The Seventy-Fifth Annual Meeting of the Illinois Section of the MAA was held March 1 and 2, 1996, on the campus of Illinois Wesleyan University in Bloomington, Illinois.
The 1997 ISMAA Annual Meeting will be held March 21 and 22, 1997, at Rockford College in Rockford, Illinois.
The 1996 meeting included invited addresses by Robert Osserman, John Ewing, John Conway, and Allen Schwenk, a minicourse, several panel discussions, publishers exhibits, and activities for students.
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March 13, 1996
All meeting sessions were held in Illinois Wesleyan's new Center for Natural Science and Research.
The past 75 years have changed the kinds of mathematics we work on - but not the way we work or the problems we face in our professional lives. Prof. Ewing gave a survey life and mathematics for the past 75 years.
This session provided a hands-on introduction to the TI92 graphing calculator.
This panel, discussed assessment of undergraduate programs in mathematics.
A description and historical synopsis of one of the outstanding problems in infinite dimensional linear algebra was given.
Jane Swafford of Illinois State University was elected Chair-Elect. Claire Krukenberg of Eastern Illinois University was elected Director for Public Universities. Nigel Boston of the University of Illinois at Urbana-Champaign, James Olsen of Western Illinois University, and Richard Wilders of North Central College were elected Directors at Large.
Howard Saar announced that the Board intended to propose changes to the Section's Bylaws at the 1997 Annual Meeting. The most significant of the proposed changes are an increase in the terms of office for the Chair and Past-Chair from 1 to 2 years, an increase in the term of office for the Secretary-Treasurer from 3 to 6 years, and the elimination of the Contest and Awards Committee and the Membership and Public Relations Committee. A preliminary copy of the proposed changes was distributed. Anyone with questions or comments with respect to the proposed changes should contact one of the officers or a member of the Board of Directors.
The Distinguished Service Award was presented to Al Otto of Illinois State Univeristy.
Allen Schwenk of Western Michigan University gave an after dinner talk titled A Plethora of Perplexingly Persistent Simpson Paradoxes. Professor Schwenk showed how he had designed hypothetical data that yielded remarkable inconsistencies when grouped different ways. The example illustrated the danger of relying totally on statistical evidence. He also presented some real life examples which were almost as remarkable as the hypothetical data.
Hyperbolic manifolds have been studied intensively in recent years, revealing a surprising variety of examples. One of these exotic examples may describe the shape of our universe. Professor Osserman's talk provided the background needed to understand the standard cosmological models for the shape of the universe and explained the possible role of hyperbolic geometry.
This panel described and evaluated their experiences with various reform calculus projects.
This panel of recent graduates described the role of mathematics in their positions and discussed ways to enhance undergraduate preparations in mathematics for careers.
This was an introductory talk about wavelet analysis with topics including a brief history, the main results, and current trends.
This presentation described sample activities from a reform project in college algebra which involves groups and collaborative learning through active laboratories and worksheets.
Several interactive CD-ROM projects were demonstrated using real-life context and problems.
A. D. Alexandrov's Soviet school of geometry and western differential geometry developed separately during the period of the "Cold War". Recently they have interacted to produce exciting new points of view. The basics of Alexandrov's approach were explained and current applications described.
The Hungarian mathematician Ernö Rubik made himself a household name in the early eighties with his Magic Cube. The Cube attracted attention from all corners of the world, and he followed up with Revenge and other less known puzzles. A solution to one of these less known puzzles, Triamid, was presented. Triamid is a 3-sided pyramid made up 10 small 4-sided play pieces. The player is to break it into two segments -- a triangular base of 6 pieces and a smaller pyramid of 4 pieces -- and put them back together to reconstruct the Triamid. Each face is colored with four colors and the object, obviously, is to align a single color on one face.
Given n randomly placed points in the plane, how can these points be connected by a network of minimum length? Using graph theory, the answer lies in the formation of a minimum spanning tree. If additional points can be added to the tree, then the minimum spanning tree can often be shortened even further, resulting in what is known as a Steiner minimal tree (SMT). Unfortunately, there exists no simple algorithm for finding SMTs. Chung, Gardner, and Graham partially examined this problem by attempting to buld SMTs over regular lattices in "Steiner Trees on a Checkerboard" (Mathematics Magazine, V. 62, #2). Using their paper, Ms. Voelker examined some of their results and generalized their ideas to rhombuses.
The study of the History of Mathematics can help make classroom mathematics come alive with vivid stories, people, and events. Mathematics can be seen as part of the daily lives of real people in real situations. Unfortunately, many History of Mathematics courses and texts treat it as simply a study in different types of math - the counting of the Egyptians or Babylonians, for example. Mr. Heidenreich created a supplement to those sources which places the mathematics in a social, political, and philospical context by using various maps, charts, and visual aids. The point of this project was to try and "reconnect" historical mathematics with the history in which it occurred.
Computational complexity is the (relatively new) study of the "toughness" of certain mathematical problems, measured in terms of the time and space required to compute their solutions. The speaker discussed the geography of a few important "complexity classes" of problems, as well as the notion of completeness in a class.
A Minicourse, Interdisciplinary Lively Application Projects, was presented from 9:00 - 11:30 Friday morning by LTC Rich West of the United States Military Academy at West Point. The course discussed how interdisciplinary applications can be used to weld mathematics with other disciplines. This workshop related how these projects can be used to enhance learning in undergraduate mathematics. Examples of completed projects were presented.