops -- organized by Cindy Teasley -- were oriented towards those who were new to Unix and/or the departmental Unix computing systems. The "Software Interest Group" -- organized by Anu Rao -- discussed topics of relevance to the more experienced computer user, e.g. scientific software programs that have proved useful in graduate level research.

At year's end, we have found that -- while there was considerable interest in the various talks -- most students had little free time and were often unable to attend relevant scheduled sessions. As a post-meeting reference aid, we have begun placing "Unix and Utilities" and "Software Interest Group" meeting notices and talk materials on the departmental web server ... see the Colloquia and Seminars web pages on the Math Home Page.

Current plans are to continue the Unix talks and workshop activities as an integral component of the overall departmental computer offering. In addition to providing computer users with essential technical information, the various meetings provide the Department with very useful feedback about changes and additions that should be made to the local software configurations. Please send any requests and suggestions about future computing talks and workshop activities to: system@math.arizona.edu

Software Interest Group (SWIG-95)

Andy Long, Applied Mathematics (1990-1994), began the SWIG group in the Fall of 1993. Although no formal SWIG meetings were held during the following academic year, widespread interest remained and SWIG was resurrected for 1995-1996 under the eclectic, utilitarian guidance of Anu Rao. SWIG-95 topics ranged from the introductory: let's learn how use gnuplot in 3 easy steps to the practical: what kind of PC should I buy to help get me out of here to the sublime: how POSIX threads can help get me (fired || higher paying employment).

Under Anu's spirited leadership -- with all due thanks to everyone who either volunteered or was coerced into giving a talk -- SWIG-95 had a very successful renewal.

If you see an item of interest in the following list of SWIG-95 activities, it's not too late! SWIG-95 information is available on the Math/Applied Math web server, in the "/usr/local/doc/SWIG" directory (where we keep many helpful computing hints), and (often) in the metal wall organizer in our Math 103 computer lab.

  1. "Color and Animation in Your Work", Mark Hays and Anu Rao
  2. "Color and Animation in Your Work, Part II", Mark Hays and Anu Rao
  3. "Gnuplot and Netscape", Anu Rao
  4. "Matlab and IDL", Anu Rao
  5. "TK and TCL", Cynthia Teasley
  6. "Computer Parts and Computer Systems" , Ricardo Martinez
  7. "PDE Software -- Reality, or Myth", Aric Hagberg and Mark Hays
  8. "Computer Parts and Computer Systems, Part II", Anu Rao and Bob Condon
  9. "Computer Performance", Mark Hays and Anu Rao
  10. "Symbolic Computation and Maple" , Alain Goriely
  11. "Optimization and Profiling", Anu Rao
  12. "An Introduction to PVM", Anu Rao
  13. "An Introduction to Emacs Bookmode -- Maorong Zou
  14. "Using make and makefiles", Anu Rao
  15. "Customizing Fonts for X11", Anu Rao
  16. "Mathematica Basics", Anu Rao
  17. "Creating Graphical User Interfaces", Cindy Teasley and Kevin Kremeyer
  18. "Parallel Programming with POSIX Threads", Mark Hays
  19. "Academic Computing (UK and/versus USA)", Catherine Wattebot (Warwick)
  20. "Job Hunting on the Internet", Anu Rao
  21. "Linking Matlab with Fortran and C", Joe Erker
  22. "Parallel Programming with POSIX Threads, Part II", Mark Hays
  23. "Improve Your 3D graphics: from Mathematica to POV-ray", Alain Goriely
  24. "An Introduction to LaTeX2e", Marcel Oliver
  25. "An Introduction to LaTeX2e, Part II", Marcel Oliver

Unix and Utilities Workshops

Cindy Teasley, Mathematics Department, began a series of introductory Unix talks in the Fall of 1994. Initially, these talks were organized for new faculty and graduate student Unix computer users. With the establishment of Linux/Unix capability for Mathematics majors in the Spring of 1995, an additional program of undergraduate Unix computer assistance workshops was begun. During the past year, the number of "Unix and Utilities" topics was expanded and much of the material was put on the departmental web site.

Given the general marketability of good computing skills, the Department encourages its undergraduates to make good use of the "Unix and Utilities" workshop program. At this time, the following topics are planned for next semester's meetings:

  1. "An Introduction to UNIX"
  2. "Files/Directories"
  3. "Printing and Processes"
  4. "An Introduction to Emacs"
  5. "Compilers"
  6. "Advanced Emacs"
  7. "Debuggers"
  8. "Frequently Asked EMAIL Questions"
  9. "Latex Basics"
  10. "PostScript files and LaTeX"
  11. "Account Management"
  12. "Connecting to Linux/Unix systems from PCs, Macs, and modems"
  13. "Transporting data from MACs and PCs to Linux/Unix systems"
  14. "The World Wide Web"
  15. "Shell Start-up files"
  16. "X-Windows start-up files"

Last View from the Headship

Alan Newell

7:00 a.m. Monday, May 6th, Larry's deadline day. The orange juice which has been sitting for days on the file cabinet tastes like marmalade. Just dilute enough to down the vitamins C and E essential to delusions about health and hormones. The office looks like a Motel 6 bedroom in the wake of a Rugby tournament. I should hasten to add, for all readers who do not know that I have a professional side as well, that all this is but a temporary aberration, a small blip in a neatness code which could be the envy of the U.S. Marines. No, chaos reigns because I am in the middle of the big move, to the land of Shakespeare and sheep, manners and mad cows, to that green and pleasant land swarming with in-laws. This summer, I will be joining the University of Warwick to head up their Mathematics Department. An exciting challenge because they are the Avis to Oxbridge's Hertz (where Michael Atiyah has replaced O.J. in the hurdle clearing airport commercials) and have many first rate mathematicians. And they are good and decent folks who do indeed try harder.

But I shall miss Tucson and the University and the Mathematics Department and all of you, students, staff and faculty alike, who have been so supportive and generous to me over the past fifteen years.

The last ten years have been a very happy time for me. I was extraordinarily fortunate to become Head of the Department at a time when the creative spirits of so many colleagues were ready to soar. And soar they surely did, doing so many good things.

My role was easy. Encourage, facilitate and coordinate and then stay the hell out of the way while others, such as Lomen, Lovelock, and Toubassi did great things and earned national reputations. Their efforts, together with those of Civil, Gay, Grove, Hughes-Hallet, Madden, Stevenson, Velez, and Willoughby, have vaulted Arizona into the position of a national leader in Mathematics Education. We have pioneered the integration of computers into the undergraduate experience, we have been a major player in curriculum reform, we have developed outreach activities such as the Co-op program, PRIME, Making Math Count, RIMS, way before they were generally considered popular on the national scene. Such efforts have had another important consequence. They fostered genuinely cordial, professional relations with High Schools, Community Colleges, and the greater Tucson community.

We are squarely on the international map in several areas of research, particularly in the field of Applied Mathematics/Mathematical Physics/Nonlinear Science. Further, given the talents and energies and ideas and imaginations of our younger faculty members (15 of our 58 faculty members are under 40), and given the culture of unity in which number theorists expert in Fermat's last theorem talk to physicists interested in the resonant manifolds of water waves, geometers talk to biologists, algebraists to analysts, there is every reason to have high expectations for a bright future. Moreover, everybody contributes. The accent is always on the positive. Anachronistic dichotomies, the old chestnuts such as research versus teaching, applied versus pure, have long been cast aside. The concentration has been, and is, and will, under Hermann Flaschka, continue to be on the right thing to do now, keeping in mind that time flows toward the future and not the past.

I believe Hermann's skin will quickly thicken and that he will be a great Chairman. I know him well as a personal, professional, and family friend. His integrity is unimpeachable, his judgment is sound, his common sense is solid, and if he didn't insist on singing Finnegan's Wake every time we have a few JD's together, he would be damn near perfect. I wish him and Blair, yes, Blair, you too, because you are going to have to listen to a lot that you may prefer not to, all the luck in the world in their new challenge.

But now please let me add a little serious contemplation. The optimism we feel at present should not disguise the challenges we presently face. There is an ever increasing pressure on Universities these days to do more with less. This is not part of a conspiracy to give educators their comeuppance for having had it so good for so long, but rather is simply part of a trend towards downsizing and accountability which is being experienced by almost every segment of our society and the economy. However, the manifestation of this pressure on Mathematics Departments, and indeed on Universities in general, is such that serious damage can be done unless the challenge is handled in the right way. Let me begin by describing what the pressures are.

First, John Q. Public, the taxpayer, is insisting more and more that the University's principal responsibility is education and in particular the education of his own kids. Indeed, in the minds of many, this responsibility would be best met by a faculty which spends considerably more time in the classroom. In many ways, the public is right. Universities have, through a distorted reward system, tended to encourage research over pedagogy. Whereas our Department has been in the vanguard of efforts to seek a proper balance, and those efforts have been recognized both within the University and the national mathematics community, we must be increasingly attentive to the job of telling the average citizen what it is we do and why. And I don't just mean telling them what we do in the classroom, but also what we do in our discovery and learning modes. The University can, I believe, gain the generous support of the public if it can properly convey its total mission and is able to communicate the fact that research not only has a positive effect on the undergraduate's experience while at the university, but also affects the respect which her degree commands throughout her working life. A Research I University is a learning institution where everybody, students and faculty alike, learns. The vitality of the educational experience for undergraduates is closely linked to the vitality that the faculty bring to their own discovery processes. I have seen this in action in my twenty-five years as a leader of Mathematics Departments. New ideas, such as computers in the classroom, up-to-date curriculum, are almost always the product of minds who have had or continue to have the experience of steady personal research programs.

Second, the administration of the University has responded to this pressure for more emphasis on teaching by gradually changing the reward system. Tenere and promotion decisions now take much more account of evidence of effective, classroom teaching. In many ways, this is a good thing. Unfortunately, however, the measures of what constitutes effective teaching have not been properly analyzed and very often the predominance of evidence is the student evaluations. And while certainly such feedback is an important component of the picture, it is not the whole picture. Therefore, it is important for departments such as ours to develop and implement a broader and more balanced set of criteria.

Third, the external sources of research monies, mostly the Federal Government, have less support to give out and that money they do give out is becoming more and more tagged for work that, in the minds of those that control the budget, is mission oriented or directly aimed at areas which have an immediate technological impact or which directly support work done in some government laboratory. As a result, there is increasing pressure on faculty to tailor their research programs to fit the government predictions of what areas will or will not be important ten years from now. I have no need to remind you that past predictions of governments have been lamentably off the mark. A more serious consequence is that sometimes the faculty members who are willing to accommodate a redirecting of their investigations are not those who are really the best people to control resources. In fact, instead of being in the long term interests of the nation, the investment of resources and, as a result, power in the hands of the less competent can actually impede and inhibit discovery.

On the other hand, the citizens of this country have the right to inquire as to whether the monies are being invested wisely and that the work they support will have a long term payoff in terms of technology advance and an increased quality of life. So departments and Universities have to face up to the fact that no longer can we get away with explanations of their activities that are based on the arrogance of the "we know what is best" point of view. We have the responsibility to explain to a broad audience what we are all about and why it is good for society in general that such precious (but vulnerable) institutions as Universities exist. To do this takes more than an absence of arrogance. It takes carefully considered, positive action and hard work and places even more demands on faculty time and effort.

But who will do it? This is the question that brings me to the central message of this farewell essay. Because of all these pressures, there will be an increasing temptation to compromise the quality of those hired in favor of the more willing but less talented. With the present buyer's market, it would be easy to find many who would be willing to spend more time in the classroom, who would be more willing to compromise standards and organize their classroom performance to keep the C student happy, more suitable for promoting ethnic diversity, more willing to become a contractor for industry or the federal government rather than a pioneering investigator in their own right. On paper, all these activities and/or attributes will lead to very respectable CV's. Promotion and Tenure will follow and, before too long, the leadership of a University which follows this wide road will be in the hands of the mediocre.

I believe strongly that the Universities who will survive as leaders in education and in research will have to go to great lengths to resist these temptations. I think we all know the enormous difference between the quality hire and the mediocre hire, no matter how accommodating or pliable the latter person is. But the task is not simply to hire the best person. It is also to persuade them that it is in all our best interests that they too recognize the realities of our time. It is the fact that we do have to do a better job in the preparation of undergraduates. In addition, we must provide them with experiences of discovery. It is the fact that we have to be willing to spend more personal time with them. It is the fact that departments and Universities need external money to survive as Research I Institutions and that the responsibility of raising funds to fulfill that mission belongs to the faculty. It will be harder to bring in these dollars which support graduate students, visitors and summer salaries without undue compromise but it can be done. The missions of "mission oriented research" are not tablets written in stone. We must help those who write them understand what the really important intellectual challenges are. We just have to face up to the task of taking a more active role in the setting of national priorities.

I believe that the response to this challenge will determine the relative standing of the research departments and Universities in ten years time. The best, MIT, Harvard, Chicago, Princeton, Stanford, Berkeley will stay there but there will be a reordering of standings among the State Universities. Those which can truly maintain high standards in the face of adversity will advance. Those which cannot will decline. It is my sincere hope that Arizona will belong to the former group and it is my belief that the Department of Mathematics has an important role to play in determining the outcome.

Alan

The View from Moscow

Bill Faris

This year I am a Fulbright Lecturer in Moscow. My affiliation is the Higher Mathematics College of the Independent University of Moscow. This is an elite college that was started a few years ago; the first graduates of the undergraduate program are finishing now. Many (but not all) of the students are also doing a full program (five years of math for a diploma) at the Mechanics-Mathematics Faculty of Moscow State University. During the spring semester I have been teaching a course on Martingale Ideas in Elementary Probability to second year students. The pattern is that we meet once a week in the late afternoon. After a lecture of about an hour and a half there is a two hour seminar, actually a problem session, where students work on problems with supervision from me and my assistants. I remember my surprise and pleasure when one of the students found an original and unexpected solution during the very first seminar. I should mention that all this takes place in a space borrowed from a high school; however there is supposed to be a new building downtown next year.

One of the active faculty members of the Independent University is Nikolas Konstantinov, and he has invited me to see some of what he has been doing in secondary education. His main effort is organizing competitions of various sorts. He sets them up so that they are not particularly stressful; in fact, he deliberately tries to make them fun. It is an amazing experience to see a couple of hundred young students giving up their Sunday afternoon to take exams in mathematics, physics, chemistry, biology, linguistics, history, game theory, and know that this is being repeated at various other locations around Moscow. It is even more impressive when I realize that this is without lunch.

This leads to something that I must mention: the economics of life in Russia. A mathematician without other sources of support may have to live on a hundred dollars a month, or less, in a city where the living costs exceed those of New York. External sources of research support, such as the Soros foundation, have been helpful to some of the top researchers, but even they are having to spend increasing amounts of time abroad to make enough money to live on. On the one hand there is a continuing erosion in the activity of one of the great mathematical centers of the world, and on the other hand there is still enthusiasm for mathematics and science from young people. What will prevail? The one sure rule about life in Russia is that no one knows what the future will bring. I am fortunate to be here now and to have such generous hosts. These are talented and energetic people; with luck their efforts will contribute to the continuation and renewal of the mathematics tradition here.

James Ray Clay, 1938 - 1996

Fred Stevenson

James Ray Clay was born on 5 November 1938 in Burley, Idaho. He grew up in the tiny town of Albion, Idaho and attended Albion Training School until the school closed in 1951. His family then moved to Burley so that Jim and his older sister could attend schools there. Jim graduated with the first class at the new Burley High School in 1956 and he received an appointment to the Naval Academy in Annapolis, Maryland. While taking flight training in Pensacola, Florida in the summer of 1958 he met Carol Burge. They were married in 1959 and Jim finished up his undergraduate mathematics studies at the University of Utah. He received his B.S. there in 1960 and was accepted in graduate school at the University of Washington. While teaching and working as a computer programmer for Boeing, he received his Master's degree from the University in 1962, and his Ph.D. in 1966 under the direction of Ross Beaumont.

Jim came to the University of Arizona as an Assistant Professor of Mathematics in 1966. He was promoted to Associate Professor in 1969 and became a Full Professor in 1974. He served as Associate Head of the Department from 1969-72 and was Acting Head in 1970. Jim's research interests were in algebra and geometry; in particular, the field of nearrings. He wrote 47 published research papers and two books. His 1977 book "Trigonometry - A Motivated Approach" had the definite flavor of what now is called "reform" mathematics. His book "Nearrings: Geneses and Applications", published by Oxford University Press in 1992, was a synthesis of work done in nearrings. He was a pioneer in this field in the 1960's and he saw it grow from an exciting new area to a well developed body of theory with a remarkable variety of applications to other areas of mathematics. He supervised seven Ph.D students: John Krimmel, John Suvac, Gary Grainger, Matthew Modisett, Wen-Fong Ke, Steve Olson, and Hsin-min Sun. Another, Mariamma Varghese, has a dissertation in progress.

Jim's research was especially attractive to mathematicians in Europe. This was fortunate because he loved to travel. In 1972, at the age of 34, Jim was the youngest person to receive the Distinguished Senior U.S. Scientist Award from the West German government. In the decades of the '70s, '80s, and '90s Jim lectured widely and often throughout Europe and beyond. He held Guest Professorships at numerous universities including those in Tübingen, Munich, and Hamburg, Germany; London, England; Edinburgh, Scotland; Stellenbosch, RSA; and Linz, Austria. Recently he expanded his travels to the Orient. Jim was a Guest Professor at National Cheng Kung University in Taiwan and lectured at universities in Hong Kong, Bangkok, and Singapore.

Although his accomplishments were formidable, Jim was true to his humble roots. He was a man without pretense. He would rather give credit than take credit. His pride was reserved for his family, not for himself. His immediate family includes his wife, Carol, their three daughters, and ten grandchildren.

Jim Clay died unexpectedly of heart failure on 16 January 1996.

Mathematics at the U of A

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The University of Arizona
Department of Mathematics
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