MAA Ohio Section
Fall 2016 Program
Friday, October 28
12:004:00

Registration

Freedlander Lobby

12:001:00

Committee Meetings:
 
CONCUR (Curriculum)

Taylor 205
 
CONSACT (Section Activities)

Taylor 206
 
CONTEAL (Teacher Education & Licensure)

Taylor 209
 
1:004:00

Vendor & Book Exhibits

Freedlander Lobby

1:151:30

Welcome and Announcements

McGaw Chapel

1:302:30
 Panel Discussion:
“State of Online Teaching of College Level Mathematics in Ohio” Jim Fowler, Karen Mitchell, Laura Stapelton, and Richard Uchida.
 
2:302:50

Break

Freedlander Lobby

2:503:50

Invited Address by Distinguished Teaching Award Winner: “A Study of Dynamic Equations Using Mechanical Integration” Bonita Lawrence aided by Clayton Brooks and students Chad Lott and Paige Yankey.

Lean Lecture Hall

4:005:40

Executive Committee Meeting

Taylor 308

5:006:15

Contributed Paper Sessions (6 time slots)

Taylor 110, 111, 205

6:156:50

Social Time

Kittredge Hall

6:508:00

Banquet

Kittredge Hall

8:009:00

Invited Address: “Assignment Problem, Cheater's Rubik's Cube, and Tropical Determinant” Jenya Soprunova

Kittredge Hall

Saturday, October 29
8:0010:00

Registration

Freedlander Lobby

8:0010:00

Book Vendors and Exhibits

Freedlander Lobby

8:009:25

Coffee and Pastries

Freedlander Lobby

8:509:25

Committee On Local Arrangements and Executive Committee Meeting (if needed)

Taylor 308

9:259:35

Welcome and Announcements

Lean Lecture Hall

9:3510:35

Invited Address: “Intrinsic Properties of Graphs in R^{3}” Erica Flapan

Lean Lecture Hall

10:3510:50

Break

Freedlander Lobby

10:5011:45

Contributed Paper Session (3 time slots)

Taylor 110, 111, 205

11:4512:00

Break
 
12:001:00

Invited Address: “Deblurring Images with Mathematical Models” Malena Espanol

Lean Lecture Hall

1:001:10

Closing Remarks

Lean Lecture Hall

Abstracts of Invited Addresses
Friday
Speaker: Bonita Lawrence aided by Clayton Brooks and students Chad Lott and Paige Yankey, all of Marshall University
Title: “A Study of Dynamic Equations Using Mechanical Integration”
Abstract: The Marshall Differential Analyzer Lab offers undergraduate and graduate students the opportunity to investigate both the quantitative and qualitative behavior of solutions of certain classes of differential equations using primarily mechanical differential analyzers. After a bit of training to use the machines, students have the freedom to plan their research study, program the machine, run the problem and analyze the results. Recently, the team has been studying the behavior of solutions on sets known as time scales. In particular, the group has been studying time scales that are unions of closed intervals. The goal is to study the behavior of solutions as the sets converge to a single closed interval. A discussion of the relationship between the mechanics of the machine and the mathematics that it models will be presented as well as a demonstration by my graduate students of how we run a problem on one of the small traveling machines known as DA Vinci!
Biography: Inspired by her high school mathematics teacher, Mary Helen Miller, Dr. Bonita Lawrence began her formal mathematics training at Cameron University in Lawton, Oklahoma. After a short career as a classroom teacher, she returned to the university to continue her education, earning a Master’s degree at Auburn University and a Ph. D. at the University of Texas at Arlington. Her Ph. D. dissertation was written in the area of Stochastic Differential Equations.
Intrigued by studies of the similarities and differences between the differential and difference equations, her research studies now focus on results in the area of Dynamic Equations on Time Scales. Dr. Lawrence is a Professor of Mathematics at Marshall University and is the Lead Researcher for the Marshall University Differential Analyzer Lab. Her lab houses the only publicly accessible differential analyzer of its size in the USA (and beyond). She is the recipient of several College and University teaching and research awards and was named the 2009 – 2010 West Virginia Professor of the Year. Dr. Lawrence is married to Dr. Clayton Brooks, also a Professor of Mathematics at Marshall University.
Jenya Soprunova, Kent State University
Speaker: Jenya Soprunova, Kent State University
Title: “Assignment Problem, Cheater's Rubik's Cube, and Tropical Determinant”
Abstract: Consider n workers and n jobs, where we know how much each worker charges for each job. The classical assignment problem deals with assigning the jobs, one for each worker, so that the overall cost is as small as possible. We will discuss a polynomialtime algorithm for solving this problem that was developed by Harold Kuhn in 1955.
Next, consider the usual Rubik’s cube with 9 square stickers on each side colored in one of six colors. We want to solve Rubik’s cube by peeling off the stickers and replacing them so that each of the faces has all stickers of one color. We will figure out how many stickers we would need to peel off and replace in the worst case scenario and will also discuss a few generalizations of this problem.
We will explain a connection between these two seemingly very different problems and will also talk about tropical determinants, linear programming, Hall's marriage theorem, and the Birkhoff polytope.
Biography: Jenya Soprunova is an Associate Professor of Mathematics at Kent State University. She received her Ph.D. from the University of Toronto in 2002.
Jenya has worked as coordinator and advisor for the NSF funded REU program at Kent State. She coordinates the Choose Ohio First: Success in Math program and a Masters’ program for secondary mathematics teachers at Kent State.
Her research interests include combinatorial and computational algebraic geometry, discrete geometry, and algebraic coding theory.
Saturday
Erica Flapan, Pomona College
Speaker: Erica Flapan, Pomona College
Title: Intrinsic Properties of Graphs in ℝ
Abstract: Knot theory is the study of embeddings of simple closed curves in ℝ. A natural extension of knot theory is the study of embeddings of graphs in ℝ. 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 ℝ contains a knot. In this talk, I will discuss intrinsic knotting and other intrinsic properties of graphs.
Biography: Erica Flapan joined the faculty at Pomona College in 1986. Since 2006, she has been the Lingurn H. Burkhead Professor of Mathematics at Pomona College. In addition to teaching at Pomona College, Flapan taught at the Summer Mathematics Program for freshmen and sophomore Women at Carleton College from 2000 until 2015. In 2011, Flapan won the Mathematical Association of America’s Haimo award for distinguished college or university teaching of mathematics. Then in 2012, she was selected as an inaugural fellow of the American Mathematical Society. She is currently a Polya Lecturer for the MAA.
Erica Flapan has published extensively in topology and its applications to chemistry and molecular biology. In addition to her research papers, she has published an article in the College Mathematics Journal entitled “How to be a good teacher is an undecidable problem,” as well as four books. Her first book, entitled ``When Topology Meets Chemistry" was published jointly by the Mathematical Association of America and Cambridge University Press. Her second book entitled ``Applications of Knot Theory," is a collection of articles that Flapan coedited with Professor Dorothy Buck of Imperial College London. Flapan also coauthored a textbook entitled ``Number Theory: A Lively Introduction with Proofs, Applications, and Stories" with James Pommersheim and Tim Marks, published by John Wiley and Sons. Finally, the AMS recently published her book entitled “Knots, Molecules, and the Universe: An Introduction to Topology”, which is intended for first and second year college students.
Malena Espanol, The University of Akron
Speaker: Malena Espanol, The University of Akron
Title: Deblurring Images with Mathematical Models
Abstract: When we use a camera, we want the recorded image to be an accurate representation of the scene that we see. However, in some situations such as photographing a moving object, what we obtain can be a blurred image. In image deblurring, we seek to recover the original, sharp image by using a mathematical model of the blurring process. In this lecture, we will see a brief introduction to the basic image deblurring problem and some mathematical tools to address it.
Biography: Malena Espanol is an Assistant Professor of Applied Mathematics at The University of Akron. Originally from Argentina, she received her B.S. from the University of Buenos Aires in 2003 and her Ph.D. from Tufts University in 2009. After graduation, she spent 3 years as a postdoctoral fellow at the California Institute of Technology. Malena is a national Project NExT Fellow (Brown’13 dot) and has participated in several Ohio NExT workshops. She serves as the faculty advisor for both UAkron SIAM student Chapter and the Women in Math group. She is also a member of the SIAM Diversity Advisory Committee.
Malena’s research interests are in applied and computational mathematics with applications to image processing and materials science. Malena has been the recipient of several grants that include an MAATensor Women and Mathematics and two NSF grants.
Contributed Paper Sessions
*denotes
undergraduate student
**denotes
graduate student
Friday, October 28
5:00—6:15
Time

Session A
Taylor 110
Session Chair:
Keshav Pokhrel

Session B
Taylor 111
Session Chair:
Russell W. Kincaid

Session C
Taylor 205
Session Chair:
Kevin Gerstle

5:00 – 5:15

What
Can We Do to Help?
Abstract 1
Karen Mitchell
Marshall University

Disparities
in Childhood Mortality Rates in the Great Lakes Region
Abstract 2
Broderick Wagerson
*
The University of Michigan

An
Inequality for Motions with a Positive Jerk
Abstract 3
Aurel Stan
The Ohio State University
 Marion

5:20 – 5:35

Teaching
Statistics with Rmarkdown
Abstract 4
Keshav Pokhrel
The University of
MichiganDearborn

Changing
the Odds: Loaded Dice in a Probability Classroom
Abstract 5
Russell W. Kincaid
Wilmington College

Baire's
Lessons on Discontinuous Functions
Abstract 6
Philip S. Blau
Shawnee State
University

5:40 – 5:55

The
Gompertz Dynamic Equation
Abstract 7
Tom Cuchta
Fairmont State
University

Brain
and Intelligence: Why Humans Are So Dominant Part I
Abstract 8
M. B. Rao
The University of Cincinnati

Sequences
Converging to n^{th} Roots
Abstract 9
Adam E. Parker
Wittenberg
University

6:00 – 6:15

The
Precession in the Perihelion of the Orbit of Mercury
Abstract 10
Harrison D. Potter
Marietta College

Brain
and Intelligence: Why Humans Are So Dominant Part II
Abstract 11
M. B. Rao
The University of
Cincinnati

The
Beta Transmuted Pareto Distribution: Theory and Applications
Abstract 12
Sher B. Chhetri **
Florida Atlantic University

Contributed Paper Sessions
*denotes
undergraduate student
**denotes
graduate student
Saturday, October 29
10:50—11:45
Time

Session A
Taylor 110
Session Chair:
Pei Pei

Session B
Taylor 111
Session Chair:
Susan Thompson

Session C
Taylor 205
Session Chair:
Alfred Akinsete

10:50– 11:05

Transient
Distribution of a 2 Dimensional Random Walk
Abstract 13
Barbara Margolius
Cleveland State
University

A
Shidoku Exercise for Abstract Algebra
Abstract 14
Taylor Haydinger*
Defiance College

Polygonal
Numbers that Are neither a Sum nor a Difference of Two Prime Powers
Abstract 15
Dan Baczkowski
The University of
Findlay

11:10– 11:25

The
InducedSaturation Number of Cycles
Abstract 16
Cathy Erbes
Hiram College

Hamiltonian
Dynamics: A Geometric Approach to Classical and Quantum Mechanics
Abstract 17
Barbara A. Sanborn
Antioch College

Decimals,
Fractions, and Cycling Digits
Abstract 18
Patricia L. Johnson
Ohio Northern
University

11:30– 11:45

Category
of Bijective Mappings over the Finite Field of Size 8
Abstract 19
Zhijun Yin
The University of Akron

Enumeration
of Violating Configurations to the Sonar Sequence Property in 01 Matrices
Abstract 20
Christopher N. Swanson
Ashland University

The
Solution to the TwoEnvelope Paradox
Abstract 21
Ed Meyer
Baldwin Wallace
University

Abstracts of Contributed Papers
Friday 5:005:15
What Can We Do to Help?
Karen Mitchell
Marshall University
Abstract 1: The shortage of secondary math
teachers is so extreme that many states, including those in the Appalachian
region, have been forced to take extraordinary measures. How can college or university mathematics
faculty help address this shortage? This presentation will detail an alternate
certification project designed to help individuals acquire a knowledge base
that will better prepare them to teach high school mathematics.
Disparities in Childhood Mortality Rates in
the Great Lakes Region
Broderick Wagerson
The University of Michigan
Abstract 2: Childhood cancer rates have been rising
continuously since 1990. Using data from the Surveillance, Epidemiology and End
Results database we model and analyze variations in mortality and incidence
rates throughout the United States for the ages 019 and the five most
prevalent cancers. This work shows there are key differences among trends for
mortality and incidence rates among between age groups and cancer types
throughout the Great Lakes states and the whole U.S.
An Inequality for Motions with a Positive
Jerk
Aurel
Stan
The Ohio State University  Marion
Abstract 3: The HermiteHadamard inequality
says that if an object moves along a straight line with a positive jerk, then
the average velocity of the object over every finite time interval is greater
than the velocity at the midpoint of that interval, and less than the average
of the velocities at the two endpoints of the interval. We first present a
visual proof of this inequality, and then use the inequality to reprove some
sharp inequalities between the logarithmic mean and some Holder means of two
positive numbers.
Friday 5:205:35
Teaching
Statistics with Rmarkdown
Keshav Pokhrel
The University of MichiganDearborn
Abstract 4: Use of technology in the classroom
setting is not a new phenomenon these days. Teaching statistics is getting
challenging and interesting at the same time as the power of computing is
increasing almost every moment. We will discuss about the dynamic
documentation of computational outputs from a statistical software R using
Rmarkdown. This package will help students to see the statistical model
and the effects of change in a parameter instantaneously. In addition, we can
compile Rcode, Latex commands and pictures in the same document without any
hassles from importing and exporting the pictures. This could be a great
way to do homework, projects and share work with collaborators.
Changing
the Odds: Loaded Dice in a Probability Classroom
Russell W. Kincaid
Wilmington College
Abstract 5: Conventional dice were altered by the
insertion of weights for the purpose of creating dice that do not behave
according to the conventional rules of probability. The performance of these
dice was then characterized by students in the classroom through several
hundred experimental trials. These results were then compared against
theoretical calculations for one die rolls, two dice roll sums, and three dice
roll sums for conventional dice.
Baire's Lessons on Discontinuous Functions
Philip S. Blau
Shawnee State University
Abstract 6: Rene Baire's 1905 book on discontinuous
functions gives necessary and sufficient conditions for a function to be the
limit of a sequence of continuous functions. Baire first solves the problem for
functions of a single real variable and then for functions of n real variables.
Fundamental notions such as perfect sets, transfinite numbers, derived sets,
and dense sets are treated in the book, which shows the influence of Cantor's
work. Biographical facts will be given.
Friday 5:405:55
The Gompertz Dynamic Equation
Tom Cuchta
Fairmont State University
Abstract 7: The Gompertz (1st order, nonlinear)
differential equation describes a growth curve that is qualitatively different
than that of logistic growth: notably that its growth is not symmetric with
respect to its inflection point. Dynamic equations are an umbrella term that
encompasses differential equations, difference equations, qdifference
equations, and many others. We will provide a short overview of first order
dynamic equations and investigate a dynamic equation analogue of the Gompertz
differential equation.
Brain and Intelligence: Why Humans Are So
Dominant Part I
M. B. Rao
The University of Cincinnati
Abstract 8: What is intelligence? Can it be
measured across species? What is measurable across species? Some of these issues
will be discussed. A data set which provides body and brain weights for a
number of animals will be presented and analyzed. Some issues that arise in the
analysis will be discussed.
Sequences Converging to n^{th} Roots
Adam E. Parker
Wittenberg University
Abstract 9: Daniel Vargas, and 8th grader from
Texas, shared with me a sequence that appears to converge to the nth root of
k. For n=2, this algorithm is well known
from the theory of Pell's equations.
However, I had not seen this algorithm for general nth roots, nor have I
been able to find it cited anywhere. In
this talk I'll describe the sequence and discuss progress towards proving the
result, but I'm very interested if any audience members had seen this algorithm
before.
Friday 6:006:15
The Precession in the Perihelion of the
Orbit of Mercury
Harrison D. Potter
Marietta College
Abstract 10: The shift in the orbit of Mercury is a
famous confirmation of Einstein's theory of general relativity. This presentation will show how a differential
equation that describes the orbit of Mercury, which is simple enough to serve
as a classroom example, can be obtained from vector calculus and the
Schwarzschild metric. A straightforward
application of the PoincareLindstedt method, in combination with an
appropriate scaling and data from the NASA website, then yields the famous
result.
Brain and Intelligence: Why Humans Are So
Dominant Part II
M. B. Rao
The University of Cincinnati
Abstract 11: Some remedial steps will be undertaken
to resolve issues that arose in data analysis undertaken in Talk 1. An
interpretation of the analysis will be presented to explain our dominance.
Other data sets will be outlined that could throw light on our dominance.
The Beta Transmuted Pareto Distribution: Theory
and Applications
Sher B. Chhetri
Florida Atlantic University
Abstract 12: In this work, a new fiveparameter
betatransmuted Pareto distribution is introduced and studied. Some important
properties of the distribution are discussed and explicit formulas are derived
for the mean, mean deviation, entropy, orderstatistics and the reliability
analysis. The method of maximum likelihood is proposed to estimate the
parameters of the distribution. We illustrate the usefulness of the proposed
distribution by presenting its application to reallife data.
Saturday 10:5011:05
Transient Distribution of a 2 Dimensional
Random Walk
Barbara Margolius
Cleveland State University
Abstract 13: In this talk, we consider two
dimensional random walks that are defined in terms of a phase and a level.
There are a finite number of phases and an infinite number of levels in
the state space for the walk. We show connections between these random
walks and the traditional one dimensional random walk using generating
functions. The generating function for a one dimensional random walk can
be expressed as the product of two Poisson generating functions. The one
dimensional random walk generating function appears as part of the formula for
many two dimensional random walks.
A Shidoku Exercise for Abstract Algebra
Taylor Haydinger
Defiance College
Abstract 14: The Modern Abstract Algebra class at
Defiance College has been participating in a math circle type of exercise this
semester. It involves a simplified variation of Sudoku. I will be sharing what
we have discovered, some of our experiences along the way, and how it can apply
to algebra topics.
Polygonal Numbers that Are neither a Sum nor
a Difference of Two Prime Powers
Dan Baczkowski
The University of Findlay
Abstract 15: In 1742, the infamous Goldbach
conjecture states that every even integer > 3 can be written as the sum of
two primes (and hence can be written as the sum of two prime powers). In
1950, Erdos discovered integers not of the form 2^k + p with k a positive
integer and p a prime to answer a conjecture dating back to 1849 of de
Polignac. In recent work with an undergraduate collaborator, Justin
Eitner, we were able to prove there exists infinitely many triangular numbers
that cannot be written as the sum of two prime powers. Moreover, we were
able to prove the same holds, not only for the triangular numbers, but also for
infinitely many different polygonal number sequences.
Saturday 11:1011:25
The InducedSaturation Number of Cycles
Cathy Erbes
Hiram College
Abstract 16: A graph G is Hsaturated if it does not
contain H as a subgraph, but when any edge is added to G, H does appear as a
subgraph. The saturation number of H is the minimum number of edges in an
Hsaturated graph. In 2012, Martin and Smith generalized this to consider
induced copies of H. In this talk, we will present some results about the
inducedsaturation number of odd cycles and C_4, the cycle on four vertices.
Hamiltonian Dynamics: A Geometric Approach
to Classical and Quantum Mechanics
Barbara A. Sanborn
Antioch College
Abstract 17: This talk explains the fundamentals of
Hamiltonian systems and shows how the concept of a symplectic structure is
useful for understanding both classical and quantum dynamics. The theory of
geometric quantum mechanics describes a quantum system as a Hamiltonian
dynamical system with a complex projective Hilbert space as its phase space,
equipped with an extra Riemannian metric structure not found in classical
mechanics. This additional structure makes an appearance in the quantum
uncertainty principle.
Decimals, Fractions, and Cycling Digits
Patricia L. Johnson
Ohio Northern University
Abstract 18: When
expressed as decimals, many fractions have interesting repetends, and many of
these repetends form cyclic permutations of their digits. Using congruence modulo ten and theorems of
Fermat and Euler, one can predict the period of repeating decimals and classify
many fractions into cyclic “families.”
This was part of a topics course for middleschool math education majors
and so is accessible to all with knowledge of elementary number theory.
Saturday 11:3011:45
Category of Bijective Mappings over the
Finite Field of Size 8
Zhijun Yin
The University of Akron
Abstract 19: Nonlinear bijective mappings play an
important role in both system design and attack in the multivariate polynomial
public key cryptography. We will introduce the basic result over the GF(8) in
our research.
Enumeration of Violating Configurations to
the Sonar Sequence Property in 01 Matrices
Christopher N. Swanson
Ashland University
Abstract 20: An n x m sonar sequence is an n x m 01
matrix with exactly one 1 in each column such that all vectors between pairs of
ones are distinct. Given a 01 matrix
with exactly one 1 in each column, it fails to be a sonar sequence if and only
if it contains 1’s that form a (possibly degenerate) parallelogram. I will derive a formula for the number of
such distinct parallelograms.
The Solution to the TwoEnvelope Paradox
Ed Meyer
Baldwin Wallace University
Abstract 21: The TwoEnvelope Paradox is a problem
that impacts many fields; finance, mathematics, philosophy, economics and
specifically risk management. Basically,
if there are two envelopes with one that has twice as much money as the other,
if we define the amount in one envelope as x then the other envelope has an
average of 1.25x. To see this, let's
assume that you opened one envelope and it contained $20. Clearly, you should buy the other envelope
for $20, it has an average of $25. How
can one envelope be better than the other?
In my presentation I will reveal the solution to the paradox.