Illinois Section of the MAA

Abstracts of Talks at the 1998 ISMAA Annual Meeting

National Testing of Mathematics: What Are These Tests and What Do They Tell Us?

John Dossey, Illinois State University
1:20p.m. Friday March 27, 1998, Pearsons Hall

An examination of the Voluntary National Test of Mathematics for 8th graders, the National Assessment of Educational Progress, the Third International Mathematics and Science Study, and others. What are their purposes, what do they tell us about the mathematical proficiency of our students K-12 and the interface to undergraduate study?

President Clinton has proposed a national 8th grade mathematics test. It is currently on a fast track for implementation and the participation of the mathematics community is being solicited. The test has the potential to have a profound effect of how mathematics is taught in this country. John Dossey, who is the current Chair of CBMS and who chairs the Content Committee for the 8th Grade Test, has been asked by President Clinton to head up the team designing the test. In his presentation, Professor Dossey will discuss the Voluntary National Test of Mathematics for 8th graders, the National Assessment of Educational Progress, the Third International Mathematics and Science Study, and other issues.

Innovations in Undergraduate Teaching: Innovative Approaches to Teaching Entry-Level College Mathematic

Mary Marshall, Illinois College; Lanette Poteete-Young, Judson College; Sharon Robbert, Trinity Christian College
3:00p.m. Friday March 27, 1998, Voigt Science Hall, Room 122

Panelists will discuss innovative approaches and techniques which they have used in teaching college algebra, precalculus, and calculus courses.

Issues in Undergraduate Education: Articulating Applied Mathematics into a Community or Four-Year College Mathematics Curriculum

Anita Pyle, Bushnell Prairie High School; Lynae Sakshaug, Western Illinois University; Vern Kays, Richland Community College
3:00p.m. Friday March 27, 1998, Voigt Science Hall, Room 123

The national Tech Prep Initiative has been an effort to provide the middle 50% of high school students with academic and vocational skills to prepare them to enter the workforce and post secondary education. This effort has emphasized applied academics, integration of vocational and academic learning, and work-based learning for students. Since most of the careers in the future require a high level of technical skill based upon mathematics, more students are studying more mathematics, but learning using different instructional models. The 1994 School to Work Act has expanded this initiative to all learners. Partnerships have been formed to address the issue. Public schools and community colleges are currently working to respond to the School to Work initiative, which has been labeled Education to Careers in Illinois. If high school teachers are to be teaching applied math, our colleges and universities need to be providing them the skills to do this as pre-service teachers. How are we doing this? How do we articulate from community college applied science degree programs into four-year bachelor degree programs? This panel, moderated by Rita Fischback of Illinois Central College, will address these and related questions.

Trends in Mathematics: Trends in the Theory of Impulsive Differential Equations

Zahia Drici, Illinois Wesleyan University
3:00p.m. Friday March 27, 1998, Voigt Science Hall, Room 129

Many real world phenomena experience an abrupt change of state and behave in a discontinuous fashion. These evolution processes may encounter short term perturbations whose durations are negligible in comparison to the duration of the process. Hence, it is natural to assume that the perturbations act instantaneously, that is, in the form of impulses. An adequate apparatus for the mathematical modeling of such phenomena is the impulsive differential equation. The talk will survey the trends that have emerged in the theory of impulsive differential equations and will reflect results in differential inequalities, monotone iterative techniques, stability or solutions, quenching phenomena, and oscillation. Some open problems will be formulated.

The Scottish Book

Daniel Mauldin, University of North Texas
ISMAA Annual Banquet, Friday March 27, 1998, Pearsons Hall

Around 1933 or 1934, Banack brought a large notebook into the Scottish Cafe in Lwow, Poland where many now famous mathematicians regularly congregated. The mathematicians would record proposed problems and results of their cafe discussions in the book. Some promised prizes for certain problems. The book became famous and well known as the Scottish Book. It was kept by a waiter in a secret cache. It has had a fascinating history intertwined with some of this century's greatest names in mathematics. The Scottish Book survived German and Russian occupation, possibly buried during a portion of the war by Mazur. Rumor has it that Banack's son introduced it back to the public after the war. Professor Mauldin will discus some of the problems and the mathematicians involved in formulating this famous book.

The Heart Of Mathematics Is Its Problems

David R. Stone, Georgia Southern University
8:30a.m., Saturday March 28, 1998, Pearsons Hall

This title is a quote from Paul Halmos. Much of mathematics arises in response to problems which require solving, whereas mathematicians are often attracted by interesting problems. While the primary concerns of the mathematics community might be research, applications and education, its true life force is problems.

Innovations in Undergraduate Teaching: Computer Lab On Wheels

James Olsen, Western Illinois University
9:45a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 129

This will be a description of Western Illinois University's Computer Lab On Wheels (CLOW), which is twenty-four notebook computers housed in a rolling cabinet. It can be wheeled to any classroom where students use the computers at their regular classroom desks. Discussed will be the rationale and philosophy of a mobile lab, wireless communication to the LAN and WWW, and planning issues if considering a CLOW.

Issues in Undergraduate Education: What Ever Happened to College Algebra?

Russel Blyth, St. Louis University; Mike Schneider, Belleville Area College; Pat Herrington, O'Fallon High School
9:45a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 122

Ever wonder what happened to basic high school algebra topics such as the rational root theorem, synthetic division, matrices, determinants, naive set theory, etc. This panel, moderated by Doug Jones of McKendree College, will discuss the demise of these and other topics in high school algebra.

Trends in Mathematics: Combinatorial Design Theory

Walter D. Wallis, Southern Illinois University
9:45a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 123

This talk will briefly sketch the origins of combinatorial design theory in statistics, geometry and mathematical recreations, and indicate some recent trends in the theory (including computer use) and applications (experimental design, cryptography, computers).

Visualizing Functions in College Precalculus Through Technology

Innovations in Undergraduate Teaching: Matrices, Geometry and Mathematica, a totally new matrix theory course

Jerry Uhl and Ben Halperin, University of Illinois at Urbana-Champaign
10:50a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 123

This talk will survey a new matrix theory course to be taught using Mathematica courseware using a visual approach through computer graphics. This course was written at the University of Illinois, Ohio State University and Davidson College with partial support from the National Science Foundation.

Issues in Undergraduate Education: What is Involved in Receiving Tenure in Today's Colleges and Universities?

Lyle Welch, Monmouth College; Nigel Boston, University of Illinois at Urbana-Champaign; Tom Wangler, Benedictine University; Bill Blair, Northern Illinois University
10:50a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 122

A panel of mathematicians, moderated by Herb Kasube of Bradley University, will share their experiences and advice regarding the hurdles one must conquer in order to receive tenure in today's universities.

Trends in Mathematics: The Diffraction Equation, Laser Beams, and the 2D Crystals of M. C. Escher

David W. Kammler, Southern Illinois University
10:50a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 129

After producing a variety of 2D diffraction patterns with a laser and 35 MM slides, we use Huygens' principle to derive the PDE that models the phenomenon. We use the FFT to produce movies that help us understand the formal solutions and allow us to see the effects of dispersion. Solutions of the diffraction equation preserve symmetries present in the initial conditions, and we use this fact to identify the diffraction patterns that correspond to a few 2D crystals in the art of M.C. Escher.

Modelling the Spread of HIV

Christine Leroux and Brigid Lusk, Northern Illinois University
10:50a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 220

In recent years, several mathematical models of the immune response to HIV infection have been developed. As more information is gathered about how HIV interacts with the immune system, there have been newer and more refined models developed. Based on Perleson's work, a new model is developed that takes into account the use of protease inhibitors and combination drug therapy to combat the infection. Changes in the populations of actively infected, latently infected and uninfected CD4+T-Cells are considered as well as changes in the population of HIV and other long-living cells that have become infected. (Supported by Argonne National Laboratory.)

The Calculus of Measure Chains

Anders Floor, Illinois Wesleyan University
11:10a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 220

A new calculus will be explicated. Developed by Bernd Aulbach and Stefan Hilger, this calculus is based on measure chains, which are time scales (subsets of the real line) with certain basic restrictions. This calculus provides a unified approach which encompasses both discrete and continuous cases, as well as all cases possessing some combination of continuous and discrete intervals. Some fundamental theoretical results will be given, including an induction principle for measure chains.

The Search for Oil: Using Finite Difference Equations for Approximating Curvature and Stress in the Earth's Crust

Dan Meyer, Northern Illinois University
11:30a.m., Saturday, March 28, 1998, Voigt Science Hall, Room 220

Several possible routes will be considered in solving the problem of using difference equations in order to approximate the curvature and stress in the earth's crust. Ways to implement these steps into a computer program written in C++ code will be discussed.

Competing with Plato, Bach, and Shakespeare

Michael Starbird, The University of Texas at Austin
12:00 noon, Pearsons Hall

Students study the best paintings, the most glorious music, the most influential philosophy, and the greatest literature of all time. Mathematics can compete on that elevated field, but we must offer all students our grandest and most provocative ideas. Infinity, fractals, and the fourth dimension; topology, cryptography, and duality-these ideas can complete well with any other subject for depth and fascination. And having students discover mathematics for themselves can empower them in all walks of life.

March 24, 1998