Illinois Section of the MAA

Abstracts of Talks at the 2001 ISMAA Annual Meeting

Algebras That Go Up and Down

Georgia Benkart, University of Wisconsin
12:30p.m. Friday March 23, 2001, Levis 3rd floor

A partially ordered set has its ups and downs. That is, on any set with a partial order there is an up operator and a down operator. Sometimes these operators behave so nicely that they act like the operators in the Heisenberg uncertainty principle. You can be certain that during this talk will be one of those times.

Performance-Based Assessments: Implications for Content Courses

Panelists: Susan Beal, IMTE chair, St. Xavier; Susan Beal, IMTE chair, St. Xavier Carol Castellon, IMTE secretary, UIUC; Art Baroody, UIUC; Claran Einfeldt, ISBE rep; Melfried Olson, WIU; Al Otto, ISU
Moderator: Don Porzio, Illinois Mathematics and Science Academy
2:00p.m. Friday March 23, 2001, Levis 3rd floor

Many changes in teacher education have been enacted at the state and national level. This panel starts an important dialog between teacher educators and those teaching the content courses. The focus will be on how to include performance-based assessments in content courses taken by pre-service teachers.

The group running the discussion will be IMTE, which is the newly formed Illinois Mathematics Teacher Educators.

Expository Lecture for Undergraduates

Patricia Kiihne, Illinois College
2:00p.m. Friday March 23, 2001, Levis 402,403,404

Professor Kiihne from Illinois College will discuss factorization of various polynomials over different rings in a lecture designed to be accessible to undergraduate mathematics majors.

Two Complexes on the 4-ball

Tony Bedenikovic, Bradley University
2:00p.m. Friday March 23, 2001, Levis 407

We will look at a type of 3-complex known as a graph complement cone complex (i.e., a gccc). A gccc consists of known complement in a cube with handles together with the cone over the boundary of the cube with handles. We will show that every 2-complex 3-deforms to a gccc and list some consequences of this fact.

Performance-Based Assessments: Implications for Content Courses

James Olsen, Western Illinois University
3:15p.m. Friday March 23, 2001, Levis 3rd floor

This session continues the discussion begun in Session A. James Olsen of Western Illinois University will be moderator

The Art of Technical Illustration

George Morris and Brian Morris, Scientific Illustrators
2:00p.m. Friday March 23, 2001, Levis 402,403,404

How is it that the artwork for a new calculus book now costs over $150,000? Meet George and Brian Morris of Scientific Illustrators and find out. They have supplied textbook publishers with technical illustrations for over three decades.

Localization of Periodically Forced Waves

Catherine Crawford, Elmhurst, College
3:15p.m. Friday March 23, 2001, Levis 407

Many systems driven far from equilibrium undergo instabilities leading to the formation of patterns in which a periodic or ordered structure emerges.

Calculus Books

Underwood Dudley, DePauw University
Friday March 23, 2001, Altgeld 215

Calculus books are important. This talk will survey their contents from 1696 to the present, say what should and should not be in them, and draw seven important conclusions. (They will be written on transparencies so they cannot be missed, and the last is, "That's enough about calculus books.")

Assessment is not a Four Letter Word

Herb Lyon, Black Hawk College
8:30a.m., Saturday march 24, 2001, Levis 3rd floor

Exactly what are your students learning? Is this what you expect them to learn? Can you demonstrate objectively the success of your courses or program? Are you feeling pressures from your Dean to define and measure student learning outcomes? Does your institution have a North Central visit coming up? Are your students more or less successful than they were five years ago? How and why have you changed your curriculum in the past decade? Have the changes been successful? How do you know? Is your institution increasingly adopting a corporate model? Does assessment of student learning outcomes threaten your academic freedom and your independence in the classroom? Is this just another passing fad? Can you honestly say that you understand what assessment is all about? Does anyone?

The program is designed to assist academic mathematicians in coming to grips with assessment. The presentation will be followed by a panel who have had recent hands-on experience with accreditation visits and with successful programs of assessing student academic achievement.

The slides for Herb's talk are available in HTML, PDF, and Powerpoint formats at

Herb Lyon teaches regular and online mathematics courses at Black Hawk College. A North Central consultant/evaluator for over a decade, he has also served as a team chair. He is currently a member of the North Central Accreditation Review Council and he has been trained as an examiner for Illinois' Lincoln Quality Awards. His Ph.D. from the University of Michigan is in knot theory, he has worked as a faculty member and administrator in several states and countries, and he is past chair of the Illinois Community College Presidents Council.

Grant Writing Workshop

Marj Enneking, Portland State Univesrity
9:45a.m. Saturday, March 24, 2001, Levis 402,403,404
10:50a.m. Saturday, March 24, 2001, Levis 402,403,404
1:30p.m. Saturday, March 24, 2001

The Mathematical Association of America received a grant to run Grant Writing Workshops at section meetings. We are privileged to have Marj Enneking from Portland State to run our workshop this spring. Marj is a former program officer at the national Science Foundation. The workshop will show how to write successful grant proposals in mathematics.

The workshop will be held Saturday morning and afternoon in two workshop sessions. Each session will be about two hours long. To cover the cost of copying the materials given to participants, there is a $15.00 fee to participate. However, those participating in the NeXT program do not have to pay this fee. Pre-registration for this session is required

Cwatsets as codes

Jody Radowicz, North Central College
9:45a.m. Saturday, March 24, 2001, Levis 407

A cwatset is a subset of binary n-space that is closed (c) with (w) a (a) twist (t). Each coset is a permutation of the elements of the subset. This presentation discusses results obtained by considering cwatsets as linear codes.

Rational Points on Elliptic Curves

Rachel Floit, Augustana College
10:05a.m. Saturday, March 24, 2001, Levis 407

Non-trivial examples of rational points on elliptic curves will be found. It will be shown how group operations work on these points. Mathematica is used to carry out some of the more cumbersome operations.

Pieces of the Koch Curve Similar to the Whole

Kevin Murphy, Augustana College
10:25a.m. Saturday, March 24, 2001, Levis 407

The Koch curve is a well-known fractal. Its pieces will be counted and exhibited. A related counting problem will also be considered.

An Insider's Look at the Society of Actuaries' Education and Examination System

James Miles, Deliotte & Touche LLP
10:50a.m. Saturday March 24, 2001, Levis 3rd floor

Several major changes were made in the Society of Actuaries' E & E system beginning in 2000. This session will cover the current structure, the history behind the changes and current issues. No presentation related to actuarial examinations would be complete without coverage of the Casualty Actuarial Society's E & E structure and this session is no exception. A discussion of the role of colleges and universities in the education of future actuaries will be included due to popular demand. The speaker is current SoA Education Chairperson and the SoA liaison to the CAS Syllabus Committee.

Special Relativity with Acceleration

Andrew Roinestad, Augustana College
10:50a.m. Saturday, March 24, 2001, Levis 407

The article "Special Relativity with Acceleration" appeared in the American Mathematical Monthly in March 2000. Some of the effects of special relativity will be considered, using a variety of examples.

An Infinite Classs of Genealogy Graphs

Susan Struck, Augustana College
11:10a.m. Saturday, March 24, 2001, Levis 407

Genealogy graphs are graphs with males and females as vertices and edges to indicate marriage and parent-child relationships. Each couple is restriced to exactly one son and one daughter. Starting with 2 to the n couples, there is a graph such that after n+1 generations all the descendants are equally related to all of those at the start. A lower bound for the number of non-isomorphic such graphs will be found.

Weird Properties of the Rational and Irrational Numbers

Kathleen Reif, Augustana College
11:30a.m. Saturday, March 24, 2001, Levis 407

Considering the real number line, every rational lies between two irrationals and every irrational between two rationals. So are we equally likely to land on a rational as an irrational? Measure theory will be used to compare the size of the rationals to the irrationals, providing an unexpected answer to this question.

The Front End of Mathematica

Theodore Gray, Wolfram Research, Inc.
12:00 Noon Saturday, March 24, 2001, Levis 3rd floor

Theodore Gray has been an architect of the front end of Mathematica for many years, and authored The Beginner's Guide to Mathematica with Jerry Glynn. He will tell us some of the stories behind Mathematica.

March 22, 2001