The Michigan Section of the Mathematical Association of America and MichMATYC 91st Annual Meeting Hope College Holland, Michigan April 10–11, 2015 Michigan Section of the Mathematical Association of America 2014-2015 Officers and Staff Chair Michele Intermont, Kalamazoo College 4-Yr Vice Chair Brian Snyder, Lake Superior State University 2-Yr Vice Chair Jan Roy, Montcalm Community College Sec/Treas Mark Bollman, Albion College Governor Matt Boelkins, Grand Valley State University Past Chair Steve Blair, Eastern Michigan University Newsletter Ed Katie Ballentine, Mathematical Reviews Co-Dir. MMPC Kim Rescorla, Eastern Michigan University Carla Tayeh, Eastern Michigan University Webmaster Stephanie Edwards, Hope College Liaison Coord David Austin, Grand Valley State University PIO Robert Xeras, Siena Heights University, retired 2015 Annual Meeting Program Committee Chair Brian Snyder, Lake Superior State University Members Eddie Cheng, Oakland University Stephanie Edwards, Hope College Jan Roy, Montcalm Community College 2015 Annual Meeting Local Arrangements Committee Chair Stephanie Edwards, Hope College Members Aaron Cinzori, Hope College Darin Stephenson, Hope College Todd Swanson, Hope College MichMATYC 2014-2015 Officers and Staff President Jack Rotman, Lansing Community College Past President Bernard Cunningham, Mott Community College Sec/Treas Jeff Morford, Henry Ford Community College President Elect Doug Mace, Kirtland Community College Webmaster Mark Pelfrey, Southwestern Michigan College 2015 Joint MAA/MichMATYC Meeting, Hope College Friday, April 10, 2015 1:15-2:15 PM Registration (Maas Conference Room) 2:15-3:20 PM Welcome and Opening Plenary (Maas Auditorium) Bill Cook, University of Waterloo A Salesman's Tour of Combinatorial Optimization 3:25-4:00 PM Room 4:05-4:25 PM Local Invited Lecture (Maas Auditorium) Eric Mann, Hope College Changing the Culture: Developing Creative Problem Solvers MMC 158 Local Invited Lecture (MMC 158) Allen Schwenk, Western Michigan University Mathematical Induction: The Good, the Bad and the Ugly MMC 159 Steve Bacinski, Davenport Steve Schlicker, Grand Valley State University University Applied MATLAB Projects A Geometry of Sets for Linear Algebra Students Michigan Undergraduate Mathematics Conference 4:30-4:50 PM 5:00-5:30 PM 5:30-6:30 PM 6:30-9:00 PM MMC 240 Allan Bickle, Calvin College MegaMenger Graphs Paul Pearson, Hope College An Interactive Introduction to WeBWorK W C Abram and Kadeem Noray*, Hillsdale College Political Corruption and Public Advocacy: An Evolutionary Game Theoretic Analysis Business Meeting (MMC 159) Social Hour (AlpenRose Restaurant) Banquet and Plenary Lecture (AlpenRose Restaurant) Bob Devaney, Boston University The Fractal Geometry of the Mandelbrot Set Saturday, April 11, 2015 8:00-8:40 AM Breakfast and Registration (Maas Auditorium) 8:45-9:40 AM Plenary Lecture (Maas Auditorium) Ben Collins, University of Wisconsin - Platteville Basel and Beyond: An Incomplete History of a Famous Sum 9:45 - 10:20 AM 10:30-11:10 AM Location Local Invited Lecture (Maas Auditorium) Jack Rotman, Lansing Community College Curricular Change and Collaboration Across Institutions Local Invited Lecture (Maas Conference Room) Tim Pennings, Davenport University Elvis Lives: Mathematical Surprises Inspired by Elvis, the Welsh Corgi Break - Sponsored by Cengage Learning MMC 158 MMC 159 MMC 237 MMC 238 MMC 239 Michigan Undergraduate Math Conference 11:10 AM11:30 AM 11:35 AM11:55 AM 12:00 - 12:45 PM 12:55-1:50 PM Alen Astifo, Macomb Community College My Experiences as a Work-Study Student in a Math Department Jeff Miller, Evan Peters and Carl Uzarski, Grand Valley State University Combinatorial Interpretations of the Generalized Central Factorial Numbers Lindsay Czap, Grand Valley State University Guessing Games and Error Correcting Codes Raoul R. Wadhwa, Eddie Cheng, Kalamazoo College Oakland University Stochastic Kinetic Doing Research with Models of Genetic Bright High School Expression Students MUMC Pizza Lunch - Maas Conference Room Firas Hindeleh, Ed Aboufadel, Grand Barbara Britton, Grand Valley State Valley State Eastern Michigan University University University Classification of 3D Printing Projects Common Core Ideas Seven-Dimensional for Multivariate circa 1900 - What Lie Algebras with SixCalculus and College Took Us So Long? Dimensional Geometry Nilradical Victor Piercey, Ferris Darin Stephenson, State University Hope College Affective Using Algebraic Implications of Geometry to Study Curriculum and Non-commutative Instruction Choices Rings Conference Luncheon - Maas Auditorium Plenary Lecture (Maas Auditorium) Erica Flapan, Pomona College (Pólya Lecture) 3 Intrinsic Properties of Graphs Embedded in Saturday, April 11, 2015 Location MMC 158 MMC 159 MMC 237 MMC 238 MMC 239 Michigan Undergraduate Math Conference Joshua Mirth, Hillsdale College 2:00-2:20 Functional Analysis PM and the Dirichlet Problem 2:25-2:45 PM Eric Beyer, Robert Gandolfo and Tyler Pleasant, Lawrence Jonathan Oaks, Michael Bolt, Calvin Technological Macomb Community College University College Van der Pauw's The Fight Against Uses of Bases Other Theorem on Sheet Ebola: A Than Base 10 Resistance Mathematical Weapon of Attack Khairul Islam, Eastern Michigan University Tossing Coin in R: Tests for Unbiasedness and Central Limit Theorem Emmanuel Kengni Ncheuguim, Saginaw Matthew Trzcinski* Jacob Adams and Mark Panaggio, RoseValley State Grace Wiesner, Hope and Khairul Islam, Susanna Lange, Hulman Institute of University College Eastern Michigan Grand Valley State Technology Impact of Mission University University Synchronization and Allelopathic and Monteverde: Need of Graph Theory pattern formation in Spatial Interactions Mathematical Transformation: Modeling of Rook networks of coupled on a Competition Rainforest Modeling Literature Review Placements oscillators Between Two and Applications Phytoplankton Species Sandra Becker, Eastern Michigan University 2:50-3:10 Connecting Teaching PM Practice to Student Efficacy in Undergraduate Mathematics Na Yu, Lawrence Technological University How to recognize con-specifics and their motion? Ummugul Bulut, Brian McCartin, Grand Valley State Kettering University University Geometric Proofs of Derivation of the Common Tones Stochastic Biased Theorems of and Correlated Mathematical Music Random Walk Theory Models in One and Two Dimensions 3:15-3:45 PM Break 3:455:00PM Closing Plenary and Student Awards (Maas Auditorium) Ken Schilling, University of Michigan - Flint Sabermetrics for the Millions Tanweer Shapla, Eastern Michigan University Detecting the presence of Multicollinearity INVITED PLENARY LECTURES Benjamin V. C. Collins, University of Wisconsin, Platteville Saturday 8:45 - 9:40 a.m. Maas Auditorium Basel and Beyond: An Incomplete History of a Famous Sum If anyone finds and communicates to us that which thus far has eluded our efforts, great will be our gratitude. With these words, published in 1689, Jacob Bernoulli brought to the attention of European mathematicians a problem first posed by Pietro Mengoli in 1644. The problem was to find an exact sum for the infinite sum ∞ X 1 2 n=1 n The problem came to be known as the “Basel Problem,” after the Swiss university town where Bernoulli lived and worked. Fittingly, the problem was solved by Basel’s finest mathematician, Leonard Euler, in 1735. In his long and productive career, Euler provided two separate proofs, as well as two efficient ways to calculate the value of the sum. The Basel Problem continues to intrigue mathematicians. Dozens of proofs have been given, including several published within the last few years. We will discuss Euler’s first proof, and look at an interesting application of the sum in number theory. Time permitting, we will look at a few more recent proofs. William Cook, University of Waterloo Friday 2:15 - 3:20 p.m. Maas Auditorium A Salesman’s Tour of Combinatorial Optimization Given a list of cities along with the cost of travel between each pair of them, the traveling salesman problem is to find the cheapest way to visit them all and return to your starting point. Easy to state, but difficult to solve. In this talk we discuss the problem’s history, applications, and computation, along with current 6 research topics. The TSP serves as a means for discussing many broad themes in the field of combinatorial optimization, combining geometry, linear programming, and algorithms. Bob Devaney, Boston University Friday, after Dinner AlpenRose Restaurant The Fractal Geometry of the Mandelbrot Set In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand this geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the “Devaney” sequence. There might even be a joke or two in the talk. Erica Flapan, Pomona College Saturday after Lunch Maas Auditorium Intrinsic Properties of Graphs Embedded in R3 Knot theory is the study of embeddings of simple closed curves in R3 . A natural extension of knot theory is the study of embeddings of graphs in R3 . However, in contrast with knots, the structure of a graph can be complex, and this can affect all of its embeddings. If every embedding of a graph has a particular property, then we say that property is intrinsic to the graph. For example, a graph is said to be intrinsically knotted if every embedding of the graph in R3 contains a knot. In this talk I will discuss intrinsic knotting and other intrinsic properties of graphs. Ken Schilling, University of Michigan - Flint Saturday 3:45 - 4:40 p.m. Maas Auditorium Sabermetrics for the Millions Baseball fans have always been statistics-happy. That used to mean memorizing batting averages and pitchers’ win-loss records. No more. Instead, over the last few decades, baseball analysts (sabermetricians, for those who fancy five-syllable words) have 7 used fairly sophisticated mathematical tools to try to answer the big questions. Who would win a series between the 1927 New York Yankees and the 1975 Cincinnati Reds? Should you bunt the winning run to second with one out in the bottom of the ninth? Could Willie Mays hit a ball so far that he himself could not catch it? LOCALLY INVITED SPEAKERS Eric Mann, Hope College Friday, April 10 3:25 - 4:00 p.m. Maas Auditorium Changing the Culture: Developing Creative Problem Solvers Mathematics embraces creativity and beauty yet often our children are immersed in classroom activities where these attributes are hidden by an overemphasis on algorithms, computational speed and known answers that can be found in the back of the book or with a quick Google search. This learning environment creates a false perception of what it means to be “good at math.” From the research we know than many of our elementary school teachers have negative attitudes towards mathematics; an attitude students pick up and adopt which may foster the development of the reluctant, impatient problem solvers we find in our undergraduate classrooms. A change in the culture to one that both acknowledges and values the creative nature of mathematics is long overdue. The Partnership for 21st Century Skills in conjunction with the National Council of Teachers of Mathematics and the Mathematical Association of America developed the 21st Century Skills Map for mathematics. In the Learning and Innovation skills area the emphasis is on the 4C’s: Creativity, Critical Thinking, Communication and Collaboration, skills that have been topics of discussion in math education for over a century. This talk shares examples of efforts to infuse the 4C’s into K-12 mathematics classrooms in hopes of stimulating further collaborations between mathematicians and educators to restore wonder and beauty to mathematics taught in today’s classrooms. 8 Tim Pennings, Davenport University Saturday 9:45 - 10:20 a.m. Maas Conference Room Elvis Lives: Mathematical Surprises Inspired by Elvis, the Welsh Corgi A worthwhile mathematical model should not only confirm and inform one’s intuition; it should sometimes challenge or contradict it. In this talk we review the mathematical surprises from three papers involving the retrieving behavior of Elvis, the Welsh corgi. The first describes how Elvis became famous when he found the quickest - and sometimes nonintuitive - route down the beach and through the water to his ball. A second paper revealed more unexpected results as we analyzed the bifurcation occurring when Elvis, starting in the water, had to decide whether or not to come to land. And the last paper uncovers several surprising conclusions as we determine when and why a locally greedy route coincides with the globally optimal path. Jack Rotman, Lansing Community College, MichMATYC President Saturday 9:45 - 10:20 a.m. Maas Auditorium Curricular Change and Collaboration Across Institutions In a state without a higher education system controlling the curriculum, each institution accepts responsibility for decisions, and exercises autonomy than is seen in states with such a system. One positive consequence is that changes are not initiated from a state office; one negative consequence is that changes are not initiated from a state office. This talk will consider how we change and collaborate on curricular issues, using some typical courses as examples (college algebra, finite math, pre-calculus). We will cite some references from our national organizations (MAA, AMATYC) to indicate some possible areas of improvement. A conjecture for your consideration is: “Collegiate mathematics in Michigan needs deliberate and organized state-wide leadership based in a diverse group of faculty working together, supported by both MichMAA and MichMATYC.” 9 Allen Schwenk, Western Michigan University Friday, April 10 3:25 - 4:00 p.m. MMC 158 Mathematical Induction: The Good, the Bad and the Ugly Of course math induction is good. But some of my students have picked up bad habits when using induction; and many of the examples we use to teach the topic are, sad to say, just plain ugly. I wish to show a number of examples of proof by induction. Many of them are elegant, but not the standard examples we see in textbooks. Induction does not always proceed one step at a time. Some proofs that look good, can contain hidden errors. Can you discern the difference between the good proofs, the bad ones, and the ugly? CONTRIBUTED TALKS Ed Aboufadel, Grand Valley State University Saturday 11:10 - 11:30 a.m. MMC 237 3D Printing Projects for Multivariate Calculus and College Geometry Multivariate Calculus and College Geometry are two courses which have natural ways to introduce undergraduates to 3D printing. In this talk, we will provide some information about 3D printing and describe projects that can be assigned in these courses, where students can design and print 3D objects. The objects are designed in Mathematica and make use of planar and other multivariate functions, trigonometry, polyhedra, and more. Steve Bacinski, Davenport University Friday 4:05 - 4:25 p.m. MMC 159 Applied MATLAB Projects for Linear Algebra Students Linear algebra provides us with many powerful tools that are widely used in areas such as computer graphics, facial recognition, and big data analytics just to name a few. I have made an effort to incorporate many of these interesting applications in my undergraduate linear algebra course. In doing so, I have developed eight MATLAB-based projects that serve as a foundation for a course titled Applied Linear Algebra. Because of 10 the time constraint for the session, I will focus on my three favorite projects: Matrix Transformations with Puzzles, Airplane Bounding Box, and Image Compression with Wavelets. Allan Bickle, Calvin College Friday 4:30 - 4:50 p.m. MMC 158 MegaMenger Graphs In October 2014, many faculty and students at Calvin College worked to build a model of the Menger sponge, a type of fractal, out of business cards. This model can itself be modeled using graph theory, with each vertex representing a small cube, and an edge between two vertices whenever they share a face. We study graphs representing different steps of building the Menger sponge and Sierpinski carpet to determine their order, size, vertex degrees, chromatic number, and degeneracy, along with the surface area of the Menger sponge. Calculating these quantities requires solving many recurrence relations using several different techniques. Michael Bolt, Calvin College Saturday 2:00 - 2:20 p.m. MMC 238 Van der Pauw’s Theorem on Sheet Resistance The sheet resistance of a semiconducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply connected sample of the material. The method still is in wide use today. In this talk, we give a statement and proof of the van der Pauw theorem. The relevant mathematics is from complex analysis and touches on topics such as electrostatic potentials, cross-ratio, conformal mapping, and the Riemann mapping theorem. Barbara Britton, Eastern Michigan University Saturday 11:10 - 11:30 a.m. MMC 238 Common Core Ideas circa 1900 - What Took Us So Long? Back in 1900, David Eugene Smith introduced a philosophy 11 of teaching elementary mathematics that sounds very similar to the foundation of the Common Core State Standards of today. Learn about this pioneer in mathematics education, his ideas, and his connection to Michigan! Ummugul Bulut, Grand Valley State University Saturday 2:50 - 3:10 p.m. MMC 238 Derivation of Stochastic Biased and Correlated Random Walk Models in One and Two Dimensions Stochastic partial differential equations are derived to model the biased and correlated random walk (BCRW) in one and two dimensions. Deterministic equation is given for one dimensional BCRW where particles have a tendency to move in a particular direction, either right or left. In the present investigation, discrete time stochastic models are developed by determining the possible changes in direction for a small time interval. As the time interval decreases, the discrete stochastic models lead to systems of Ito stochastic differential equations. As the position intervals decrease, stochastic partial differential equations are derived to model BCRW in one and two dimensions. Comparisons between numerical solutions of the stochastic partial differential equations and independently formulated Monte Carlo calculations support the accuracy of the derivations. Eddie Cheng, Oakland University Saturday 11:35 - 11:55 a.m. MMC 237 Doing Research with Bright High School Students Many bright high school students are interested in doing research in mathematics. Over the past 12 years, I have worked with about 30 talented high school students who participated at the Oakland University Summer Mathematics Institute. In this talk, I will discuss my experience working with them as well as how to choose projects that are accessible to motivated and gifted high school students. Firas Hindeleh, Grand Valley State University Saturday 11:10 - 11:30 a.m. MMC 239 Classification of Seven-Dimensional Lie Algebras with Six12 Dimensional Nilradical Low dimensional solvable Lie algebra classification started back in 1963 by Mubarakzyanov. Solvable Lie algebras were completely classified up to dimension six. A general theorem asserts that if g is a solvable Lie algebra of dimension n, then the dimension of the nilradical is at least n2 . For the sevendimensional algebras, the nilradical’s dimension could be 4, 5, 6 or 7. The four and seven dimensional nilradical cases were classified. We examine the six-dimensional nilradical case, and depending on the structure of this nilradical there are six classes. This talk will introduce the basic tools needed for the classification problem in a way that is accessible to undergraduate students. I will discuss the progress made on this problem and outline the next piece of the project. Please encourage students who are interested in summer research opportunity to attend this talk. Khairul Islam, Eastern Michigan University Saturday 2:00 - 2:20 p.m. MMC 239 Tossing Coin in R: Tests for Unbiasedness and Central Limit Theorem Often, we toss a coin to introduce probability. How do we do it using technology, particularly in R? How do we test the unbiasedness of the coin? How do we introduce Central Limit Theorem using R? In this presentation, we address answers to these questions along with the flexibility of R for applications. Emmanuel Kengni Ncheuguim, Saginaw Valley State University Saturday 2:25 - 2:45 p.m. MMC 238 Impact of Allelopathic and Spatial Interactions on a Competition Between Two Phytoplankton Species We propose a model of two phytoplankton species competing for a single growth limiting, nonreproducing resource. The model incorporates allelopathic interactions of one toxin-producing species, both on itself (autotoxicity) and on its nontoxic competitor (phytotoxicity). We show that a stable coexistence 13 equilibrium exists as long as (a) there are allelopathic effects and (b) the input nutrient concentration is above a critical value. The spatial interactions among nutrient and the phytoplankton species are incorporated in the model in the form of reactiondiffusion equations. The reaction-diffusion equations account for the fact that nutrient and species of phytoplankton are distributed over a considerably large spatial regime in natural waters. We investigate suitable parametric conditions under which Turing patterns may or may not evolve around the locally stable interior equilibrium. Brian McCartin, Kettering University Saturday 2:50 - 3:10 p.m. MMC 237 Geometric Proofs of the Common Tones Theorems of Mathematical Music Theory The twin pillars of Mathematical Music Theory are the Common Tones Theorems for Transposition (rotation) and Inversion (reflection). As a counterpoint to the traditional algebraic proofs of these foundational results, this talk will present simple geometric proofs of these theorems as well as some related corollaries. Time permitting, the geometrical relationship of the Common Tones Theorems to such diverse topics as the Orbit-Stabilizer Theorem, Hexachordal Combinatoriality and the Complementary Chords Theorems will be explored. Jonathan Oaks, Macomb Community College Saturday 2:00 - 2:20 p.m. MMC 237 Uses of Bases Other Than Base 10 Most people are familiar with base 10 because it is what is used most commonly. Many people are even familiar with base 2. But what are some of the other bases used for - base 3, base 4, etc.? What about base e or base π? And what about the negative bases and the hybrid bases? This presentation will cover some of the uses of all of these other bases. Mark Panaggio, Rose-Hulman Institute of Technology Saturday 2:25 - 2:45 p.m. MMC 237 14 Synchronization and pattern formation in networks of coupled oscillators From the flashing lights of a swarm of fireflies to the footfalls of pedestrians on a bridge, synchronization is observed in a variety of natural and engineered systems. This coordination, which can emerge spontaneously out of disordered initial states, has an important role in the transport of blood throughout the human body, electricity on the power grid, and information in telecommunication devices. Breakdowns of synchrony can be detrimental to the efficient operation of those systems, and as a result, it is essential to be able to predict when synchronization is likely to occur and under what conditions it can be disrupted. In this talk, I will explore the Kuramoto model, a minimal mathematical model that describes the dynamics of a network of coupled phase-oscillators. Analysis of this model will reveal that the interactions between these idealized oscillators can give rise to a variety of unexpected behaviors that have been observed in experiments including phase transitions from asynchrony to synchrony and pattern formation with coexisting domains of coherent and incoherent oscillation. The bistability of these partially synchronized steady state patterns (known as chimera states) with a fully synchronized state may shed light on the origin of transitions between synchronized and desynchronized behavior in nature. Paul Pearson, Hope College Friday 4:05 - 4:50 p.m. MMC 240 An Interactive Introduction to WeBWorK WeBWorK is an open-source, web-based homework delivery system designed to make homework more effective and efficient for students of mathematics and the sciences. It has been used for over 18 years by hundreds of professors and in a wide variety of instructional environments. Participants in this workshop will be introduced to the WeBWorK online homework system and learn how to use it in their own classes. The workshop will be held in a computer lab so that participants do not need 15 to bring their own computers. Space is limited to 20 participants. There will be approximately 30 minutes of unstructured time after the workshop has ended to ask more questions and experiment further with WeBWorK. Victor Piercey, Ferris State University Saturday 11:35 - 11:55 a.m. MMC 238 Affective Implications of Curriculum and Instruction Choices Imagine a typical student in your developmental or general education course. What do you think their attitudes or beliefs about mathematics are? Might they experience math anxiety? How do curricular choices or our instructional choices impact those attitudes and beliefs? In this talk, I will describe three different curriculum and instruction models we used for general education and share data concerning the impact on math anxiety and beliefs about math. Steven Schlicker, Grand Valley State University Friday 4:05 - 4:25 p.m. MMC 158 A Geometry of Sets The Hausdorff metric provides a way to measure distance between sets. The metric is important for its applications in fractal geometry, image matching, visual recognition by robots, and computer-aided surgery. Beyond the practical applications, the Hausdorff metric imposes an interesting geometry on the space of non-empty compact subsets or Rn . We will discuss some details about circles, lines, and segments in this geometry, and then focus on recent work attempting to define angles and angle measure in this geometry. This research was conducted as part of the 2014 REU program at Grand Valley State University. Tanweer Shapla, Eastern Michigan University Saturday 2:50 - 3:10 p.m. MMC 239 Detecting the presence of Multicollinearity Multicollinearity is a situation when several predictors appear to be correlated, which is a violation of least squares regression model. As such, the estimates of regression coefficients become indeterminate and the standard errors of estimates become in16 finitely large, leading to invalid inferences. The first step in fitting a model is to determine if multicollinearity exists among predictors. In this talk, we explore some popular methods of detecting multicollinearity applied to real life data. Darin Stephenson, Hope College Saturday 11:35 - 11:55 a.m. MMC 239 Using Algebraic Geometry to Study Noncommutative Rings I will give an example-oriented survey of some results developed by others on the classification and study of noncommutative rings using the tools of algebraic geometry. I will indicate how this study gives rise to a theory of “noncommutative algebraic geometry” for certain noncommutative graded rings. I will also give a survey of related problems that I have been working on recently, along with some preliminary results. Matthew Trzcinski and Khairul Islam, Eastern Michigan University Saturday 2:25 - 2:45 p.m. MMC 239 Need of Transformation: Literature Review and Applications Many statistical methods require normality of the data. For example, to implement t-test and ANOVA, the first assumption that we make is the normality of the populations the samples come from. Transformation towards normality exists in literature to enable us to implement these tests. What if the normality of the population is unmet and the t-test or ANOVA is still applied in violation of the normality of the population? In this presentation, we review some transformation techniques and justify the need of transformation in the violation of normality with examples and Monte Carlo simulations. Na Yu, Lawrence Technological University Saturday 2:50 - 3:10 p.m. MMC 159 How to recognize conspecifics and their motion? Effectively processing information from a sensory scene is essential for animal survival. Motion in a sensory scene complicates this task by dynamically modifying signal properties. To address this general issue, we focus on weakly electric fish. Each 17 fish produces a weak electrical carrier signal with a characteristic frequency. Electroreceptors on its skin encode the modulations of this carrier caused by nearby objects and other animals, enabling this fish to thrive in its nocturnal environment. Little is known about how swimming movements influence natural electrosensory scenes, specifically in the context of detection and identification of, and communication with conspecifics. Using recordings involving free-swimming fish, we characterize the amplitude modulations of the carrier signal arising from small groups of fish. The differences between individual frequencies (beats) are prominent features of these signals, with the number of beats reflecting the number of neighbours. We also find that the distance and motion of a free-swimming fish are represented in a slow modulation of the beat at the receiving fish. Modeling shows that these stimulus features can be effectively encoded in the activity of the electroreceptors, but that encoding quality of some features can be degraded by motion, suggesting that active swimming could hinder conspecific identification. MICHIGAN UNDERGRADUATE MATHEMATICS CONFERENCE TALKS Jacob Adams and Susanna Lange, Grand Valley State University Saturday 2:25 - 2:45 p.m. MMC 158 Graph Theory Modeling of Rook Placements In a non-attacking rook placement on a board we place rooks in such a way that no two lie in the same row or column. Such a placement models a way to match two sets of objects, such as jobs and job applicants including any possible restrictions on which job can be matched with which applicants represented as restricted cells on the board. During this talk, we will discuss the modeling of these rook placements as matchings in bipartite graphs, and further investigate connections to gridline graphs. We will then generalize this modeling to rook placements in three and higher dimensions. Alen Astifo, Macomb Community College 18 Saturday 11:10 - 11:30 a.m. MMC 158 My Experiences as a Work-Study Student in a Math Department This presentation will focus on what a student does as a workstudy student in a math department. Some of the duties include assisting professors with tasks that they may need help with and learning more about how the math department functions as a whole. But the best part about the position is actually working with students in an intermediate algebra class and helping them succeed and become better students. Being a work-study student in a math department is a great opportunity for any mathematics student to see mathematics from a different perspective and to see the ins-and-outs of how the department works on a day-to-day basis. Eric Beyer, Robert Gandolfo and Tyler Pleasant, Lawrence Technological University Saturday 2:00 - 2:20 p.m. MMC 159 The Fight Against Ebola: A Mathematical Weapon of Attack The West African Ebola Epidemic started in March 2014 yet, even with medical help from other countries, the epidemic still is not under control. The outbreak needs to be fought and brought under control as soon as possible. In order to understand and predict the future of the virus and the effects of control measures, we created a mathematical model which gives a control strategy that revolves around the effective reproductive rate Re , defined as the average number of people infected by a person who gets the disease. There are two main ways to lower the effective reproduction rate: improving control measures and administering vaccination. To model the nature of the disease, we split and track six groups within the population. Our homogeneous deterministic model simulates disease dynamics, vaccination production, and transportation processes in order to determine Re at any given time which allows optimal use of vaccine. Lindsay Czap, Grand Valley State University Saturday 11:35 - 11:55 a.m. MMC 158 19 Guessing Games and Error Correcting Codes A two-player “guessing game” is a game in which the first participant picks a number from a certain range. Then, the second participant asks only yes-or-no questions in order to guess the number. A technique for minimizing the number of questions uses questions that divide the range of possible choices in half each time. We will prove that the minimum number of necessary questions is directly related to the log2 of the number of possible choices. Next, we will introduce guessing games that contain a “lie” or an error. Guessing games with lies are closely linked to error correcting codes, which are codes that allow for us to detect an error in the information that we receive and correct for these errors. We will use basic definitions in coding theory and discuss how error correcting codes will help us to still guess the correct number even if a lie is involved. Jeff Miller, Evan Peters and Carl Uzarski, Grand Valley State University Saturday 11:10 - 11:30 a.m. MMC 159 Combinatorial Interpretations of the Generalized Central Factorial Numbers Placing rooks on a chess board so that they cannot attack one another provides us a way to match rows with columns. If we place restrictions on these matchings so that the possible matches are allowed only on one triangular half of the board, we find interesting results about the number of possible rook placements. These numbers relate to the famous Stirling numbers of the second kind, which count ways of partitioning a set into non-empty subsets. In fact, there is a natural correspondence between the rook placements on a triangular board and the partitions of a set. In this talk, we describe how to extend triangular boards to three and higher dimensions, and how the rook placements on these boards provide new combinatorial interpretations of central factorial and generalized central factorial numbers. Joshua Mirth, Hillsdale College 20 Saturday 2:00 - 2:20 p.m. MMC 158 Functional Analysis and the Dirichlet Problem Dirichlet boundary value problems arise in many physical situations. However, simple analytic solutions only exist in a limited number of cases. We examine methods for solving Dirichlet problems on other regions, focusing on the unit right triangle. We prove the existence of such a solution and attempt to write a closed form solution by two different methods: first, using the Schwarz-Christoffel formula from complex analysis, and second, by drawing on functional analysis techniques and using Green’s functions. These solutions are then compared to numerical approximations. Kadeem Noray, Hillsdale College Friday 4:30 - 4:50 p.m. MMC 159 Political Corruption and Public Advocacy: An Evolutionary Game Theoretic Analysis We consider a two population evolutionary game that models the role of public advocacy as a deterrent to political corruption. A population of politicians chooses whether or not to engage in corrupt behavior, and a population of citizens decide whether or not to advocate for corruption reform, with the potential to impact detection and punishment levels for corruption. We study the pure and mixed strategy Nash equilibrium structure of this game. We also conduct an evolutionary analysis, finding evolutionary stable strategies and studying the evolution of strategies over time via the replicator dynamics for a two population game. Lastly, we explain the different types of dynamics that can result from realistic parameters in our model. Raoul R. Wadhwa, Kalamazoo College Saturday 11:35 - 11:55 a.m. MMC 159 Stochastic Kinetic Models of Genetic Expression Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model im21 plementation of the circular gene hypothesis, which suggests interactions between the synthesis and degradation of mRNA. Qualitative and quantitative changes in the shape and in the numerical characteristics of the stationary distributions suggest that more combined experimental and theoretical studies should be done to uncover the details of the kinetic mechanism of gene expression. Grace Wiesner, Hope College Saturday 2:25 - 2:45 p.m. MMC 159 Mission Monteverde: Mathematical Rainforest Modeling The tropical rainforest is one of earth’s most diverse and dynamic ecosystems. Tree or branch falls in the forest can open gaps in the canopy, allowing light to reach the forest floor. Pioneer plants are adapted to take advantage of these conditions, sometimes emerging many years after being deposited as seeds. Light conditions change as the gap closes, impacting rates of growth and reproduction. For the past 30 years, sizes and reproductive outputs of individuals of 6 pioneer plant species have been measured along 5 transects in the Monteverde Cloud Forest Preserve in Monteverde, Costa Rica. Each 500m transect was chosen to be representative of different conditions in some part of the cloud forest. To model the pioneer plant demographics, we classified canopy gaps by age and size and developed a matrix population model that accounts for the differing gap environments. We also created a stochastic matrix model of gap formation and evolution to simulate the dynamics of rainforest canopy gaps. Combined, these models will allow us to simulate pioneer plant population dynamics in the changing forest environment, and to explore how reproduction and growth rate parameters, such as seed predation rates, impact pioneer population dynamics. 22 Conference events will be located in the following two buildings on the Hope College campus: Maas Center, 264 Columbia Ave., Holland Martha Miller Center, 257 Columbia Ave., Holland The Friday evening banquet will be held at Alpen Rose Restaurant, 4 East 8th Street, Holland Alpen Rose Restaurant is within easy walking distance of the conference site and downtown hotels. Parking: Parking will be permitted in any campus lot on either day. Parking on campus Friday will be more complicated Friday due to construction and several campus events. You may also park in one of several downtown Holland free parking areas (including a city parking garage on 7th Street, about 3 blocks from the meeting site). The closest campus lots are Lot 41 (Martha Miller Center) and Lot 62/63 (DeVos Fieldhouse). Lot 41 is directly adjacent to the conference location, and there should be spaces available on Saturday. Saturday morning break sponsored by:

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