**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

**Abstract:**

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.

**Title:** Challenge in the Classroom

**Length:** 60 minutes

**Abstract:**

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.

**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.