2012-2013 Academic Year Colloquium Schedule

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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 well-known 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 graph-theoretic 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 Hamilton-Jacobi-Bellmann 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 performance---finding 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 large-scale traveling salesman problems can lead to beautiful continuous line drawings. We will conclude by presenting other examples of Opt Art---art 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 Near-Skolem 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 near-Skolem 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 hands-on 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

Title: Math in my World (Business to Politics)
Speaker:Art Kale, '71
Calhoun County Commissioner, Board Chair
Calhoun County
Albion, Michigan
Abstract:
Location: Palenske 227
Time: 3:30 PM
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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 envy-freeness). 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 Fair-Division Procedure, Mathematics Teacher 94 (3) 2004: 170-174. and Michael A. Jones, Equitable, Envy-free, and Efficient Cake Cutting for Two People and Its Application to Divisible Goods, Mathematics Magazine 75 (4) 2002: 275-283.
Location: Palenske 227
Time: 3:30 PM
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December 6, 2012

Title: Yo-Yo Trick Combinatorics
Speaker:Alexandra L. Sovansky, `13
Mathematics Major
Mathematics and Computer Science
Albion College
Albion, Michigan
Abstract: Oftentimes, multiple different yo-yo tricks can be done sequentially before the yo-yo 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 yo-yo trick combos, and also how real-world restrictions on yo-yo 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 mirror-reverse 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 Escher-like 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

Title:Careers in Mathematics and Computer Science
Speaker:David A. Reimann
Associate Professor
Mathematics and Computer Science
Albion College
Albion, MI, USA
Abstract:A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation. Slides from the talk are available at http://zeta.albion.edu/~dreimann/talks/careers/careers.html.
Location:Palenske 227
Time:3:10 PM
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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 large-scale 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 cyber-activities (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 long-term 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 least-squares regression, stepwise regression, weighted least-squares, zero-inflated 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 long-term 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 eight-sided dice instead of six-sided. 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 discrete-time 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 8-year-long 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 discrete-state 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
  1. 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 294:602-605.
    http://www.andrews.edu/~henson/HensonEtAlScience2001.pdf
  2. 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 71:277-303.
    http://www.andrews.edu/~henson/EcoMongr01.pdf
  3. 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 270:1549-1553.
    http://www.andrews.edu/~henson/MeanModeReprint.pdf
  4. 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 model-predicted patterns revealed in population data. Proceedings of the National Academy of Sciences 101:408-413.
    http://www.andrews.edu/~henson/PNAS2004.pdf
Location: Palenske 227
Time: 3:30 PM
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