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## 2010-2011 Academic Year Colloquium Schedule

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### September 2, 2010

 Title: The Rubik's Cube Speaker: David A. Reimann Associate Professor Department of Mathematics and Computer Science Albion College Albion, Michigan Abstract: For over 30 years people around the world have been captivated by the Rubik's cube. Why is it so popular? What makes it a good puzzle? This talk will cover the history and design of the cube, explore some mathematics related to the cube, discuss solving the cube, and explore some possible and impossible patterns. I will bring several cubes for the audience to play with after the talk. Location: Palenske 227 Time: 3:10 pm Citation Click for BibTeX citation

### September 9, 2010

 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: 3:10 Citation Click for BibTeX citation

### September 23, 2010

 Title: Mesocale Modeling of Damage Nucleation in Titanium Aluminum Grain Boundaries Speaker: Darren E. Mason Associate Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: Is there a way to predict when and where such failure occurs? In this talk I will discuss some recent research directed at providing answers to these critical real-world problems. After a brief tutorial on the basic math, physics, and metallurgy required to attempt to answer such questions, I will review prior work that used a well characterized patch of Titanium Aluminum (TiAl) to evaluate the utility of a scalar fracture initiation parameter (fip) to predict the relative resistance of grain boundaries to microcracking when subjected to stress. I will then discuss new research that has generalized the idea of a scalar fip to a physically motivated damage tensor D that measures the amount of physical damage that accumulates at stressed grain boundaries as they evolve through space and time. Local lattice curvature near the grain boundary, local elastic and plastic stress evolution, and accumulated dislocation content at the grain boundary are among the quantities considered. Then, using data generated from a three dimensional, nonlinear, crystal plasticity finite element simulation of the same experimental TiAl region, the ability of this the tensor D to predict the location of "weak" grain boundary locations where micro-cracking is likely to occur. This work is funded by the NSF Materials World Network Grant DMR-0710570, the Deutsche Forschungsgemeinschaft (DFG) Grant EI 681/2-1, and the Department of Mathematics and Computer Science at Albion College. Location: Palenske 227 Time: 3:10 Citation Click for BibTeX citation

### September 30, 2010

 Title: Random Hard Problems Speaker: Harold S. Connamacher Assistant Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: If it is easy to verify the solution to a problem, is it easy to solve that problem? This is the famous P vs NP problem. There are other important open questions we can ask. Is a uniformly randomm instance of a hard to solve problem still hard to solve? Are there specific structures in the solution space to a problem that will prevent certain algorithm techniques from working? This talk explores what is currently known about these questions, and we will use the well-known problems 3-SAT and factoring as examples. The talk will also introduce some new work in defining a random problem model that has many of the properties of 3-SAT but for which we can prove behavior that we observe experimentally but not yet prove for 3-SAT. Location: Palenske 227 Time: 3:10 Citation Click for BibTeX citation

### October 7, 2010

 Title: Grade School Triangles and Ailles' Rectangle Speaker: Jack Calcut Assistant Professor Department of Mathematics Oberlin College Oberlin, Ohio Abstract: In grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45-45-90 and 30-60-90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question and present an elegant complement, called Ailles' rectangle, that deserves to be in every geometry teacher's toolkit. Location: Palenske 227 Time: 3:10 Citation Click for BibTeX citation

### October 21, 2010

 Title: Are you smarter than a 19th century mathematician? Speaker: Timothy A. Sipka Associate Professor Mathematics and Computer Science Alma College Alma, Michigan Abstract: The Four Color Theorem is a simple and believable statement: at most four colors are needed to color any map drawn in the plane or on a sphere so that no two regions sharing a boundary receive the same color. It might be surprising to find out that mathematicians searched for a proof of this statement for over a century until finally finding one in 1976. In this talk, we'll consider the "proof" given by Alfred Kempe, a proof published in 1879 and thought to be correct until an error was found in 1890. You're invited to look carefully at Kempe's proof and see if you can do what many 19th century mathematicians could not do—find the flaw. Location: Palenske 227 Time: 3:10 Citation Click for BibTeX citation

### October 28, 2010

 Title: Spirals in Planes and Space Speaker: Aaron Cinzori Associate Professor and Chair Department of Mathematics Hope College Holland, Michigan Abstract: We'll explore an algorithm that takes $n$ points in $\mathbb{R}^2$ or $\mathbb{R}^3$ and produces a piecewise-linear spiral that uses the given points as its initial nodes. We generate further points in the spiral by repeatedly taking a convex combination of $m \le n$ (existing) points at a time. In particular, let $P_0,\ldots,P_{n-1}$ be the initial points, and let $0\le t_1, t_2, \ldots, t_m \le 1$ be fixed parameters with $t_1+t_2+\cdots+t_m=1$. Produce more points by using the formula $P_{k+n} = t_1P_k + t_2P_{k+1}+ \cdots + t_mP_{k+m-1}$ for each $k\ge 0$. We can then ask a lot of questions: Where does the spiral end up?, How long is it? When and how can we arrange things so that the segment lengths are a geometric series? What is the general behavior of the spiral as it approaches its limit? The tools we'll use will come from linear algebra, complex analysis, infinite series, and linear recurrences. We'll also talk a bit about how this problem evolved from a Problem of the Week to several REU projects and papers (including one in the Spring 2010 $\Pi$ME Journal). Location: Palenske 227 Time: 3:10 Citation Click for BibTeX citation

### November 4, 2010

 Title: Utility Theory and Deal or No Deal Speaker: Michael A. Jones Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, Michigan Abstract: Deal or No Deal was a prime time game show on the National Broadcasting Corporation network in which a Contestant selects one of 26 suitcases. Inside each suitcase is a different dollar amount; all 26 dollar amounts are known beforehand. In a series of rounds, the Contestant is asked to "deal" (in which she accepts a monetary offer from a Banker) or to "no deal" (in which she has to open a specified number of suitcases, thereby revealing the dollar amounts inside the suitcases). The game ends when either she accepts an offer or, after opening all of the suitcases except the one she selected at the outset, she receives the monetary amount in her selected suitcase. Because each suitcase may contain any of the fixed monetary amounts, selecting a suitcase is analogous to a lottery in which each value has an equal likelihood of being selected. Assuming the Banker's offer is based on a utility function that describes the Contestant's utility or value for money and incorporates the Contestant's view toward the risk of participating in the lottery, the Banker makes an offer so that the Contestant is indifferent between accepting the Banker's offer and continuing to play the game. In this talk, I will introduce the basics of utility theory and will explain how the Banker could use a utility function to determine an offer. I will demonstrate how data from televised episodes may be used to recover the utility function. Further, I will examine a paradoxical offer from NBC's online version of the game. A forthcoming paper of the same name is co-authored with Jennifer Wilson, New School University, New York. Location: Palenske 227 Time: 3:10 pm Citation Click for BibTeX citation

### November 11, 2010

 Title: Summer and Off-Campus Programs Speaker: David A. Reimann Associate Professor Department of Mathematics and Computer Science Albion College Albion, Michigan Abstract: Have you ever wondered if you can study mathematics and/or computer science off-campus? Either during the summer or during the academic year? Each year a number of high-quality academic opportunities are availableto Albion College students. Options include research/study internships at academic institutions both within the United States and abroad, numerous federal government agencies, and a number of government scientific laboratories.In this presentation we will tour a new portion of the Albion College Math/CS website that illustrates these various opportunities as well as provide adviceon how to apply, deadlines, any other pertinent information. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### November 18, 2010

 Title: Combinatorial Problems Arising from English Country Dance Speaker: Robert A. Messer Emeritus Professor Mathematics and Computer Science Albion College Albion, Michigan, USA Abstract: A popular form of folk dance is English country dance. In one simple English country dance, four couples dance as two groups of two couples. As the dance progresses, each couple moves to a new position and dances with another couple. Can you have such a dance where each couple dances in each of the four positions with each of the other three couples? What are other mathematical restrictions on such dances? Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### December 2, 2010

 Title: Student Presentations Speaker: Students Mathematics and Computer Science Albion College Albion, Michigan, USA Abstract: Robert Calvert, "Decoding the Enigma" Through my talk I will talk about the enigma's build, the main people involved in decoding it, and the methods used in decoding it. Cassie Labadie, "Incorporating Mathematical Museum Exhibits into Classrooms" How do you make learning math fun? Studies show that learning through traditional means, such as lecture and taking notes, does not make the information the students are gaining commit to memory. We will take a look at the importance of creative pedagogical practices in the classroom, and how you apply these to a math classroom. We will be focusing on different mathematical museums and museum exhibits that can be implemented in the classroom, and how you change both simple and complicated exhibits into fun learning experiences for students in the classroom. Culver Redd, "Meaningful Play: How Games Can Be Productive In Our Society" During this past October, I attended a conference at Michigan State University called Meaningful Play. This talk will disseminate my experience of this conference. Meaningful Play was held to display the potential for games to be used to enhance education, general learning, academic study, and many other aspects of our lives, as well as to examine the current state of the industry that creates games for these purposes. The results, ideas, and opinions expressed at this conference are, I believe, extremely valuable to students—particularly those with interest in computer science—as they detail the forefront of a quickly growing aspect of computer science, as well as one possible future for the educational systems of America and the world. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### January 27, 2011

 Title: Introduction to Decision Analysis Speaker: Gregory M. Saltzman Professor and Chair Department of Economics and Management Albion College Albion, MI Abstract: Decision analysis is a procedure for identifying, clearly representing, and formally assessing important aspects of a decision involving uncertainty. The procedure, developed by operations research and business professors, now is widely used in research evaluating medical treatments. Greg Saltzman, Professor of Economics and Management at Albion College, taught a course in 2008 and 2010 at the University of Michigan School of Public Health for medical researchers, "Cost Utility and Decision Analysis." He will present an introduction to decision analysis during his talk. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### February 3, 2011

 Title: Cops and Robbers on Graphs Speaker: Robert W. Bell Assistant Professor of Mathematics Department of Mathematics Michigan State University East Lansing, MI Abstract: Suppose G is a finite graph. Two players play a game on G as follows: one player takes n markers (which represent "cops") and assigns each one to a vertex of G; then the second player takes one marker (representing a "robber") and assigns it to a vertex of G. The players then alternate turns, each moving any number of his or her markers to adjacent vertices each turn. If a cop is moved to the same vertex as the robber, the cop player wins. If the robber player can always avoid such an outcome the robber player wins. Certainly the cop player can win on a given graph G if sufficiently many cops are at his disposal. But what is the fewest number of cops needed to guarantee that the robber can always be captured? This was a topic at a summer Research Experience for Undergraduates (REU) at Michigan State University in the 2010. The investigations of several of the participants will also be highlighted. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### February 10, 2011

 Title: Fractals : Hunting The Hidden Dimension Speaker: NOVA DVD Abstract: What do movie special effects, the stock market, heart attacks, and the rings of Saturn have in common? They all consist of fractals, irregular repeating shapes that are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, and even in the rhythm of the human heart. This video takes viewers on a fascinating quest with a group of pioneering mathematicians determined to decipher the rules that govern fractal geometry. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### February 17, 2011

 Title: Quadratic Approximations to Pi, or What if Archimedes Had Had Mathematica? Speaker: Mark Bollman Associate Professor Department of Mathematics and Computer Science Albion College Abstract: Archimedes (c. 287 BCE--c. 212 BCE) used polygons inscribed within and circumscribed about a circle to approximate pi. In this talk, we will extend his work by approximating the areas of circular sectors. This is done by adjoining parabolic segments to triangular subregions of his inscribed regular polygons. While much of the mathematics would have been familiar to Archimedes, the calculations involved quickly outstrip the computational power of ancient Greece, and so Mathematica is used to facilitate calculations. The method allows us to derive recurrence relations that can be used to approximate pi more accurately. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### February 24, 2011

 Title: From Atoms to Sky Scrapers: The Role of Crystallography in Deformation, Damage, and Fracture Speaker: Martin A. Crimp Professor Chemical Engineering and Materials Science Michigan State University East Lansing, MI Abstract: Why is copper soft and ductile while rock salt is hard and brittle? One would guess that the mechanical behavior of crystalline materials is inextricably linked to how their atoms are bonded, but just as important is how their atoms are arranged in crystal structures. Plastic (permanent) deformation is achieved through the motion of crystal defects, while failure through fracture results from the rupture of atomic bonds. In order to fully understand and optimize mechanical behavior of materials, it is therefore necessary to understand the arrangement of atoms. But how can we determine the positions of atoms in a material? Atomic arrangements are typically studied using diffraction techniques (x-ray, electron, neutron) by implementing Bragg&apos s Law and Structure Factor calculations to determine not only the size and shape of the unit cell, but also the atom positions and types within the unit cell. Armed with this information, it is possible to understand the details of mechanical behavior, in particular the anisotropic nature of plastic deformation. This talk will review and build on these concepts to illustrate how the macroscopic deformation and fracture behavior, and the ultimate performance of planes, trains, and automobiles, is a function of the crystallographic orientation distribution in both single and polycrystalline materials. Examples of the role of non-random crystallographic orientation distribution in the anisotropic behavior of a number of materials, including FeAl, TiAl, and Ti will be presented. The implications of this anisotropic behavior will be discussed. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### March 24, 2011

 Title: Fractals and Number Theory Speaker: Vivek Dhand Postdoctoral Fellow Department of Mathematics Michigan State University East Lansing, Michigan Abstract: We give several examples of interesting self-similar structures which appear in elementary number theory: visible points, Pascal's triangle, the dragon curve, and Pythagorean music. Location: Palenske 227 Time: 3:10 pm Citation Click for BibTeX citation

### March 31, 2011

 Title: Optimal Prediction: An overview of the history, applications, and potential directions Speaker: Albert Cohen Actuarial Specialist / Program Coordinator Department of Mathematics Michigan State University Abstract: Optimal prediction is about a decade old now, but has fast become one of the most exciting new areas in Optimal Stopping. The original paper by Graversen, Peskir, and Shiryaev showed, in an elegantly simple way, that one could compute the best time to stop a Brownian motion "as close as possible" to its ultimate maximum over a finite time interval. Since then, researchers have worked to extend this idea to other diffusions, different measures of "close", and to financial applications. In this talk, we review the original approach, extensions, and current research including the recent application to infinite horizon prediction The area is rich with potential for new research, and it is hoped that young mathematicians will be encouraged to read more on the subject after this talk. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 7, 2011

 Title: Unusual Behavior in Rubber Cubes Speaker: Darren E. Mason Associate Professor Mathematics and Computer Science Albion College Abstract: In this talk we will consider the mathematical problem associated with special linear deformations of an incompressible and nonlinear elastic cube. We will discover that the problem admits a wide variety of different solutions, depending on the magnitude and direction of external isotropic forces. To understand why certain solutions are preferred by nature, we will then study an associated energy minimization problem that leads to a selection criterion to determine the optimal deformed state of the cube. Finally, we will connect the mathematical appearences of these multiple solutions, natural and mathematical stability, and the fundamentals of bifurcation theory. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 21, 2011

 Title: Games and Their Connections to Numbers Speaker: Michael A. Jones Associate Editor Mathematical Reviews American Mathematics Society Ann Arbor, MI Abstract: I will show how optimal moves in the combinatorial games Nim, Wythoff, and Euclid are related to binomial representations of integers, the Fibonacci numbers, and a proof that the positive rational numbers are countable, respectively. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: Parallel Processing and It's Involvement in Making the Future Better Speaker: Neil Copeland Albion Computer Science Major Department of Mathematics and Computer Science Albion College Abstract: Parallel computing is a method in which many calculations can be carried out simultaneously. Not every algorithm or problem can gain an increase in speed from being executed in parallel. In recent years the bottlenecks of output of a single computer processor has increase a demand for multicore processors. At the same time our trusty graphics processors have helped in such acts of massive computation. Using these techniques there are global computation projects that you can use your very own equipment at home in order to help better understand illness and disease by simulating problems millions of time in order to exceed what was previously understood. Other applications include deep oil exploration and finances. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: Comparison of Quantization Results from Two-dimensional Cosmologies Quantized with Different Factor Orderings Speaker: Christopher Creighton Albion Mathematics and Physics Major Department of Mathematics and Computer Science Albion College Abstract: During the Big Bang, a point of infinite curvature of spacetime, the basic rules for how the universe behaves break down. While general relativity accurately describes the universe and the effects of gravity on the larger scale, it struggles with points of singularity such as the Big Bang. It needs to be infused with quantum mechanics, the rules of behavior for the very small, to explain the likes of the Big Bang and black holes. With quantum mechanics applied to general relativity, there arise ambiguities in the ordering of factors in the definitive equation for the state of the universe. To find out the proper ordering of factors, we turn to a computer model of the universe that has arguably made a good choice using a completely different methodology, simplified to the toy model of one space and one time dimension. We do this by comparing our varied possibilities to the computer model to try and ascertain hints to how our universe behaves in the realm of the very small. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: The Zoomba: Designing and Developing an Application to Control the iRobot Create Speaker: Shea McCavit Albion Computer Science Major Department of Mathematics and Computer Science Albion College Abstract: The development of a software program can often be a long and difficult task. I was recently part of a development team for the creation of an application to control the iRobot Create, which I call Zoomba. This application remote controls the speed, direction, and movement of the iRobot Create via an Android phone. This talk will discuss the design, implementation, coding, and testing of our application as well as give an overview of the software development process in general. I will also give a brief demonstration of how the application works. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: Working with Perl and SQL at OnRoto Fantasy Sports Speaker: Geoff Keyes Albion Computer Science Major Department of Mathematics and Computer Science Albion College Abstract: Fantasy sports have been extremely popular among sports fan for many years now, and starting this summer I was lucky enough to get a job with one of these companies. Running a fantasy sports website does not mean manually inputting stats in for each player and calculating each teams results, but instead writing software that will automatically handle all of this. Working at OnRoto Fantasy Sports, I had to learn the computer languages of Perl, C, and SQL to be able to write scripts to improve the website at OnRoto. I will focus on a few projects that I have completed over the past year including the new mobile site that is in the late development stages that I am currently working on. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: TBA Speaker: Nicholas Steigerwald Albion Mathematics Major Department of Mathematics and Computer Science Albion College Abstract: I will discuss the company MCP asset management from the the outside as well as the inside. I will discuss the decisions that are made by the workers of the company to make money as well as the decisions made by the company to choose quality clients. These decisions include people who they choose to allow to invest their money with as well as who they should accept money from. Both of these decisions involve who the company thinks is reliable and using legal means to acquire their money. Many possible clients and investors use questionable means to acquire and grow their money. Overall this is a dog eat dog market that can eat a company up quickly if they do not do reliable research on clients and investors. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: Using Integer Programming to Convert Image Files Speaker: Taylor Watkins Albion Mathematics Major Department of Mathematics and Computer Science Albion College Abstract: My Colloquium talk involves using binary programming to convert image files to pixel art. I created a model for choosing what values should be used in creating a smaller image based on the larger image. In order to get data for the image I used a program called Gimp to save it in a format that I could use and create a binary value matrix to base my function on. I used the program MPL to minimize the function that I created. Unfortunately I needed to split the problem into 4 problems because when I made the model I needed more variables to convert the image than I had. I took the result matrices and combined them and used the resulting matrix in Mathematica to create an image. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### April 28, 2011

 Title: Elementary School Math Education in China and the U.S. Speaker: Shu He Albion Mathematics Major Department of Mathematics and Computer Science Albion College Abstract: The oral talk will show the current situation and comparison of elementary school math education in China and US. I will focus on the differences and similarities in two different math education system by collecting data and information on the history of elementary school math education, the materials they are using for math study, teaching methods to inspire students interests in math. At the same time, I will show the importance of math education that affects students life. And finally, I will talk about the pros and cons of two different math education system and effects on students math ability. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation