20122013 Academic Year Colloquium Schedule 

September 6, 2012
Title: 
Point of View: Scientific Imagination in the Renaissance (Program 3 from The Day the Universe Changed)

Speaker:  James Burke (Virtual)
Science Historian
James Burke Institute

Abstract: 
The introduction of perspective techniques transforms Europe's use of art, architecture,
geography and navigation among others with its revolutionary concept of remote positioning.
Available on YouTube.

Location: 
Palenske 227

Time: 
3:30 PM

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September 13, 2012
Title: 
On God's Number(s) for Rubik's Slide

Speaker:  Brittany Shelton
Ph.D. Candidate
Mathematics Department
Lehigh University
Bethlehem, PA

Abstract: 
Rubik's Slide is a puzzle which consists of a $3 \times 3$ grid of squares that is reminiscent of a face of the wellknown cube. Each square may be lit one of two colors or remain unlit. The goal is to use a series of moves, which we view as permutations, to change a given initial arrangement to a given final arrangement. Each play of the game has different initial and final arrangements.
To examine the puzzle, we use a simpler $2 \times 2$ version of the puzzle to introduce a graphtheoretic approach, which views the set of all possible puzzle positions as the vertices of a (Cayley) graph. For the easy setting of the puzzle, the size of the graph depends on the initial coloring of the grid. We determine the size of the graph for all possible arrangements of play and determine the associated god's number (the most moves needed to solve the puzzle from any arrangement in the graph). We provide a Hamiltonian path through the graph of all puzzle arrangements that describes a sequence of moves that will solve the easy puzzle for any initial and final arrangements. Further, we use a computer program to determine an upper bound for god's number associated to the graph representing the medium and hard versions of the puzzle.
This is joint work with Michael A. Jones, Mathematical Reviews, Ann Arbor MI and Miriam Weaverdyck, Bethel College, North Newton KS.

Location: 
Palenske 227

Time: 
3:30 PM

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September 20, 2012
Title: 
Planning for Graduate Study in Mathematics and Computer Science

Speaker:  David A. Reimann
Associate Professor
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation.

Location: 
Palenske 227

Time: 
3:30

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September 27, 2012
Title: 
Tessellations and Symmetries of the Plane

Speaker:  David A. Reimann
Associate Professor
Mathematics and
Computer Science
Albion College
Albion, Michigan

Abstract: 
Pattern, repetition, and symmetry play important roles in the aesthetics of imagery. Tessellations use patterns of repeated geometric shapes to cover the plane. Uniform tessellations use regular polygons to cover the plane with no gaps or overlaps. The polygons in such tessellations can be decorated in such a way to give rise to interesting visual patterns. The inherent symmetry of regular polygons gives rise to tessellations containing symmetry patterns. Example symmetric tessellation patterns will be presented. An explanation of algorithmic techniques for constructing uniform tessellations will also be presented.

Location: 
Palenske 227

Time: 
3:30 PM

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October 4, 2012
Title: 
Stochastic Optimal Control Models for Online Stores

Speaker:  Albert Cohen
Actuarial Program Director
Mathematics AND Statistics and Probability
Michigan State University
East Lansing, MI

Abstract: 
We present a model for the optimal design of an online auction/store by
a seller. The framework we use is a stochastic optimal control problem. In
our setting, the seller wishes to maximize her average wealth level, where
she can control her price per unit via her reputation level. The corresponding
HamiltonJacobiBellmann equation is analyzed for an introductory case,
and pulsing advertising strategies are recovered for resource allocation.
Paper is available on ArXiv at http://arxiv.org/pdf/1103.1918.pdf

Location: 
Palenske 227

Time: 
3:30 PM

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October 11, 2012
Title: 
Rational Approximations of $\sqrt{2}$:
An Introduction to Isosceles Almost Right Triangles

Speaker:  David Friday, '04
Instructor
Mathematics
Macomb Community College
Clinton Township, Michigan

Abstract: 
While visiting the Calculus and Physical Sciences Tutorial Lab at Grand Rapids
Community College, a question was posed: for what values of
$n$ will the sum of the first $n$
positive integers be a perfect square? A thorough investigation of the problem and the
introduction of the concept of an isosceles "almost" right triangle yielded a number of
interesting results. One of the results involves a sequence of rational numbers that converges to $\sqrt{2}$,
yielding some excellent approximations.

Location: 
Palenske 227

Time: 
3:30 PM

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October 25, 2012
Title: 
Opt Art

Speaker:  Robert Bosch
Mathematics
Oberlin College
Oberlin, Ohio

Abstract: 
Optimization is the branch of mathematics concerned with optimal performancefinding the best way to complete a task. It has been put to good use in a great number of diverse disciplines: advertising, agriculture, biology, business, economics, engineering, manufacturing, medicine, telecommunications, and transportation (to name but a few). In this lecture, we will showcase its amazing utility by demonstrating its applicability in the area of visual art, which at first glance would seem to have no use for it whatsoever! We will begin by describing how to use integer programming to construct a portrait out of complete sets of double nine dominoes. We will then describe how high quality solutions to certain largescale traveling salesman problems can lead to beautiful continuous line drawings. We will conclude by presenting other examples of Opt Artart constructed with the assistance of mathematical optimization techniques.

Location: 
Palenske 227

Time: 
3:30 PM

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November 1, 2012
Title: 
Skolem, Langford, Extended, and NearSkolem Sequences, Oh My!

Speaker:  Heather Jordon
Associate Editor
Mathematical Reviews
Ann Arbor, MI

Abstract: 
A Skolem sequence of order $t$ is a sequence $2t$ integers such that each integer between 1 and $t$ appears twice and two instances of the integer $k$ are $k$ apart. For example, 5242354311 is a Skolem sequence of order 5. These sequences, and their generalizations, are very interesting from a combinatorial point of view and have many applications. In this talk, we will discuss Skolem sequences and some generalizations: extended, Langford, and nearSkolem sequences. We will also discuss a few applications of these sequences, including integer partitioning
and graph decompositions.

Location: 
Palenske 227

Time: 
3:30 PM

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November 8, 2012
Title: 
Symmetry + Cardboard = Sculpture

Speaker:  George W. Hart
Sculptor and Mathematician
New York, New York

Abstract: 
George Hart, the
designer of the sculpture Comet!, which hangs in the
science complex atrium,
will return to Albion for a handson workshop on mathematical sculpture.
During his visit to Albion, he will lead participants in a hands on construction of a brand new never seen geometrical sculpture. During the workshop, the mathematical ideas behind the sculpture will be explained and participants will build their own personal sculpture with playing cards. For other examples of his work, see
georgehart.com.

Location: 
Palenske 227

Time: 
3:30 PM

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November 15, 2012
November 29, 2012
Title: 
What does Fairness have to do with Cake and Chicken?

Speaker:  Michael A. Jones
Associate Editor
Mathematical Reviews
Ann Arbor, MI

Abstract: 
The Adjusted Winner procedure is a fair division procedure used to divide contested items between two people so that the allocation satisfies three desirable properties (efficiency, equitability, and envyfreeness). After reviewing these properties and the procedure, I'll explain how the procedure is related to cake cutting. Further, exploiting information and manipulating the Adjusted Winner procedure is an example of the game of Chicken.
This talk combines ideas from two previously published papers:
Michael A. Jones and Stanley F. Cohen, Fairness: How to Achieve It and How to Optimize in a FairDivision Procedure, Mathematics Teacher 94 (3) 2004: 170174.
and
Michael A. Jones, Equitable, Envyfree, and Efficient Cake Cutting for Two People and Its Application to Divisible Goods, Mathematics Magazine 75 (4) 2002: 275283.

Location: 
Palenske 227

Time: 
3:30 PM

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December 6, 2012
Title: 
YoYo Trick Combinatorics

Speaker:  Alexandra L. Sovansky, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
Oftentimes, multiple different yoyo tricks can be done
sequentially before the yoyo returns to the user's hand. Tricks can
be done like that due to the fact that some tricks end where others
begin, and vice versa. If we take these common start/end points to be
nodes on a directed graph, all sorts of possibilities for mathematical
examination open up. In this talk, we will look at how interesting
parts of graphs (such as cycles) translate into yoyo trick combos,
and also how realworld restrictions on yoyo trick combos affect what
we can do with the graphs.

Location: 
Palenske 227

Time: 
3:30 PM

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December 6, 2012
Title: 
An Introduction to Fractals

Speaker:  Marc Winter, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
This presentation intends to cover the basics of what a fractal is. Since fractals don't tend to have
integer dimensions like we are used to this will include how to determine the dimension of fractals. We
will also discuss some simpler fractals that are easy to conceptualize many of these will come from a
group of fractals known as the polygaskets. The polygaskets are fractals that are based on recursively
using a polygon shape to create them. A prime example of these is Sierpinski's triangle which is a fractal
based off of a triangle.

Location: 
Palenske 227

Time: 
3:30 PM

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January 31, 2013
Title: 
Necessity and Scope in the Logic of Quantification

Speaker:  Jeremy Kirby
Associate Professor
Philosophy
Albion College
Albion, MI

Abstract: 
When I say "Eight is necessarily greater that seven," I state something that is true. In contrast, when I say "The number of planets is necessarily greater than seven," I say something that is false. (We can conceive of a smaller solar system, indeed at times the number of planets is revised.) Furthermore, the locutions "eight" and "the number of planets" seem to pick out the same thing? How can it be both true and false of the same thing that it is necessarily greater than seven?

Location: 
Palenske 227

Time: 
3:30 PM

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February 7, 2013
Title: 
The $25,000,000,000 Eigenvector

Speaker:  Dawn Archey
Assistant Professor of Mathematics
Mathematics and Software Engineering
University of Detroit Mercy
Detroit, MI

Abstract: 
This talk will describe the mathematics behind Google's page rank algorithm. We will see how Google sets up and solves an
eigenvector problem to decide which of the web pages containing your search terms are most relevant. The talk will also touch briefly on graph theory and computational complexity.

Location: 
Palenske 227

Time: 
3:30 PM

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February 14, 2013
Title: 
The Trivial Owl Bundle on a Goat

Speaker:  Rachel Maitra
Visiting Assistant Professor
Physics
Albion College
Albion, MI

Abstract: 
In this colloquium, we will see how to construct not only the trivial owl bundle on a goat (and a bonus nontrivial owl bundle), but a fish tank that can mirrorreverse your fish. Fiber bundles are more than just something you should be eating for breakfast every day. They can be used to describe and construct forces of nature in this universe and the next. They are also good for hours of pure topological fun.

Location: 
Palenske 227

Time: 
3:30 PM

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February 21, 2013
Title: 
The Math and Algorithms behind TesselManiac and Tessellations

Speaker:  Kevin Lee
Instructor Math/CSCI
Math/CSCi
Normandale Community College
Bloomington, Minnesota

Abstract: 
Modern computer graphics cards have GPUs (graphic processing units) that can do several hundred million calculations per second. I will demonstrate my new algorithms that exploit this power to create and animate Escherlike tessellations (tilings) of the plane in real time. Besides being fun, the animations dramatically illustrate the geometry behind the tessellations. I will also discuss how parametric equations, symmetry groups, homogenous coordinates, linear algebra, computational geometry, computer graphics, and data structures all come together to create the algorithms behind the animations. TesselManiac is my third major tessellation program, my previous programs include TesselMania and Tessellation Exploration.

Location: 
Palenske 227

Time: 
3:30 PM

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February 28, 2013
March 7, 2013
Title: 
Computer Security Visualization and Economics of Security

Speaker:  Dr. Qi Liao
Assistant Professor
Computer Science
Central Michigan University
Mount Pleasant, Michigan

Abstract: 
In this talk, I will give a brief overview of a few current research projects on two important topics: 1) security data analysis and visualization, and 2) economics of computer security. In the first part, I will focus on anomaly detection in largescale networks. Algorithms in graph theory, graph data mining and graph visualization techniques can be useful, in which automation is combined with knowledge from domain experts. Through demos and case studies, I will show the tools we developed and their usefulness in situation awareness, network management and security investigation. In my second part of talk, I will approach computer security from a different angle, i.e., economic perspective. Most hard security problems are essentially economic problems. Given that money is perhaps the single determining force driving the growth of many malicious cyberactivities (such as botnet attacks), we propose interesting economic approaches to take away the root cause of botnets, i.e.,
the financial incentives. In addition, many security problems involve interactions between attackers and defenders. This can be naturally modeled in a game theoretical framework and Nash equilibria may be derived. Through modeling security problems in economic model, we show their usefulness for better understanding and ultimately solving the security problems.

Location: 
Palenske 227

Time: 
3:30 PM

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March 28, 2013
Title: 
Azerbaijan and the Peace Corps

Speaker:  Jarrett Dunn, '09
East Leroy, Michigan

Abstract: 
In September 2010 I began a 27 month long journey to Azerbaijan as a Peace Corps volunteer working in Youth Development. As some in the audience may not know anything about Azerbaijan or the Peace Corps, we will first discuss Azerbaijan's geographic location, brief history, holidays, national meals, the people and culture. Secondly, we will discuss Peace Corps' goals and mission, my work as a Youth Development volunteer, and how to apply. This talk will consist of many pictures with the aim of giving the audience a visual understanding of Azerbaijan. The goals of this talk is to give the audience a better understanding of Azerbaijan, to learn more about Peace Corps and the life of a Peace Corps volunteer, and to perhaps inspire a few to consider Peace Corps service.

Location: 
Palenske 227

Time: 
3:30 PM

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April 4, 2013
Title: 
Take Time to Smell the Prairie Rose Gentians: Statistical analysis of a longterm population data set

Speaker:  Nadiya Fink
Mathematics and Computer Science
Albion College

Abstract: 
Seven populations of prairie rose gentian in Illinois were studied for as many as 18 years to understand what environmental influences impact population numbers. Multiple leastsquares regression, stepwise regression, weighted leastsquares, zeroinflated models for count data and negative binomial regression were examined to determine the most appropriate statistical analysis. Years following disturbance, and spring precipitation were concluded to be significant predictors of the number of plants occurring in the growing season.

Location: 
Palenske 227

Time: 
3:30 PM

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April 11, 2013
Title: 
Breaking Chaos

Speaker:  Ryan Huddy
Graduate Student
Mathematics
Clarkson University
Potsdam, New York

Abstract: 
In mathematics, chaos can be defined as a deterministic dynamical system which has aperiodic longterm behavior and exhibits sensitive dependence on initial conditions. Surprisingly, such systems can be coupled together and made to synchronize. If their communication is delayed, this chaotic behavior can also be broken and stable periodic behaviors will emerge from the coupled system. Join me as we study the basics of chaotic systems and explore some examples of the synchronization of chaos (with and without delay).

Location: 
Palenske 227

Time: 
3:30 PM

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April 25, 2013
Title: 
Proving Zero Equals One

Speaker:  Jeremey Yu, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
In this talk I will provide a number of proofs that attempt to show that zero and one are
actually the same number. Some proofs are more serious while others are more comedic in nature.
The "purpose" behind all of this is to explore the importance of knowing the underlying
principles of the math involved in solving a problem.
The actual purpose is to be mildly entertaining.

Location: 
Palenske 227

Time: 
3:30 PM

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April 25, 2013
Title: 
Mathematical Models for treating Diabetes Mellitus

Speaker:  Jacqueline Chung, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
Diabetes Mellitus is an autoimmune disease characterized by the depletion of the pancreatic $\beta$
cells responsible for the production of insulin in the human body. However, an early diagnosis of
diabetes will allow the individual to adopt therapies that in turn will help postpone certain serious
effects for later. Using ordinary differential equations, partial differential equations, and matrix
analysis mathematical models of glucose and insulin kinetics have been developed that deal with
different aspects of diabetes. In this presentation, I hope to further your understanding of a few
of them and the way these models help predict and determine the pathology of the disease suffered
by the individual.

Location: 
Palenske 227

Time: 
3:30 PM

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April 25, 2013
Title: 
A Dialogue between Additive Functions and Squared Rectangles

Speaker:  Mingjia Yang, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
Rectangles that can be partitioned into squares are called squared rectangles.
This talk will demonstrate and prove one surprising property of squared rectangles:
the ratio of width/length is rational!
Which means, if we have a rectangle of width $\sqrt{2}$ and length 0.8 (of the same unit),
then we know this rectangle cannot be squared! We will go over a proof of this result using
additive functions. The proof itself is almost as beautiful as the result,
since we see how different areas of mathematics interact with each other in a deep way.

Location: 
Palenske 227

Time: 
3:30 PM

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April 25, 2013
Title: 
Spider Craps: Simulation and Statistical Analyses of Game Variations

Speaker:  Jacob Engel, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
Since the establishment of casino table games such as Craps, Black Jack, and Roulette,
mathematicians and gambling enthusiasts have been seeking to create the next big game.
Some game developers choose to create variations of original casino games. Spider Craps,
a game variation created during FURSCA 2011, is a variation of the original game Craps
that uses eightsided dice instead of sixsided. In order to calculate the odds of certain bets,
a Java simulation was created. An undergraduate thesis was written about the game as well.
The rules of Spider Craps and a short explanation of the simulation are included in this talk.
Also, a Markov chain analysis to find the average length of the shooter's hand was preformed,
and its results will be discussed.

Location: 
Palenske 227

Time: 
3:30 PM

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May 2, 2013
Title: 
Chaotic Dynamics and Lattice Effects Documented in Experimental Insect Populations

Speaker:  Shandelle M. Henson
Professor and Chair
Department of Mathematics
Andrews University
Berrien Springs, MI

Abstract: 
Guided by the predictions of a discretetime mathematical model, we induced a sequence of bifurcations (dynamic changes) in laboratory insect populations by manipulating one of the biological parameters in the system. In particular, we were able to induce chaotic dynamics. The data from these 8yearlong time series show the fine structure of the deterministic chaotic attractor as well as lattice effects (dynamic effects arising from the fact that organisms come in discrete units). We show that "chaos" is manifest in discretestate noisy biological systems as a tapestry of patterns that come from the deterministic chaotic attractor and the lattice attractors, all woven together by stochasticity.
References
 Henson, S. M., Costantino, R. F., Cushing, J. M., Desharnais, R. F., Dennis, B., and A. A. King 2001. Lattice effects observed in chaotic dynamics of experimental populations. Science 294:602605.
http://www.andrews.edu/~henson/HensonEtAlScience2001.pdf
 Dennis, B., Desharnais, R. A., Cushing, J. M., Henson, S. M., and R. F. Costantino 2001. Estimating Chaos and Complex Dynamics in an Insect Population. Ecological Monographs 71:277303.
http://www.andrews.edu/~henson/EcoMongr01.pdf
 Henson, S. M., King, A. A., Costantino, R. F., Cushing, J. M., Dennis, B., and R. A. Desharnais 2003. Explaining and predicting patterns in stochastic population systems. Proceedings of the Royal Society of London B 270:15491553.
http://www.andrews.edu/~henson/MeanModeReprint.pdf
 King, A. A., Costantino, R. F., Cushing, J. M., Henson, S. M., Desharnais, R. A., and B. Dennis 2004. Anatomy of a chaotic attractor: Subtle modelpredicted patterns revealed in population data. Proceedings of the National Academy of Sciences 101:408413.
http://www.andrews.edu/~henson/PNAS2004.pdf

Location: 
Palenske 227

Time: 
3:30 PM

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