Abstracts for Papers and Sessions at ISMAA 2005

Panel Discussion

Participants: Bill Blair (Northern Illinois University), Lisa Townsley (Benedictine University), and Roberta Christie (Shawnee Community College)
Title: What's the Interview Process Really Like? An Informational Panel for Graduate Students
Length: 60 minutes

In this panel representatives from various types of institutions of higher education (Ph.D. granting institution, 4-year college, community college) will describe the hiring and interviewing processes at their schools and take questions. This presentation is aimed at graduate students but is open to all.

Film Showing

Title: Challenge in the Classroom
Length: 60 minutes

This sixty minute video, originally produced by the MAA in 1967, shows the "Moore method" of discovery-based learning in action. Portions of the video will be used during the workshop on discovery-based learning. During this session, the entire video will be shown in its entirety.

Presented Papers

Alphabetical by Primary Author

Name: Fedor Andreev
Affiliation: Western Illinois University
Title: Visualizing Mobius transformations and plane tilings
Length: 30 minutes
Abstract: Applets developed by the author are used to demonstrate Mobius transformations (including simple shifts and rotations). The applet also incorporates simple graphical editor that is used to create basic shapes like circles, arcs, triangles, rectangles, and polygons. Mobius transformations then can be applied to the shapes. Applet also features loading a picture (or a photo) and transforming it in various ways. The early prototypes of the applet can be found at the author's web page: http://www.wiu.edu/users/fa101/, but the presentation will feature a new and tremendously improved applet (which is currently submitted to JOMA published by MAA). Most of the material required to understand the presentation is very elementary (even though some more advanced things like Fuchsian and Schottky groups will be mentioned), so everybody interested in using the applets in the classrooms is welcome!

Name: Tony Bedenikovic
Affiliation: Bradley University
Title: Two-complexes with Nontrivial Self-Covers
Length: 30 minutes
Abstract: Nice two-complexes with nontrivial finite-sheeted self-covers are characterized by having decompositions into annuli. I will describe this characterizing property and prove an interesting consequence: Any two-complex with this characterization is necessarily aspherical.

Name: Paul Bialek
Affiliation: Trinity College
Title: Bald answers, table-scrapping and inoculation: Grading the AP Calculus exam
Length: 30 minutes
Abstract: Each year, high school and college mathematics teachers from across the country gather to grade the Advanced Placement Calculus exam. In this talk, we will discuss how the exam is written, how 600 people can grade by hand 6 questions on 200,000 exams with remarkable consistency, and how one can be hired as a grader.

Name: Leonard Blackburn
Affiliation: Parkland College
Title: Math Contests: Friendly Problem Solving for Everyone
Length: 30 minutes
Abstract: We will take a brief tour of the various math competitions available to undergraduates (and younger), including the William Lowell Putnam Mathematical Competition and the Mathematical Olympiads. We will present some of the more interesting (i.e. frustrating) problems and their elegant solutions.

Name: Jean Bee Chan
Affiliation: Sonoma State University
Title: How Should We View an Art Gallery?
Length: 60 minutes
Abstract: How many paintings can we view from any one point in an art gallery? We will first give a brief history and proof of the Art Gallery Theorem for polygonal galleries. Next, what about galleries in the shape of arbitrary closed and connected sets in the plane? Finally, we will view art via arcwise convex arcs in simply connected and compact galleries. The talk will conclude with some open problems in this area.

Name: John Chisholm
Affiliation: Western Illinois University
Title: Dividing the Goods
Length: 30 minutes
Abstract: When Mom gets tired of the twins fighting over the last piece of cake, she can tell them to work out a fair division themselves, using the time-honored method of having one twin cut the cake and letting the other twin have first choice among the two pieces. This method will guarantee a fair share to each twin, even when they disagree about the desirability of different parts of the cake. But if the cake needs to be divided among three children, how can they proceed among themselves to guarantee a fair share for each child? Not until the twentieth century did mathematicians successfully to devise "fair division" methods for more than two people, and active research in this field continues to make new discoveries. This talk will present an overview of the mathematics of fair division, including discussion of such questions as: What should we mean to say a division is "fair"? Are there different possible meanings? How can three people divide a cake among themselves so that their shares are "proportional"? Or "envy-free"? Can we PROVE that these methods are guaranteed always to work? Can these methods be used for more than three people? What happens if we want to divide an inheritance consisting of several pieces of furniture? (We don't want to be cutting any furniture into pieces!) We will conclude with a recently discovered "envy-free" method for this situation.

Name: Timothy Comar
Affiliation: Benedictine University
Title: A Calculus Sequence for Biology Students
Length: 30 minutes
Abstract: In an effort to better prepare biology and pre-medical students for the increasing level of mathematical background needed for their future coursework, the Department of Mathematics at Benedictine University has begun to offer a two-semester calculus sequence for this audience. Although these this new course sequence is offered at the same level of mathematical rigor as the traditional sequence for students majoring in mathematics, physics, and engineering, the content is specifically geared to meet the needs of the biology and pre-med students. In this talk, we discuss the developing collaboration between the mathematics and biology departments to continually update this course sequence, differences in between our course outline and the standard calculus syllabus, issues related to instituting such a sequence in a small university, and opportunities for students to participate in the development of future materials for this course sequence.

Name: Mehmet Dik
Affiliation: Rockford College
Title: On Tauberian Conditions of Slowly Oscillating Type
Length: 30 minutes
Abstract: Let (u_n) be a sequence of real numbers and L be an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of (u_n) belonging to some class of sequences is a Tauberian condition for L, then convergence or subsequentially convergence of (u_n) out of L is recovered depending on the conditions on the classical control modulo of the oscillatory behavior of different order.

Name: Underwood Dudley
Affiliation: Florida State University
Title: Formulas for primes
Length: 60 minutes
Abstract: Formulas are fascinating and so are primes, so formulas for primes should be doubly fascinating. This talk surveys the field and ends with a moral conclusion. Exactly one theorem will be proved.

Name: Underwood Dudley
Affiliation: Florida State University
Title: Why Teach Mathematics? (Sponsored by Project NExT)
Length: 60 minutes
Abstract: Why do we make all students study mathematics? I will give six reasons, five of them wrong, and end with the correct one. Not everyone agrees with me on its correctness.

Name: Howard Dwyer
Affiliation: Monmouth College
Title: How Could Anyone Discover the Laplace Transform?
Length: 30 minutes
Abstract: Many students accept the Laplace transform as a gift from the Gods, but the better students will wonder how could anyone possibly have discovered/developed it. Rather than simply pulling this magic rabbit from a hat, I have developed a presentation for ODE students which offers a plausible (hopefully) progression of thoughts which leads us to the Laplace transform. I do not claim that this is actually how it was developed--historical accuracy is not the goal. Rather, I hope to show students how mathematics builds on familiar concepts to construct new techniques.

Name: Roger Eggleton
Affiliation: Illinois State University
Title: Equal Sums of Squares
Length: 30 minutes (Saturday)
Abstract: The following pairs of multisets have equal sums of squares: X={3,4}, Y={5}; X={1,2,2}, Y={3}; X={5,5}, Y={1,7}; X={4,7}, Y={1,8}. How can we find such multisets? A "magic matrix" which produces new solutions from known solutions will be noted. The general solution in integers will be discussed.

Name: Jeff Hildebrand
Affiliation: Knox College
Title: Fairness in scheduling: Using a Monte Carlo model to simulate a baseball season
Length: 30 minutes
Abstract: Can the schedule used by a sports league influence who wins titles? An overview of the question is presented using major league baseball as an example, and a Monte Carlo model is used to offer one approach for a solution.

Name: Steve Hinthorne
Affiliation: Principia College
Title: Insights into Teaching Future Elementary Teachers: What I've Learned from Pre-Service Math Content Courses
Length: 30 minutes
Abstract: Over the past 4 years, I've written a manuscript and taught courses on "Foundations of Number" and "Geometry for Elementary Teachers." These courses and texts were designed at the request of and in fulfillment of the requirements of our Education major for mathematics content prior to the math methods courses -- usually taught in the Junior year. During this time, I've learned what content and pedagogy work for these important future educators. The realizations about why numbers work the way they do encourages me to stay the course with my course content and materials. This talk will present some of these ideas for discussion, comment, and criticism.

Name: Dan Hrozencik
Affiliation: Chicago State University
Title: Finding Median Sets of Tree Structures in Synchronous Distributed Systems
Length: 30 minutes
Abstract: Finding the central sets, such as the median sets, of a network topology is a fundamental step in the design and analysis of general distributed systems. This talk presents an alternative synchronous distributed algorithm for finding the median set in general tree structures, based on a revision of a simple sequential algorithm. When this algorithm terminates, every vertex in the tree structure knows the median set of the whole structure, and not just whether or not itself is a median vertex.

Name: Dan Kalman
Affiliation: American University
Title: The Fibonacci Numbers -- Exposed
Length: 60 minutes
Abstract: Everyone knows about the Fibonacci Numbers. With all of its amazing and fascinating attributes, it is a sort of super-sequence. But what if, like superman, it is really just a rather pedestrian speciman of an entire super-race? Perhaps it acquires all of its powers from the planet of its birth, and in that setting would be neither amazing nor unusual. In this case, the home world is the planet of two-term recurrences, where Fibonacci is just an ordinary Joe.

Name: Manmohan Kaur
Affiliation: Benedictine University
Title: Some Uses of WebCT in Calculus
Length: 30 minutes
Abstract: This talk will discuss some of the ways in which we've made use of WebCT in our introductory calculus classes at Benedictine University, from creating and administering electronic quizzes to placement exams.

Name: Patricia Kiihne
Affiliation: Illinois College
Title: Mathematics and the Maya
Length: 30 minutes
Abstract: In this talk I will report the National Science Foundation Chautauqua #28 "Ancient Maya Mathematics in the Ruins of the Yucatan Peninsula, Mexico." I examine some of the mathematical ideas of the ancient Maya, including their use of zero as a placeholder and their intricate calendar system. I will also look at the Maya use of mathematics in their architecture, both in their building placement to coincide with astronomical events and their use of proportion stemming from their creation myths and still in use today.

Name: Andrew Leahy
Affiliation: Knox College
Title: James Gregory's Proof of the Fundamental Theorem of Calculus
Length: 30 minutes
Abstract: Everybody knows that Newton and Leibniz invented calculus. In particular, they were the first mathematicians to prove the fundamental theorem of calculus, right? It turns out that the first published proof of the FTC can be found buried in a geometry text by the 17th Century Scottish mathematician James Gregory. We will present his proof in all of its Euclidean glory.

Name:Douglas Lewit
Affiliation: Northeastern Illinois University
Title:Using Maple to Simulate the Negative Binomial Distribution with Applications to Modeling the Spread of HIV
Length: 30 minutes
Abstract: The negative binomial distribution presents a special challenge to the programmer because the programmer does not know ahead of time how large the array or list has to be for the storage of failures and successes. I will use Maple's built-in programming language and random number generator to show how it is possible to simulate the negative binomial distribution. The simulated distribution will then be compared to the theoretical distribution. Finally, the negative binomial distribution has applications to communicable diseases, where the probability of 'success' is understood to be the probability of infection. I will use HIV as a relevant example of this.

Name: Dawn Wagner Lindquist
Affiliation: University of St. Francis
Title: Introducing Math Majors to Journal Article Reading
Length: 30 minutes
Abstract: As instructors of undergraduate math majors, our mission in many courses is to cover the basic theorems, proofs, methods, and classic problems in a particular area of mathematics. Pressed for time, focused on our particular interests, and utilizing textbooks already packed with problems, we run the risk of failing to expose our students to the rich world of mathematics journals. I will present examples of assignments designed to familiarize majors with the existence of mathematics journals and strategies to assist them in learning how to read articles.

Name: David Lukens
Affiliation: Shimer College
Title: From Euclid to Godel by way of Lobachevsky
Length: 30 minutes
Abstract: I describe a course that every Shimer students must take, in which we examine whether Euclid's parallel postulate is a postulate or a theorem. The presentation will include an exercise on what postulates are and how their independence can be tested and how this test leads to Godel's work. We will also look closely at Lobachevsky's postulate that replaces Euclid's.

Name: Vince Matsko
Affiliation: Quincy University
Title: A High School Course on Polyhedra
Length: 30 minutes
Abstract: Quincy University and Quincy High School (Quincy, IL) are involved in an innovative collaboration. A trigonometry-based course on the theory and construction of polyhedra and geodesic domes is being offered to seniors who have taken calculus during their junior year. Hands-on constructions are a significant part of the course. Genesis of the course, course content, and instructional materials will be discussed.

Name: Ollie Nanyes
Affiliation: Bradley University
Title: Limits of Functions of Two Variables
Length: 30 minutes
Abstract: We give an example of a two variable function f that has the following property: f is continuous everywhere except for the origin and f has a limit when evaluated over the graph of any real analytic function that runs through the origin. This shows that analytic paths are inadequate to detect discontinuities of a two variable function.

Name: Todd Oberg
Affiliation: Illinois College
Title: The Impact of KTEM on Preservice Elementary Teachers' Beliefs on Learning and Teaching Whole Number Operations
Length: 30 minutes
Abstract: Results of attempts to change the attitudes and beliefs of preservice elementary teachers at five universities through the use of excerpts from Liping Ma's book "Knowing and Teaching Elementary Mathematics" are reported. We demonstrate how KTEM provided a catalyst for some change in the attitudes and beliefs of our preservice teachers.

Name: Sharon K. Robbert and Katie DeKoekkoek
Affiliation: Trinity Christian College
Title: A Crash Course for Connecting Curve Cryptology
Length: 30 minutes
Abstract: Most mathematician-teachers are vaguely aware that Andrew Wiles made remarkable and largely incomprehensible connections between elliptic curves, modular forms, and the non-existence of positive integer solutions to a^n + b^n = c^n in his proof of Fermat's Last Theorem. However, an investigation of elliptic curves reveals interesting and accessible connections to mathematical content in analytic geometry, calculus, modular arithmetic, and abstract algebra. In this talk the basic structure of elliptic curve cryptology will be discussed leading to illustrations of some of these accessible connections.

Name: Vali Siadat
Affiliation: Richard J. Daley College
Title: Applications of the Axial Representation of Trigonometric Functions
Length: 30 minutes
Abstract: In this presentation we will discuss some applications of the axial representation of trigonometric functions in proving trigonometric identities and also in calculus. We will show how the axial method can be used to prove the derivatives of certain trigonometric functions as an alternative to the traditional methods.

Name: Phil Straffin
Affiliation: Beloit College
Title: Explorations in the Mathematics of Other Cultures
Length: 60 minutes
Abstract: For the past ten years at Beloit we have taught a course in ethnomathematics, introducing students to mathematical thinking in non-Western cultures. The course has been extremely popular among students and great fun for the faculty. I'll describe the course briefly, and then focus on mathematical explorations which have grown out of it, involving Tshokwe sona, Malekulan nitus, the symmetries of bi-strips, and the Ghanian game of Achi.

Name: Lisa Townsley
Affiliation: Benedictine University
Title: The New CLEP Precalculus Exam
Length: 30 minutes
Abstract: Beginning in January 2006, the College Board will offer a new CLEP exam in Precalculus, to replace the Trigonometry exam. (CLEP stands for College Level Examination Program) Please join this information session to meet a member of the test development committee and to see how your students can earn college credit for Precalculus via external examination. The test development process, grade-setting, and an outline of the content covered by this exam will be presented.

Name: Nader Vakil
Affiliation: Western Illinois University
Title: Construction of Completions, A New Approach Using Modern Infinitesimals
Length: 30 minutes
Abstract: Let X be a metric or a uniform space. In the literature on the application of infinitesimal methods, the completion of a metric space or a uniform space is presented as the class of all the monads of pre-near-standard elements of a nonstandard extension of X. This approach to construction of completions cannot be implemented within Nelson's Internal Set Theory. In this paper, we present a new method that does not require the use of monads, and this allows us to implement the construction both within Robinson's model theoretic framework and within Nelson's Axiomatic framework.

Name: Rich Wilders
Affiliation: North Central College
Title: Galileo's Computation of the Tangent Line to a Parabola
Length: 30 minutes
Abstract: While Galileo is best known for his advocacy of the heliocentric model of the universe, he did some very interesting work in the study of motion as well. This talk will explore Galileo's derivation of the tangent to the parabola as it appeared in his last book: Dialogues on Two New Sciences.