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## 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 Citation Click for BibTeX citation Flyer Click for a printable flyer

### 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 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 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 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 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 Citation Click for BibTeX citation Flyer Click for a printable flyer