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The Michigan Section
of the
Mathematical Association
of America
and
MichMATYC
91st Annual Meeting
Hope College
Holland, Michigan
April 10–11, 2015
Michigan Section of the
Mathematical Association of America
2014-2015 Officers and Staff
Chair
Michele Intermont, Kalamazoo College
4-Yr Vice Chair
Brian Snyder, Lake Superior State University
2-Yr Vice Chair
Jan Roy, Montcalm Community College
Sec/Treas
Mark Bollman, Albion College
Governor
Matt Boelkins, Grand Valley State University
Past Chair
Steve Blair, Eastern Michigan University
Newsletter Ed
Katie Ballentine, Mathematical Reviews
Co-Dir. MMPC
Kim Rescorla, Eastern Michigan University
Carla Tayeh, Eastern Michigan University
Webmaster
Stephanie Edwards, Hope College
Liaison Coord
David Austin, Grand Valley State University
PIO
Robert Xeras, Siena Heights University, retired
2015 Annual Meeting Program Committee
Chair
Brian Snyder, Lake Superior State University
Members
Eddie Cheng, Oakland University
Stephanie Edwards, Hope College
Jan Roy, Montcalm Community College
2015 Annual Meeting Local Arrangements Committee
Chair
Stephanie Edwards, Hope College
Members
Aaron Cinzori, Hope College
Darin Stephenson, Hope College
Todd Swanson, Hope College
MichMATYC 2014-2015 Officers and Staff
President
Jack Rotman, Lansing Community College
Past President
Bernard Cunningham, Mott Community College
Sec/Treas
Jeff Morford, Henry Ford Community College
President Elect
Doug Mace, Kirtland Community College
Webmaster
Mark Pelfrey, Southwestern Michigan College
2015 Joint MAA/MichMATYC Meeting, Hope College
Friday, April 10, 2015
1:15-2:15
PM
Registration (Maas Conference Room)
2:15-3:20
PM
Welcome and Opening Plenary (Maas Auditorium)
Bill Cook, University of Waterloo
A Salesman's Tour of Combinatorial Optimization
3:25-4:00
PM
Room
4:05-4:25
PM
Local Invited Lecture (Maas Auditorium)
Eric Mann, Hope College
Changing the Culture: Developing Creative
Problem Solvers
MMC 158
Local Invited Lecture (MMC 158)
Allen Schwenk, Western Michigan University
Mathematical Induction: The Good, the Bad
and the Ugly
MMC 159
Steve Bacinski, Davenport
Steve Schlicker, Grand Valley State
University
University
Applied MATLAB Projects
A Geometry of Sets
for Linear Algebra
Students
Michigan Undergraduate
Mathematics Conference
4:30-4:50
PM
5:00-5:30
PM
5:30-6:30
PM
6:30-9:00
PM
MMC 240
Allan Bickle, Calvin College
MegaMenger Graphs
Paul Pearson, Hope
College
An Interactive
Introduction to WeBWorK
W C Abram and Kadeem
Noray*, Hillsdale College
Political Corruption and
Public Advocacy: An
Evolutionary Game
Theoretic Analysis
Business Meeting (MMC 159)
Social Hour (AlpenRose Restaurant)
Banquet and Plenary Lecture (AlpenRose Restaurant)
Bob Devaney, Boston University
The Fractal Geometry of the Mandelbrot Set
Saturday, April 11, 2015
8:00-8:40 AM
Breakfast and Registration (Maas Auditorium)
8:45-9:40 AM
Plenary Lecture (Maas Auditorium)
Ben Collins, University of Wisconsin - Platteville
Basel and Beyond: An Incomplete History of a Famous Sum
9:45 - 10:20
AM
10:30-11:10
AM
Location
Local Invited Lecture
(Maas Auditorium)
Jack Rotman, Lansing Community College
Curricular Change and Collaboration Across
Institutions
Local Invited Lecture
(Maas Conference Room)
Tim Pennings, Davenport University
Elvis Lives: Mathematical Surprises Inspired by Elvis,
the Welsh Corgi
Break - Sponsored by Cengage Learning
MMC 158
MMC 159
MMC 237
MMC 238
MMC 239
Michigan Undergraduate Math Conference
11:10 AM11:30 AM
11:35 AM11:55 AM
12:00 - 12:45
PM
12:55-1:50 PM
Alen Astifo, Macomb
Community College
My Experiences as a
Work-Study Student
in a Math
Department
Jeff Miller, Evan
Peters and Carl
Uzarski, Grand
Valley State
University
Combinatorial
Interpretations of
the Generalized
Central Factorial
Numbers
Lindsay Czap, Grand
Valley State
University
Guessing Games
and Error Correcting
Codes
Raoul R. Wadhwa,
Eddie Cheng,
Kalamazoo College Oakland University
Stochastic Kinetic Doing Research with
Models of Genetic
Bright High School
Expression
Students
MUMC Pizza Lunch - Maas Conference
Room
Firas Hindeleh,
Ed Aboufadel, Grand
Barbara Britton,
Grand Valley State
Valley State
Eastern Michigan
University
University
University
Classification of
3D Printing Projects
Common Core Ideas Seven-Dimensional
for Multivariate
circa 1900 - What Lie Algebras with SixCalculus and College
Took Us So Long?
Dimensional
Geometry
Nilradical
Victor Piercey, Ferris Darin Stephenson,
State University
Hope College
Affective
Using Algebraic
Implications of
Geometry to Study
Curriculum and
Non-commutative
Instruction Choices
Rings
Conference Luncheon - Maas Auditorium
Plenary Lecture (Maas Auditorium)
Erica Flapan, Pomona College (Pólya Lecture)
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Intrinsic Properties of Graphs Embedded in
Saturday, April 11, 2015
Location
MMC 158
MMC 159
MMC 237
MMC 238
MMC 239
Michigan Undergraduate Math Conference
Joshua Mirth,
Hillsdale College
2:00-2:20
Functional Analysis
PM
and the Dirichlet
Problem
2:25-2:45
PM
Eric Beyer, Robert
Gandolfo and Tyler
Pleasant, Lawrence
Jonathan Oaks,
Michael Bolt, Calvin
Technological
Macomb Community
College
University
College
Van der Pauw's
The Fight Against Uses of Bases Other Theorem on Sheet
Ebola: A
Than Base 10
Resistance
Mathematical
Weapon of Attack
Khairul Islam,
Eastern Michigan
University
Tossing Coin in R:
Tests for
Unbiasedness and
Central Limit
Theorem
Emmanuel Kengni
Ncheuguim, Saginaw
Matthew Trzcinski*
Jacob Adams and
Mark Panaggio, RoseValley State
Grace Wiesner, Hope
and Khairul Islam,
Susanna Lange,
Hulman Institute of
University
College
Eastern Michigan
Grand Valley State
Technology
Impact of
Mission
University
University
Synchronization and
Allelopathic and
Monteverde:
Need of
Graph Theory
pattern formation in Spatial Interactions
Mathematical
Transformation:
Modeling of Rook
networks of coupled on a Competition
Rainforest Modeling
Literature Review
Placements
oscillators
Between Two
and Applications
Phytoplankton
Species
Sandra Becker,
Eastern Michigan
University
2:50-3:10
Connecting Teaching
PM
Practice to Student
Efficacy in
Undergraduate
Mathematics
Na Yu, Lawrence
Technological
University
How to recognize
con-specifics and
their motion?
Ummugul Bulut,
Brian McCartin,
Grand Valley State
Kettering University
University
Geometric Proofs of
Derivation of
the Common Tones
Stochastic Biased
Theorems of
and Correlated
Mathematical Music
Random Walk
Theory
Models in One and
Two Dimensions
3:15-3:45
PM
Break
3:455:00PM
Closing Plenary and Student Awards (Maas Auditorium)
Ken Schilling, University of Michigan - Flint
Sabermetrics for the Millions
Tanweer Shapla,
Eastern Michigan
University
Detecting the
presence of
Multicollinearity
INVITED PLENARY LECTURES
Benjamin V. C. Collins, University of Wisconsin,
Platteville
Saturday 8:45 - 9:40 a.m.
Maas Auditorium
Basel and Beyond: An Incomplete History of a Famous Sum
If anyone finds and communicates to us that which
thus far has eluded our efforts, great will be our gratitude.
With these words, published in 1689, Jacob Bernoulli brought
to the attention of European mathematicians a problem first
posed by Pietro Mengoli in 1644. The problem was to find an
exact sum for the infinite sum
∞
X
1
2
n=1 n
The problem came to be known as the “Basel Problem,” after the Swiss university town where Bernoulli lived and worked.
Fittingly, the problem was solved by Basel’s finest mathematician, Leonard Euler, in 1735. In his long and productive career,
Euler provided two separate proofs, as well as two efficient ways
to calculate the value of the sum.
The Basel Problem continues to intrigue mathematicians.
Dozens of proofs have been given, including several published
within the last few years. We will discuss Euler’s first proof, and
look at an interesting application of the sum in number theory.
Time permitting, we will look at a few more recent proofs.
William Cook, University of Waterloo
Friday 2:15 - 3:20 p.m.
Maas Auditorium
A Salesman’s Tour of Combinatorial Optimization
Given a list of cities along with the cost of travel between each
pair of them, the traveling salesman problem is to find the cheapest way to visit them all and return to your starting point. Easy
to state, but difficult to solve. In this talk we discuss the problem’s history, applications, and computation, along with current
6
research topics. The TSP serves as a means for discussing many
broad themes in the field of combinatorial optimization, combining geometry, linear programming, and algorithms.
Bob Devaney, Boston University
Friday, after Dinner
AlpenRose Restaurant
The Fractal Geometry of the Mandelbrot Set
In this lecture we describe several folk theorems concerning
the Mandelbrot set. While this set is extremely complicated
from a geometric point of view, we will show that, as long as
you know how to add and how to count, you can understand this
geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the
Fibonacci sequence. And we will find many soon-to-be-famous
objects as well, like the “Devaney” sequence. There might even
be a joke or two in the talk.
Erica Flapan, Pomona College
Saturday after Lunch
Maas Auditorium
Intrinsic Properties of Graphs Embedded in R3
Knot theory is the study of embeddings of simple closed
curves in R3 . A natural extension of knot theory is the study of
embeddings of graphs in R3 . However, in contrast with knots,
the structure of a graph can be complex, and this can affect all
of its embeddings. If every embedding of a graph has a particular property, then we say that property is intrinsic to the graph.
For example, a graph is said to be intrinsically knotted if every
embedding of the graph in R3 contains a knot. In this talk I
will discuss intrinsic knotting and other intrinsic properties of
graphs.
Ken Schilling, University of Michigan - Flint
Saturday 3:45 - 4:40 p.m.
Maas Auditorium
Sabermetrics for the Millions
Baseball fans have always been statistics-happy. That used to
mean memorizing batting averages and pitchers’ win-loss records.
No more. Instead, over the last few decades, baseball analysts
(sabermetricians, for those who fancy five-syllable words) have
7
used fairly sophisticated mathematical tools to try to answer the
big questions. Who would win a series between the 1927 New
York Yankees and the 1975 Cincinnati Reds? Should you bunt
the winning run to second with one out in the bottom of the
ninth? Could Willie Mays hit a ball so far that he himself could
not catch it?
LOCALLY INVITED SPEAKERS
Eric Mann, Hope College
Friday, April 10 3:25 - 4:00 p.m.
Maas Auditorium
Changing the Culture: Developing Creative Problem Solvers
Mathematics embraces creativity and beauty yet often our
children are immersed in classroom activities where these attributes are hidden by an overemphasis on algorithms, computational speed and known answers that can be found in the back
of the book or with a quick Google search. This learning environment creates a false perception of what it means to be “good
at math.” From the research we know than many of our elementary school teachers have negative attitudes towards mathematics; an attitude students pick up and adopt which may foster
the development of the reluctant, impatient problem solvers we
find in our undergraduate classrooms. A change in the culture
to one that both acknowledges and values the creative nature of
mathematics is long overdue.
The Partnership for 21st Century Skills in conjunction with
the National Council of Teachers of Mathematics and the Mathematical Association of America developed the 21st Century
Skills Map for mathematics. In the Learning and Innovation
skills area the emphasis is on the 4C’s: Creativity, Critical
Thinking, Communication and Collaboration, skills that have
been topics of discussion in math education for over a century.
This talk shares examples of efforts to infuse the 4C’s into K-12
mathematics classrooms in hopes of stimulating further collaborations between mathematicians and educators to restore wonder and beauty to mathematics taught in today’s classrooms.
8
Tim Pennings, Davenport University
Saturday 9:45 - 10:20 a.m.
Maas Conference Room
Elvis Lives: Mathematical Surprises Inspired by Elvis, the
Welsh Corgi
A worthwhile mathematical model should not only confirm
and inform one’s intuition; it should sometimes challenge or contradict it. In this talk we review the mathematical surprises
from three papers involving the retrieving behavior of Elvis, the
Welsh corgi. The first describes how Elvis became famous when
he found the quickest - and sometimes nonintuitive - route down
the beach and through the water to his ball. A second paper
revealed more unexpected results as we analyzed the bifurcation occurring when Elvis, starting in the water, had to decide
whether or not to come to land. And the last paper uncovers
several surprising conclusions as we determine when and why a
locally greedy route coincides with the globally optimal path.
Jack Rotman, Lansing Community College, MichMATYC President
Saturday 9:45 - 10:20 a.m.
Maas Auditorium
Curricular Change and Collaboration Across Institutions
In a state without a higher education system controlling the
curriculum, each institution accepts responsibility for decisions,
and exercises autonomy than is seen in states with such a system.
One positive consequence is that changes are not initiated from
a state office; one negative consequence is that changes are not
initiated from a state office.
This talk will consider how we change and collaborate on curricular issues, using some typical courses as examples (college
algebra, finite math, pre-calculus). We will cite some references
from our national organizations (MAA, AMATYC) to indicate
some possible areas of improvement. A conjecture for your consideration is: “Collegiate mathematics in Michigan needs deliberate and organized state-wide leadership based in a diverse
group of faculty working together, supported by both MichMAA
and MichMATYC.”
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Allen Schwenk, Western Michigan University
Friday, April 10 3:25 - 4:00 p.m.
MMC 158
Mathematical Induction: The Good, the Bad and the Ugly
Of course math induction is good. But some of my students
have picked up bad habits when using induction; and many of
the examples we use to teach the topic are, sad to say, just plain
ugly. I wish to show a number of examples of proof by induction.
Many of them are elegant, but not the standard examples we see
in textbooks. Induction does not always proceed one step at a
time. Some proofs that look good, can contain hidden errors.
Can you discern the difference between the good proofs, the bad
ones, and the ugly?
CONTRIBUTED TALKS
Ed Aboufadel, Grand Valley State University
Saturday 11:10 - 11:30 a.m.
MMC 237
3D Printing Projects for Multivariate Calculus and College
Geometry
Multivariate Calculus and College Geometry are two courses
which have natural ways to introduce undergraduates to 3D
printing. In this talk, we will provide some information about
3D printing and describe projects that can be assigned in these
courses, where students can design and print 3D objects. The
objects are designed in Mathematica and make use of planar
and other multivariate functions, trigonometry, polyhedra, and
more.
Steve Bacinski, Davenport University
Friday 4:05 - 4:25 p.m.
MMC 159
Applied MATLAB Projects for Linear Algebra Students
Linear algebra provides us with many powerful tools that are
widely used in areas such as computer graphics, facial recognition, and big data analytics just to name a few. I have made
an effort to incorporate many of these interesting applications
in my undergraduate linear algebra course. In doing so, I have
developed eight MATLAB-based projects that serve as a foundation for a course titled Applied Linear Algebra. Because of
10
the time constraint for the session, I will focus on my three favorite projects: Matrix Transformations with Puzzles, Airplane
Bounding Box, and Image Compression with Wavelets.
Allan Bickle, Calvin College
Friday 4:30 - 4:50 p.m.
MMC 158
MegaMenger Graphs
In October 2014, many faculty and students at Calvin College
worked to build a model of the Menger sponge, a type of fractal,
out of business cards. This model can itself be modeled using
graph theory, with each vertex representing a small cube, and
an edge between two vertices whenever they share a face. We
study graphs representing different steps of building the Menger
sponge and Sierpinski carpet to determine their order, size, vertex degrees, chromatic number, and degeneracy, along with the
surface area of the Menger sponge. Calculating these quantities
requires solving many recurrence relations using several different
techniques.
Michael Bolt, Calvin College
Saturday 2:00 - 2:20 p.m.
MMC 238
Van der Pauw’s Theorem on Sheet Resistance
The sheet resistance of a semiconducting material of uniform
thickness is analogous to the resistivity of a solid material and
provides a measure of electrical resistance. In 1958, L. J. van
der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from
four points on the edge of a simply connected sample of the
material. The method still is in wide use today. In this talk,
we give a statement and proof of the van der Pauw theorem.
The relevant mathematics is from complex analysis and touches
on topics such as electrostatic potentials, cross-ratio, conformal
mapping, and the Riemann mapping theorem.
Barbara Britton, Eastern Michigan University
Saturday 11:10 - 11:30 a.m.
MMC 238
Common Core Ideas circa 1900 - What Took Us So Long?
Back in 1900, David Eugene Smith introduced a philosophy
11
of teaching elementary mathematics that sounds very similar to
the foundation of the Common Core State Standards of today.
Learn about this pioneer in mathematics education, his ideas,
and his connection to Michigan!
Ummugul Bulut, Grand Valley State University
Saturday 2:50 - 3:10 p.m.
MMC 238
Derivation of Stochastic Biased and Correlated Random Walk
Models in One and Two Dimensions
Stochastic partial differential equations are derived to model
the biased and correlated random walk (BCRW) in one and two
dimensions. Deterministic equation is given for one dimensional
BCRW where particles have a tendency to move in a particular
direction, either right or left. In the present investigation, discrete time stochastic models are developed by determining the
possible changes in direction for a small time interval. As the
time interval decreases, the discrete stochastic models lead to
systems of Ito stochastic differential equations. As the position
intervals decrease, stochastic partial differential equations are
derived to model BCRW in one and two dimensions. Comparisons between numerical solutions of the stochastic partial differential equations and independently formulated Monte Carlo
calculations support the accuracy of the derivations.
Eddie Cheng, Oakland University
Saturday 11:35 - 11:55 a.m.
MMC 237
Doing Research with Bright High School Students
Many bright high school students are interested in doing research in mathematics. Over the past 12 years, I have worked
with about 30 talented high school students who participated
at the Oakland University Summer Mathematics Institute. In
this talk, I will discuss my experience working with them as well
as how to choose projects that are accessible to motivated and
gifted high school students.
Firas Hindeleh, Grand Valley State University
Saturday 11:10 - 11:30 a.m.
MMC 239
Classification of Seven-Dimensional Lie Algebras with Six12
Dimensional Nilradical
Low dimensional solvable Lie algebra classification started
back in 1963 by Mubarakzyanov. Solvable Lie algebras were
completely classified up to dimension six. A general theorem
asserts that if g is a solvable Lie algebra of dimension n, then
the dimension of the nilradical is at least n2 . For the sevendimensional algebras, the nilradical’s dimension could be 4, 5, 6
or 7. The four and seven dimensional nilradical cases were classified. We examine the six-dimensional nilradical case, and depending on the structure of this nilradical there are six classes.
This talk will introduce the basic tools needed for the classification problem in a way that is accessible to undergraduate
students. I will discuss the progress made on this problem and
outline the next piece of the project. Please encourage students
who are interested in summer research opportunity to attend
this talk.
Khairul Islam, Eastern Michigan University
Saturday 2:00 - 2:20 p.m.
MMC 239
Tossing Coin in R: Tests for Unbiasedness and Central Limit
Theorem
Often, we toss a coin to introduce probability. How do we
do it using technology, particularly in R? How do we test the
unbiasedness of the coin? How do we introduce Central Limit
Theorem using R? In this presentation, we address answers to
these questions along with the flexibility of R for applications.
Emmanuel Kengni Ncheuguim, Saginaw Valley State
University
Saturday 2:25 - 2:45 p.m.
MMC 238
Impact of Allelopathic and Spatial Interactions on a Competition Between Two Phytoplankton Species
We propose a model of two phytoplankton species competing for a single growth limiting, nonreproducing resource. The
model incorporates allelopathic interactions of one toxin-producing species, both on itself (autotoxicity) and on its nontoxic
competitor (phytotoxicity). We show that a stable coexistence
13
equilibrium exists as long as (a) there are allelopathic effects and
(b) the input nutrient concentration is above a critical value.
The spatial interactions among nutrient and the phytoplankton
species are incorporated in the model in the form of reactiondiffusion equations. The reaction-diffusion equations account
for the fact that nutrient and species of phytoplankton are distributed over a considerably large spatial regime in natural waters. We investigate suitable parametric conditions under which
Turing patterns may or may not evolve around the locally stable
interior equilibrium.
Brian McCartin, Kettering University
Saturday 2:50 - 3:10 p.m.
MMC 237
Geometric Proofs of the Common Tones Theorems of Mathematical Music Theory
The twin pillars of Mathematical Music Theory are the Common Tones Theorems for Transposition (rotation) and Inversion (reflection). As a counterpoint to the traditional algebraic proofs of these foundational results, this talk will present
simple geometric proofs of these theorems as well as some related corollaries. Time permitting, the geometrical relationship of the Common Tones Theorems to such diverse topics
as the Orbit-Stabilizer Theorem, Hexachordal Combinatoriality
and the Complementary Chords Theorems will be explored.
Jonathan Oaks, Macomb Community College
Saturday 2:00 - 2:20 p.m.
MMC 237
Uses of Bases Other Than Base 10
Most people are familiar with base 10 because it is what is
used most commonly. Many people are even familiar with base
2. But what are some of the other bases used for - base 3,
base 4, etc.? What about base e or base π? And what about
the negative bases and the hybrid bases? This presentation will
cover some of the uses of all of these other bases.
Mark Panaggio, Rose-Hulman Institute of Technology
Saturday 2:25 - 2:45 p.m.
MMC 237
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Synchronization and pattern formation in networks of coupled
oscillators
From the flashing lights of a swarm of fireflies to the footfalls of pedestrians on a bridge, synchronization is observed in
a variety of natural and engineered systems. This coordination, which can emerge spontaneously out of disordered initial
states, has an important role in the transport of blood throughout the human body, electricity on the power grid, and information in telecommunication devices. Breakdowns of synchrony
can be detrimental to the efficient operation of those systems,
and as a result, it is essential to be able to predict when synchronization is likely to occur and under what conditions it can
be disrupted. In this talk, I will explore the Kuramoto model,
a minimal mathematical model that describes the dynamics of
a network of coupled phase-oscillators. Analysis of this model
will reveal that the interactions between these idealized oscillators can give rise to a variety of unexpected behaviors that
have been observed in experiments including phase transitions
from asynchrony to synchrony and pattern formation with coexisting domains of coherent and incoherent oscillation. The
bistability of these partially synchronized steady state patterns
(known as chimera states) with a fully synchronized state may
shed light on the origin of transitions between synchronized and
desynchronized behavior in nature.
Paul Pearson, Hope College
Friday 4:05 - 4:50 p.m.
MMC 240
An Interactive Introduction to WeBWorK
WeBWorK is an open-source, web-based homework delivery
system designed to make homework more effective and efficient
for students of mathematics and the sciences. It has been used
for over 18 years by hundreds of professors and in a wide variety
of instructional environments. Participants in this workshop
will be introduced to the WeBWorK online homework system
and learn how to use it in their own classes. The workshop
will be held in a computer lab so that participants do not need
15
to bring their own computers. Space is limited to 20 participants. There will be approximately 30 minutes of unstructured
time after the workshop has ended to ask more questions and
experiment further with WeBWorK.
Victor Piercey, Ferris State University
Saturday 11:35 - 11:55 a.m.
MMC 238
Affective Implications of Curriculum and Instruction Choices
Imagine a typical student in your developmental or general
education course. What do you think their attitudes or beliefs
about mathematics are? Might they experience math anxiety?
How do curricular choices or our instructional choices impact
those attitudes and beliefs? In this talk, I will describe three
different curriculum and instruction models we used for general
education and share data concerning the impact on math anxiety
and beliefs about math.
Steven Schlicker, Grand Valley State University
Friday 4:05 - 4:25 p.m.
MMC 158
A Geometry of Sets
The Hausdorff metric provides a way to measure distance
between sets. The metric is important for its applications in
fractal geometry, image matching, visual recognition by robots,
and computer-aided surgery. Beyond the practical applications,
the Hausdorff metric imposes an interesting geometry on the
space of non-empty compact subsets or Rn . We will discuss
some details about circles, lines, and segments in this geometry,
and then focus on recent work attempting to define angles and
angle measure in this geometry. This research was conducted as
part of the 2014 REU program at Grand Valley State University.
Tanweer Shapla, Eastern Michigan University
Saturday 2:50 - 3:10 p.m.
MMC 239
Detecting the presence of Multicollinearity
Multicollinearity is a situation when several predictors appear
to be correlated, which is a violation of least squares regression
model. As such, the estimates of regression coefficients become
indeterminate and the standard errors of estimates become in16
finitely large, leading to invalid inferences. The first step in
fitting a model is to determine if multicollinearity exists among
predictors. In this talk, we explore some popular methods of
detecting multicollinearity applied to real life data.
Darin Stephenson, Hope College
Saturday 11:35 - 11:55 a.m.
MMC 239
Using Algebraic Geometry to Study Noncommutative Rings
I will give an example-oriented survey of some results developed by others on the classification and study of noncommutative rings using the tools of algebraic geometry. I will indicate
how this study gives rise to a theory of “noncommutative algebraic geometry” for certain noncommutative graded rings. I will
also give a survey of related problems that I have been working
on recently, along with some preliminary results.
Matthew Trzcinski and Khairul Islam, Eastern Michigan University
Saturday 2:25 - 2:45 p.m.
MMC 239
Need of Transformation: Literature Review and Applications
Many statistical methods require normality of the data. For
example, to implement t-test and ANOVA, the first assumption
that we make is the normality of the populations the samples
come from. Transformation towards normality exists in literature to enable us to implement these tests. What if the normality of the population is unmet and the t-test or ANOVA is
still applied in violation of the normality of the population? In
this presentation, we review some transformation techniques and
justify the need of transformation in the violation of normality
with examples and Monte Carlo simulations.
Na Yu, Lawrence Technological University
Saturday 2:50 - 3:10 p.m.
MMC 159
How to recognize conspecifics and their motion?
Effectively processing information from a sensory scene is essential for animal survival. Motion in a sensory scene complicates this task by dynamically modifying signal properties. To
address this general issue, we focus on weakly electric fish. Each
17
fish produces a weak electrical carrier signal with a characteristic frequency. Electroreceptors on its skin encode the modulations of this carrier caused by nearby objects and other animals,
enabling this fish to thrive in its nocturnal environment. Little is known about how swimming movements influence natural electrosensory scenes, specifically in the context of detection
and identification of, and communication with conspecifics. Using recordings involving free-swimming fish, we characterize the
amplitude modulations of the carrier signal arising from small
groups of fish. The differences between individual frequencies
(beats) are prominent features of these signals, with the number
of beats reflecting the number of neighbours. We also find that
the distance and motion of a free-swimming fish are represented
in a slow modulation of the beat at the receiving fish. Modeling
shows that these stimulus features can be effectively encoded in
the activity of the electroreceptors, but that encoding quality of
some features can be degraded by motion, suggesting that active
swimming could hinder conspecific identification.
MICHIGAN UNDERGRADUATE MATHEMATICS
CONFERENCE TALKS
Jacob Adams and Susanna Lange, Grand Valley State
University
Saturday 2:25 - 2:45 p.m.
MMC 158
Graph Theory Modeling of Rook Placements
In a non-attacking rook placement on a board we place rooks
in such a way that no two lie in the same row or column. Such
a placement models a way to match two sets of objects, such
as jobs and job applicants including any possible restrictions on
which job can be matched with which applicants represented as
restricted cells on the board. During this talk, we will discuss
the modeling of these rook placements as matchings in bipartite
graphs, and further investigate connections to gridline graphs.
We will then generalize this modeling to rook placements in
three and higher dimensions.
Alen Astifo, Macomb Community College
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Saturday 11:10 - 11:30 a.m.
MMC 158
My Experiences as a Work-Study Student in a Math Department
This presentation will focus on what a student does as a workstudy student in a math department. Some of the duties include
assisting professors with tasks that they may need help with and
learning more about how the math department functions as a
whole. But the best part about the position is actually working
with students in an intermediate algebra class and helping them
succeed and become better students. Being a work-study student in a math department is a great opportunity for any mathematics student to see mathematics from a different perspective
and to see the ins-and-outs of how the department works on a
day-to-day basis.
Eric Beyer, Robert Gandolfo and Tyler Pleasant, Lawrence Technological University
Saturday 2:00 - 2:20 p.m.
MMC 159
The Fight Against Ebola: A Mathematical Weapon of Attack
The West African Ebola Epidemic started in March 2014 yet,
even with medical help from other countries, the epidemic still is
not under control. The outbreak needs to be fought and brought
under control as soon as possible. In order to understand and
predict the future of the virus and the effects of control measures,
we created a mathematical model which gives a control strategy
that revolves around the effective reproductive rate Re , defined
as the average number of people infected by a person who gets
the disease. There are two main ways to lower the effective reproduction rate: improving control measures and administering
vaccination. To model the nature of the disease, we split and
track six groups within the population. Our homogeneous deterministic model simulates disease dynamics, vaccination production, and transportation processes in order to determine Re
at any given time which allows optimal use of vaccine.
Lindsay Czap, Grand Valley State University
Saturday 11:35 - 11:55 a.m.
MMC 158
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Guessing Games and Error Correcting Codes
A two-player “guessing game” is a game in which the first
participant picks a number from a certain range. Then, the
second participant asks only yes-or-no questions in order to guess
the number. A technique for minimizing the number of questions
uses questions that divide the range of possible choices in half
each time. We will prove that the minimum number of necessary
questions is directly related to the log2 of the number of possible
choices. Next, we will introduce guessing games that contain a
“lie” or an error. Guessing games with lies are closely linked
to error correcting codes, which are codes that allow for us to
detect an error in the information that we receive and correct
for these errors. We will use basic definitions in coding theory
and discuss how error correcting codes will help us to still guess
the correct number even if a lie is involved.
Jeff Miller, Evan Peters and Carl Uzarski, Grand Valley State University
Saturday 11:10 - 11:30 a.m.
MMC 159
Combinatorial Interpretations of the Generalized Central Factorial Numbers
Placing rooks on a chess board so that they cannot attack
one another provides us a way to match rows with columns. If
we place restrictions on these matchings so that the possible
matches are allowed only on one triangular half of the board,
we find interesting results about the number of possible rook
placements. These numbers relate to the famous Stirling numbers of the second kind, which count ways of partitioning a set
into non-empty subsets. In fact, there is a natural correspondence between the rook placements on a triangular board and
the partitions of a set. In this talk, we describe how to extend
triangular boards to three and higher dimensions, and how the
rook placements on these boards provide new combinatorial interpretations of central factorial and generalized central factorial
numbers.
Joshua Mirth, Hillsdale College
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Saturday 2:00 - 2:20 p.m.
MMC 158
Functional Analysis and the Dirichlet Problem
Dirichlet boundary value problems arise in many physical situations. However, simple analytic solutions only exist in a limited number of cases. We examine methods for solving Dirichlet
problems on other regions, focusing on the unit right triangle.
We prove the existence of such a solution and attempt to write
a closed form solution by two different methods: first, using the
Schwarz-Christoffel formula from complex analysis, and second,
by drawing on functional analysis techniques and using Green’s
functions. These solutions are then compared to numerical approximations.
Kadeem Noray, Hillsdale College
Friday 4:30 - 4:50 p.m.
MMC 159
Political Corruption and Public Advocacy: An Evolutionary
Game Theoretic Analysis
We consider a two population evolutionary game that models
the role of public advocacy as a deterrent to political corruption.
A population of politicians chooses whether or not to engage in
corrupt behavior, and a population of citizens decide whether or
not to advocate for corruption reform, with the potential to impact detection and punishment levels for corruption. We study
the pure and mixed strategy Nash equilibrium structure of this
game. We also conduct an evolutionary analysis, finding evolutionary stable strategies and studying the evolution of strategies
over time via the replicator dynamics for a two population game.
Lastly, we explain the different types of dynamics that can result
from realistic parameters in our model.
Raoul R. Wadhwa, Kalamazoo College
Saturday 11:35 - 11:55 a.m.
MMC 159
Stochastic Kinetic Models of Genetic Expression
Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model im21
plementation of the circular gene hypothesis, which suggests
interactions between the synthesis and degradation of mRNA.
Qualitative and quantitative changes in the shape and in the
numerical characteristics of the stationary distributions suggest
that more combined experimental and theoretical studies should
be done to uncover the details of the kinetic mechanism of gene
expression.
Grace Wiesner, Hope College
Saturday 2:25 - 2:45 p.m.
MMC 159
Mission Monteverde: Mathematical Rainforest Modeling
The tropical rainforest is one of earth’s most diverse and dynamic ecosystems. Tree or branch falls in the forest can open
gaps in the canopy, allowing light to reach the forest floor. Pioneer plants are adapted to take advantage of these conditions,
sometimes emerging many years after being deposited as seeds.
Light conditions change as the gap closes, impacting rates of
growth and reproduction.
For the past 30 years, sizes and reproductive outputs of individuals of 6 pioneer plant species have been measured along
5 transects in the Monteverde Cloud Forest Preserve in Monteverde, Costa Rica. Each 500m transect was chosen to be
representative of different conditions in some part of the cloud
forest.
To model the pioneer plant demographics, we classified canopy
gaps by age and size and developed a matrix population model
that accounts for the differing gap environments. We also created a stochastic matrix model of gap formation and evolution
to simulate the dynamics of rainforest canopy gaps. Combined,
these models will allow us to simulate pioneer plant population
dynamics in the changing forest environment, and to explore
how reproduction and growth rate parameters, such as seed predation rates, impact pioneer population dynamics.
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Conference events will be located in the following two buildings
on the Hope College campus:
Maas Center, 264 Columbia Ave., Holland
Martha Miller Center, 257 Columbia Ave., Holland
The Friday evening banquet will be held at
Alpen Rose Restaurant, 4 East 8th Street, Holland
Alpen Rose Restaurant is within easy walking distance of the
conference site and downtown hotels.
Parking: Parking will be permitted in any campus lot on either day. Parking on campus Friday will be more complicated
Friday due to construction and several campus events. You may
also park in one of several downtown Holland free parking areas
(including a city parking garage on 7th Street, about 3 blocks
from the meeting site).
The closest campus lots are Lot 41 (Martha Miller Center) and
Lot 62/63 (DeVos Fieldhouse). Lot 41 is directly adjacent to
the conference location, and there should be spaces available on
Saturday.
Saturday morning break sponsored by: