201516 Academic Year Colloquium Schedule
September 10, 2015 

Title:  Counting Without Seeing 
Speaker:  Eric Kamischke Mathematics & Engineering Jackson College Jackson, MI 
Abstract:  The National Park Service asked for an estimate of the number of elk taken by the wolves introduced to the park. As there was no method guaranteed to find all the kills in the wilds of the park, a design was created to estimate what was not seen. The estimate involved a double count procedure, logistic regression modeling and parameter approximation. Once the estimate was found, the search and verification of the standard error involved delta methods, bootstrapping and simulation. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
September 17, 2015 

Title:  Planning for Gradute Study in Mathemaitics and Computer Science 
Speaker:  David A. Reimann, Professor Albion College 
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 p.m. 
Citation:  BibTeX citation 
September 24, 2015 

Title:  The Mathematical Connection between Patterns in Moorish Architecture and the Artwork of M.C. Escher 
Speaker:  David A. Reimann, Professor Albion College 
Abstract:  The Mathematical structure of symmetrical patterns can be studied using group theory. The Moors built many magnificent buildings richly decorated with geometic patterns during their rule of the Iberian peninsula (7111492). The graphic artist M.C. Escher visited southern Spain in 1922 amd was capitivated by the patterns that richly decorate the archtecture of the Alhambra, Alcazar, and other Moorish building. After a second visit to Spain in 1935, Escher became obsessed with creating patterns of interlocking figures based on these elaborate tiling patterns. While Escher had no formal mathematical training, he used mathematical methods grounded in scientific literature to study these patterns. We will view these patterns through the lens of group theory, one of the great mathematical accomplishments of the 19th century. This talk will be highly visual with many pictures of Escher's work and Moorish architecture. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
October 1, 2015 

Title:  Finding the Best Way From Here to There  A Primer on Variational Calculus 
Speaker:  Darren Mason, Professor Albion College 
Abstract: 
Given a task to accomplish, it is natural to ask what is the best way to achieve your goal? Maybe you are flying from Beijing to London and need the shortest flight path. Or you are selling fuel and you want to find the optimal time t to sell it so that you can maximize your profit. Or you are crossing a river with a strong current and want to determine a propeller direction (as a function of time) so that you cross the river in the least amount of time. The number of possible questions of this type seems endless. During this lecture we will discuss some of the above problems, a famous brainteaser called the brachistochrone problem, and illustrate how to find solutions to these problems using a version of calculus that makes sense in infinite dimensions — the interesting field of variational calculus! 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
October 8, 2015 

Title:  Spider Craps: Mathematical Development of the New Casino Games 
Speaker:  Dr. Mark Bollman, Professor Albion College 
Abstract: 
Games of chance have been found in the relics of ancient cultures for as far back as one cares to look. The popular game of craps, played with two sixsided dice, traces its origins to the Old English game of Hazard, which was then transplanted to New Orleans by French settlers and evolved into one of the most popular casino table games. This talk will describe research in both theoretical and experimental probability that modified craps to use eightsided dice, leading to the invention of a new game called "Spider Craps". Mathematical points of interest for casino game developers including reasonable win probabilities, a meaningful house advantage, and efficient gameplay will be described. This research was carried out under a grant from Albion College's Foundation for Undergraduate Research, Scholarship, and Creative Activity (FURSCA) with recent Albion alumnus Jacob Engel. 
Location:  Palenske 227 
Time:  3:30 PM 
Citation:  BibTeX citation 
October 15, 2015 

Title:  Pizza and Pamphlets 
Speaker:  Bring your friends, bring your questions; bring your schedule! 
Abstract: 
Pizza and Pamphlets is the event where the Mathematics and Computer Science Department provides information about spring courses in Mathematics and Computer Science. All Math majors/minors, Computer Science minors, Math/Physics majors, Math/Econ majors, prospective majors, and friends of the department are invited to join us. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
October 22, 2015 

Title:  Building Better Biological Models 
Speaker:  Elizabeth Skubak Wolf, Assistant Professor 
Abstract: 
Randomness is inherent in many biological processes, from the dynamics of the populations in an ecosystem down to the systems of biochemical reactions occurring within a single cell. Therefore, when trying to analyze these processes, we might consider using a stochastic model — that is, one that includes some form of randomness. Can stochastic models behave significantly differently from deterministic models? (Yes!) What might a stochastic model look like? How exactly does one use a stochastic model to say anything useful? We'll look at a few biological examples, introduce a particular stochastic model called a Markov chain, and see how, using a tool called Monte Carlo simulation, we can gain some insight into the biological systems we model. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
October 29, 2015 

Title:  The weak cop number of a graph 
Speaker:  Robert Bell The weak cop number of an infinite graph Lyman Briggs College & Department of Mathematics Michigan State University East Lansing, MI 
Abstract:  The cop number of a finite graph G is defined as the minimal number of cops a player needs to capture an opponent's robber in a game of cops and robbers on G. In this game, the cop player places each of her cop pawns on vertices of G; and then the opponent places his robber pawn on a vertex of G. Both players have complete information about G and the location of the pawns. The players alternate turns, with the cop player playing first, by moving any number of his or her pawns along edges of G to adjacent vertices. If a cop is moved to the same vertex as the robber, then the robber is captured. In this talk, we explore the notion of a weak cop number due to Florian Lehner. Suppose G is a possibly infinite graph. The weak cop number of G is the minimal number of cops needed to either capture the robber or prevent the robber from visiting any vertex of G infinitely often. We compute the weak cop numbers of several families of infinite graphs, extend several theorems to this new setting, and give examples of how some of the foundational theorems for finite graphs fail to extend to infinite graphs. In particular, we will outline how one can bound the weak cop number of a connected, countable, locally finite planar graph. This is joint work with undergraduate participants in the 2015 summer REU program at MSU. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
November 5, 2015 

Title:  Random Chess: Piece Strength; End Games; and Large Sparse Eigenvalue Problems 
Speaker:  Allan Struthers, Professor Mathematical Sciences, Michigan Technological University 
Abstract:  Chess books all include an assessment of the relative strength of pieces and a detailed analysis of various end game situations. Modern computer algebra systems make it easy to build transition matrices for random walks by various pieces on chess boards. The eigenvectors of these large sparse matrices quantify piece strength and provide interesting endgame information. The talk will provide all necessary background in both Chess and Linear Algebra. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
November 12, 2015 

Title: 
TwoColored Motzkin Paths, Set Partitions and Restricted Growth Functions 
Speaker: 
Samantha Dahlberg, Mathematics  Michigan State University 
Abstract: 
This talk is based on the research done with a Research Experience for Undergraduates (REU) group at Michigan State University in the summer of 2014. The goal of this talk is to first introduce three commonly studied objects in combinatorics: set partitions, restricted growth functions (RGFs) and twocolored Motzkin paths. We will introduce and explore these seemingly different objects, but we will find that they are actually closely related to each other. This is joint work with Robert Dorward, Jonathan Gerhard, Thomas Grubb, Carlin Purcell, Lindsey Reppuhn, and Bruce Sagan. 
Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 
November 19, 2015 

Title:  Tennis Rankings over Time 
Speaker:  Michael A. Jones, Associate Editor Mathematical Reviews 
Abstract: 
In 2010, Kim Clijsters won the U.S. Open, but had her world ranking drop from #3 to #5 by the Women's Tennis Assocation (WTA). How can a tennis player win a tournament but drop in the rankings? The WTA uses a moving window to determine the rankings. We explain how discounting older results in the window can prevent such counterintuitive behavior and consider geometric and arithmetic discounting methods. We examine real data from the WTA, and comment on discounting methods already in use by the Federation Internationale de Football Association (FIFA) for ranking national teams for the World Cup and by the Professional Golf Association for ranking golfers. This talk is based on joint work with Alex Webb (undergraduate at Macalaster College) and Jennifer Wilson (Eugene Lang College, New School University).

Location:  Palenske 227 
Time:  3:30 p.m. 
Citation:  BibTeX citation 