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## 2016-2017 Academic Year Colloquium Schedule

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### September 8, 2016

 Title: Creating Escher-like Tessellations Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: The artist M.C. Escher was a master at creating interlocking shapes that could be used to fill space without overlaps or gaps. We will learn how to create special shapes in several ways and explore how these relate to symmetry. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### September 22, 2016

 Title: Adventures In Gambling Mathematics: Selected Short Subjects Speaker: Mark Bollman Professor and Chair, Department of Mathematics and Computer Science Mathematics & Computer Science Albion College Albion, MI Abstract: Games of chance provide a rich source of questions in applied probability. The field of casino game development, much like gambling itself, is a high-risk proposition that carries a very small probability of high reward for the designer of a successful new game. This talk will examine a number of nonstandard casino and lottery games and the mathematics involved to analyze them. Examples are drawn from card games, dice games, and lotteries. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### September 29, 2016

 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 available to 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. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### October 6, 2016

 Title: Undergraduate Research in Combinatorics/Graph Theory Speaker: Heather Jordon Associate Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: In last week's seminar, opportunities for funding for summer research projects were discussed but what would you actually DO in a summer research project? In this talk, several projects that undergraduate students worked on during the Spring 2016 semester in the mathematical area of combinatorics/graph theory will be discussed. We'll describe the projects, talk about the process, and what the students were required to do. The students did this work as part of a course entitled "Introduction to Undergraduate Research in Mathematics" at Illinois State University. Eight students participated who were all math majors; some pursuing secondary teaching and some going on to graduate school. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 20, 2016

 Title: Group Testing: From Syphilis to Sparse Fourier Transforms Speaker: Mark Iwen Assistant Professor Dept. of Mathematics, and Dept. of ECE Michigan State University East Lansing, Michigan Abstract: Periodic functions with a relatively small number of energetic Fourier coefficients appear in many applications including communication protocols, image processing problems, and numerical methods for solving some partial differential equations. In this talk we will discuss some algorithms for recovering such functions more quickly than possible via traditional discrete Fourier transform methods. In the process we will encounter world war two history, number theory, combinatorics, error correcting codes, and movie stars. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 27, 2016

 Title: Answering Condorcet's Omission Speaker: Tomas McIntee Mathematics Virginia Tech Blacksburg, VA Abstract: M. J. A. N. de Caritat, the Marquis de Condorcet, raised concerns about the Borda Count in "Essay on the Application of Analysis to the Probability of Majority Decisions" (1785), introducing several concepts that now bear the name of Condorcet; in particular a voting paradox and voting criteria. One of the latter was used by M. J. A. N. de Caritat to criticize a positional voting method introduced by contemporary J. C. de Borda in 1770. In this presentation, the question of how probability applies to the voting paradox and the application of the related criteria to positional voting rules is raised, leading to a spectrum of answers of varying plausibility. The most plausible answers can be seen to be those given for Borda's voting system. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 3, 2016

 Title: Not so sinister after all: How mathematical models can explain the resilience of the left-handed minority Speaker: Mark. J Panaggio Assistant Professor Mathematics Hillsdale College Hillsdale, MI Abstract: Every human population in recorded history has been predominantly right-handed with a small left-handed minority that persists often despite intense societal pressure to conform. Although numerous explanations for individual handedness have been proposed, none of these explanations can account for this population-wide bias. In this talk, I will present a minimal mathematical model describing competition between groups of left- and right-handed individuals in a population that can explain our right-handed world. Analysis of the equilibrium states of this dynamic model will shed light on why most humans are right-handed, why most animals are not, why left-handed athletes overachieve in baseball, why they underachieve in golf and will demonstrate that even simple models built using tools from calculus can provide meaningful into the behavior of complex systems. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 10, 2016

 Title: Critical Thinking and Debugging Software Speaker: James T. Streib Professor of Computer Science Computer Science Illinois College Jacksonville, Illinois College Abstract: This presentation examines various difficulties that beginning programmers sometimes encounter when attempting to debug software. Unfortunately, some beginning programmers make repetitive guesses in an attempt to solve a problem. First, this presentation examines how to break this cycle of guessing. Second, although there are a number of definitions of critical thinking, this presentation will examine one of the original ones proposed by John Dewey. Next, it looks at how critical thinking can be employed when walking through code to debug a logic error. Lastly, it offers some suggestions and provides some closing thoughts. The audience for this presentation is students, tutors, lab assistants, teaching assistants, and instructors, especially ones new to their roles. For those who may already possess good debugging skills, it might help articulate what they have already been practicing. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 17, 2016

 Title: The Mathematics of Apportionment in U.S. Presidential Primaries and the General Election Speaker: Michael A. Jones Associate Editor Mathematical Reviews Ann Arbor, MI Abstract: Apportionment is a mathematical way to round integers proportionally. Although well known to determine how many seats each state receives in the U.S. House of Representatives, apportionment methods are also used in the U.S. presidential primaries and the general election. We'll examine the geometry of two types of paradoxical behavior that may occur in these settings, using real data when appropriate. We'll also touch on some recent proposed laws and how they would affect the paradoxical behavior. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 1, 2016

 Title: How does variation in life history strategies effect long term population trajectories of eelgrass? Speaker: Stephanie Thurner, '17 Senior Mathematics Major Mathematics Albion College Albion, Michigan Abstract: Seagrasses are important habitat forming marine angiosperm in coastal ecosystems. Contemporary declines in seagrass habitats worldwide warrant understanding factors that may allow managers to predict change and recovery in these habitats. In the Pacific Northwest, eelgrass (Zostera marina) forms these critically productive meadows and has experienced instances of localized population decline. These site specific declines are often persistent, lacking natural recovery. In an attempt to combat these declines, human aided restoration is endeavored with worldwide success rates around 30%. Eelgrass reproduces using two different life history strategies, asexual and sexual reproduction, with varying life history strategies between populations. It is unknown how variation in life history strategy affects the long term population trajectories of eelgrass. In this study we develop a stage-based matrix population model, parameterized by field data collection, previous experiments, and data mining to map the effects of life history variation on population growth. The eelgrass lifecycle was mathematically defined as three stages (vegetative shoots, flowering shoots, and seeds) as well as by the vital rates describing the transitions between these stages (branching rate, flowering rate, fecundity, germination rate, and seedling survival rate). By analyzing populations with variations in sexual and asexual reproduction and validating the model through a comparison with a long term field study experiment, we saw that the model is a highly conservative estimate for solely sexually reproducing populations, and an over estimate for populations with asexual reproduction. When the field recovery experiment was analyzed, we could also see that recovery of a population back to initial population levels after a disturbance is different when density is determined spatially rather than by looking at the entire area. Further data collection and refinement of vital rates as well as the addition of other environmental conditions will increase the accuracy of the model and help inform management and conservation strategies. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 1, 2016

 Title: Monte Carlo Integration and Implementation in the R Programming Language Speaker: Ethan Sutton, '17 Senior Mathematics Major Mathematics Albion College Albion, Michigan Abstract: This integral can not be solved analytically and therefore the solution is found using a numerical method" is something occasionally stumbled upon in the textbook of a first or second year calculus student. In this talk we will examine one of these numerical methods used to solve complex integration problems using a method known as "Monte Carlo Integration." This method is particularly useful for integration of higher dimensional functions but also computationally intensive making it very inefficient without the aid of the computer. Therefore, an implementation of this method in the R Programming Language will also be demonstrated. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 1, 2016

 Title: Bertrand's Postulate Speaker: Erik Davis, '17 Senior Mathematics Major Mathematics Albion College Albion, Michigan Abstract: Bertrand's postulate states that for all natural numbers $n>1$, there exists a prime number $p$ such that $n < p < 2n$. A proof first given by Paul Erdos will be derived for this remarkable theorem. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### January 19, 2017

 Title: You've been doing geometry wrong?! Speaker: Stephen Oloo Visiting Assistant Professor Math and CS Department Kalamazoo College Kalamazoo, MI Abstract: I will introduce projective space and discuss how it is a better setting for doing geometry than our familiar euclidean space. In truth, this discussion will really be an excuse to introduce interesting mathematical ideas such as compactifications and moduli spaces. We may even delve into some algebraic topology. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 2, 2017

 Title: Polygons, Polyhedra, and String Theory Speaker: Ursula Whitcher Associate Editor Mathematics Reviews American Mathematical Society Ann Arbor, Michigan Abstract: If you have a rubber band and a pegboard, how many polygons can you make that have only one peg in the center? The answer to this question is highly interesting to string theorists, who use shapes like these to write equations for the predicted "extra" dimensions of the universe. We'll talk about the way mathematicians use intuition from string theory to make mathematical discoveries. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 9, 2017

 Title: Careers in Mathematics and Computer Science Speaker: David A. Reimann Associate Professor Mathematics and Computer Science Albion College Albion, MI, USA Abstract: A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 16, 2017

 Title: A walk through Algebraic Curves Speaker: Chris Creighton, '11 Graduate Student Department of Mathematics Purdue University West Lafayette, Indiana Abstract: The aim of this talk is to give an introduction to Algebraic Curves, that is, the zero set of some polynomial equation in two variables. We'll mosey through varieties in general and stroll through why the coefficients of the polynomial matter. The path of choice is concepts of nonsingularity and rational functions on the curve. If time, we can go onto the side path of divisors and related topics. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 23, 2017

 Title: What would you pay for a guarantee to sell X for Y? Speaker: Darren Mason Professor Mathematics & Computer Science Albion College Albion, MI Abstract: The current price of Apple stock is $131.74. You are offered a chance to enter into the following agreement: If tomorrow Apple stock increases to$133.22, you receive nothing; If tomorrow Apple stock decreases to $129.88, you receive$1.12. you receive $1.12. Assuming that you know that starting with the initial stock price of$131.74, Apple stock has a 60% chance to increase to 133.22 and only a 40% chance to decrease to $129.88, how much are you willing to pay for this agreement? Or, in other words, what is a fair price to charge for this "contract"? The above scenario is an example of a financial option called a "put" stock option, which gives the owner the right, but not the obligation, to sell an asset to another person at a particular time (or times) in the future. In the above case, you are guaranteed that you can sell Apple for$131, regardless of stock value. How to fairly price such options, as well as other types of financial derivatives, is an interesting aspect of mathematical finance and stochastic calculus, a field that has its roots in a French mathematical thesis from 1900, resulted in the 1997 Nobel prize in economics, and provides a concrete use for such oddities of real analysis as continuous functions that are nowhere differentiable. By the end of this talk you should be able to fairly price the above Apple stock option, as well as understand and price more complicated financial derivatives, within a universe where time discretely ticks by. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### March 2, 2017

 Title: The No-Sided Möbius Band Speaker: Robert Messer Mathematics and Computer Science Albion College Albion, Michigan Abstract: Wikipedia says, "The Möbius band is a surface with only one side and one edge." We will construct some Möbius bands and verify this observation. But is it possible for a Möbius band to have two sides? We will see that the number of sides of a geometric object is not an intrinsic property of the object but instead depends on the space around it. In 1946, Martin Gardner wrote a short story about topologists who folded themselves into no-sided Möbius bands. Where can we find one of these? Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### March 23, 2017

 Title: Ramanujan's Life and Notebooks Speaker: Bruce Berndt, '61 Professor Mathematics University of Illinois Urbana, Illinois Abstract: Srinivasa Ramanujan was the greatest mathematician in the history of India. He was born in southern India in 1887 and died there in 1920 at the age of 32. He had only one year of college, but his mathematical discoveries, made mostly in isolation, have made him one of 20th and 21st centurys' most influential mathematicians. An account of Ramanujan's life will be presented. Most of Ramanujan's mathematical discoveries were recorded without proofs in notebooks, and a description and history of these notebooks will be provided. A lost notebook of Ramanujan was found in 1976. We shall also give a history and description of the lost notebook. The lecture will conclude with a brief survey of the areas of mathematics to which Ramanujan made profound contributions. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### March 30, 2017

 Title: Game. SET. Line Speaker: David Austin Professor of Mathematics Mathematics Grand Valley State University Allendale, MI Abstract: SET is a simple card game based on pattern recognition that can challenge both children and adults. It also has a surprisingly rich underlying mathematical structure that ties together ideas from a range of subjects including geometry, combinatorics, and linear algebra. In this talk, we will consider some simple questions that arise when playing SET and investigate the mathematical ideas that provide answers. We will also describe some recent and deep work from last year that gives a surprising result about a generalization of SET. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 6, 2017

 Title: Stochastic Optimal Control for Online Seller under Reputational Mechanisms Speaker: Albert Cohen, PhD Academic Director, Actuarial Program Department of Mathematics Michigan State University East Lansing, Michigan Abstract: In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store). This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller's reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. This is accomplished by designing a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from [1] and used effectively in the Stochastic Optimal Control of Advertising [2]. This model of reputation is combined with the effect of online reputation on sales price empirically verified in [3]. We derive the Hamilton-Jacobi-Bellman (HJB) differential equation, whose solution relates optimal wealth level to a seller's reputation. Finally, we formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct. [1] Sethi, S.P. Deterministic and stochastic optimization of a dynamic advertising model. Optim. Control Appl. Methods 1983, 4, 179-184. [2] Raman, K. Boundary value problems in stochastic optimal control of advertising. Automatica 2006, 42, 1357-1362. [3] Mink, M.; Seifert, S. Reputation on eBay and its Impact on Sales Prices. In Proceedings of The Group Decision and Negotiation International Conference, Karlsruhe, Germany, 25-28 June 2006; pp. 253-255. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation