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## 2014-2015 Academic Year Colloquium Schedule

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### September 4, 2014

 Title: Technical Writing with LaTeX Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: The document preparation system LaTex is a powerful program for typesetting. LaTeX was developed over 30 years ago to aid in document preparation. Like TeX, it is a markup language that takes control sequences and converts them into symbols and instructions having no normal key. It is particularly useful in creating documents with mathematical text, such as formal papers, theses, and textbooks. This talk will be interactive, allowing students to work with LaTeX on simple exercises. Location: Palenske 231 Time: 3:30 PM Citation Click for BibTeX citation

### September 11, 2014

 Title: The Numbers Behind The Neon Speaker: Mark Bollman Professor and Chair, Department of Mathematics and Computer Science Mathematics and Computer Science Albion College Albion, MI Abstract: Probability is a branch of mathematics whose roots lie in gambling. While evidence of games of chance may be found in the artifacts of many ancient civilizations, the underlying mathematics that can be used to analyze these games is a far more recent development. In this talk, the mathematics underlying games of chance will be explored and the relative house advantages of many popular (and some obscure) casino games will be examined. This talk is based on the book Basic Gambling Mathematics: The Numbers Behind The Neon, recently published by Taylor & Francis/CRC Press. Copies of the book will be available for purchase. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### September 18, 2014

 Title: Planning for Graduate Study in Mathematics and Computer Science Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation. Location: Palenske 227 Time: 3:30 Citation Click for BibTeX citation

### September 25, 2014

 Title: Relationships between Platonic Solids and Scottish Carved Stone Balls Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: In this talk, we will trace the history of Platonic Solids and Scottish carved stone balls, then examine the relationships between these objects. The first account of the Platonic solids, namely the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron, were first given by Plato in about 360 BCE. However, most scholars contend that these objects were known to others before Plato. Over 425 Neolithic stone balls with carved knobs have been found in northern Scotland and date to about 2000 BCE. There is no recorded use of these objects, which has resulted in much speculation about their purpose. A theory that these were models of Platonic solids was advanced in 1979. Yet these objects are clearly not polyhedra and thus do not represent examples of Platonic solids, despite recent claims to that effect. In some cases, the symmetry of the knob placements is consistent with the symmetries associated with Platonic solids. The symmetric form contributes to the aesthetic appeal of many carved stone balls, thus they can be considered very early examples of mathematical art. Examples are shown along with pictures of modern art that they have inspired. Could knowledge of these objects have traveled to from Scotland to Greece and helped develop the Greek theory of Platonic solids? Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 2, 2014

 Title: Bond and CDS Pricing with Stochastic Recovery Speaker: Albert Cohen Academic Director, Actuarial Sciences Program Mathematics (also appointed in Statistics and Probability) Michigan State University East Lansing, MI Abstract: Classical credit risk and pricing models typically assume that the expected recovery at default is constant, or at the very least independent of the default probability. However, a large body of recent empirical evidence has challenged this assumption and shown that default rates are in fact negatively correlated with recovery rates \cite{ABRS}. Recently, Moody's Analytics proposed a model in the context of credit capital which incorporates this empirically observed correlation within a structural framework \cite{LH}. In this work we revisit Moody's PD-LGD correlation model and in the process complete and extend several results. We then price Bond and Credit Default Swaps with recovery risk using the PD-LGD model under both the Merton and Black-Cox default assumptions, and in addition compute associated risk metrics and Greeks. Our results are then compared with classical results which assume no recovery risk. Talk Slides are available at http://www.math.msu.edu/~albert/CreditTalkAlbion.pdf. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 9, 2014

 Title: EY & Data Analytics: Building a Better Working World Speaker: Aaron Croad and Dennis O'Dowd Data Consultants - Advisory Services Analytics Ernst & Young Detroit, MI Abstract: Analytics now sits at the top of the agenda for many leading organizations as they look for new ways to create a competitive advantage. Although analytics as a business discipline has existed for decades, the explosion of data and new technology has increased the potential and promise for better business decisions informed by analytics. Analytics can be a foundational element of business transformation — challenging conventional wisdom about what we think is true. Analytics can deliver more value when sophisticated techniques are used to discover root causes, analyze micro-segments of the market, transform processes and make better predictions about cause and effect relationships. In this talk, we will provide a brief introduction to data analytics and the analytic tools we use, as well as review how our employer, EY, uses data analytics to build a better working world. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 23, 2014

 Title: Rise of the Hackers Speaker: NOVA Video Abstract: Our lives are going digital. We shop, bank, and even date online. Computers hold our treasured photographs, private emails, and all of our personal information. This data is precious—and cybercriminals want it. Now, NOVA goes behind the scenes of the fast-paced world of cryptography to meet the scientists battling to keep our data safe. They are experts in extreme physics, math, and a new field called "ultra-paranoid computing," all working to forge unbreakable codes and build ultra-fast computers. From the sleuths who decoded the world's most advanced cyber weapon to scientists who believe they can store a password in your unconscious brain, NOVA investigates how a new global geek squad is harnessing cutting-edge science—all to stay one step ahead of the hackers. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 30, 2014

 Title: Data, Data, Everywhere! Speaker: Michele Intermont Associate Professor Department of Mathematics Kalamazoo College Kalamazoo, Michigan Abstract: Everywhere we look these days there seem to be huge piles of data being generated. People collect this data, but how does it get analyzed? Recently, people have begun looking at the branch of mathematics known as topology to help organize and give some shape to data. Applied topology is still a new field, and in this talk, we'll give an introduction to it, as well as to topology itself, and talk about some of the applications. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 6, 2014

 Title: Distance-Preserving Graphs Speaker: Dennis Ross, 08 Graduate Research Assistant Computer Science and Engineering Michigan State University East Lansing, MI Abstract: Graphs provide terrific models, and some powerful mathematical machinery, to better understand many practical and theoretical problems. One important relationship between vertices of a graph is the length of the shortest path connecting them. We will explore a class of problems which seek to fix this distance between vertices while reducing the order of the graph. Consider a simple graph $G$ of order $n$. We say $G$ is distance-preserving if, for all integers $k$ such that $1 < k < n$, there exists an order $k$ induced subgraph of $G$ where $d_G(x,y)=d_H(x,y)$ for all pairs of $x,y\in H$. We will explore the definitions and properties of distance-hereditary graphs, distance-preserving graphs, and distance-preserving trees. We will then continue with an extremal proof on the constructability of regular distance-preserving graphs. Additionally, we will discuss some open problems and see some practical applications. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 13, 2014

 Title: Tempered fractional processes Speaker: Farzad Sabzikar Visiting assistant professor Statistics and Probability Michigan State East Lansing, Michigan Abstract: Tempered fractional Brownian motion (TFBM) is defined by exponentially tempering the power law kernel in the moving average representation of a fractional Brownian motion (FBM). TFBM is a Gaussian process with stationary increments, and we call those increments tempered fractional Gaussian noise (TFGN). TFGN exhibits semi-long range dependence. That is, its autocovariance function closely resembles that of fractional Gaussian noise on an intermediate scale, but then it eventually falls off more rapidly. The spectral density of TFGN resembles a negative power law for low frequencies, but eventually converges to zero at very low frequencies. This behavior of the spectral density is consistent with the Davenport spectrum that extends the $5/3$ Kolmogorov theory of turbulence beyond the inertial range. TFBM is a linear combination of tempered fractional integrals (or derivatives) of a white noise. Using that fact, we developed the theory of stochastic integration for TFBM. Replacing the Gaussian random measure in the moving average or harmonizable representation of TFBM by a stable random measure, we obtained a linear tempered fractional stable motion (LTFSM), or a real harmonizable tempered fractional stable motion (HTFSM), respectively. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 20, 2014

 Title: A Geometric Perspective on Counting Nonnegative Integer Solutions and Combinatorial Identities Speaker: Michael A. Jones Associate Editor Mathematical Reviews Ann Arbor, MI Abstract: We consider the effect of constraints on the number of nonnegative integer solutions of $x + y + z = n$, relating the number of solutions to linear combinations of triangular numbers. Our approach is geometric and may be viewed as an introduction to proofs without words. We use this geometrical perspective to prove identities by counting the number of solutions in two different ways, thereby combining combinatorial proofs and proofs without words. This will be an interactive talk where those in attendance will get to use triangular graph paper to construct proofs of some of the results. This talk is based on a paper of the same name that is co-authored with Matt Haines and Ryan Huddy. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 4, 2014

 Title: The RSA Public Key Encryption System Speaker: Preston M. Arquette, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: RSA is a public-key cryptosystem named after Ron Rivest, Adi Shamir and Leonard Adleman who invented it at MIT. In using RSA, a user publishes a "public key" that is the product of two large primes. A secret "private key" is held by all parties to the message. RSA is used in a wide variety of internet applications and is currently in the public domain. There are a variety of attacks on RSA-encrypted systems, however they are all hindered by the mathematical difficulty of factoring large primes. Most methods of determining prime factorization of large numbers are essentially brute force. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 4, 2014

 Title: Marriage: No Longer a Domestic Matter Speaker: Tram Hoang, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: The Mekong River Delta in Southern Vietnam sees the nation's highest number of women marrying men from wealthier East Asian countries (i.e. Taiwan and Korea). The brides—disproportionately from rural areas—cite their number one reason being to improve the financial situation at home. Using statistical analysis, my research attempts to examine the massive record of emigrant brides in this region and assess their claim of monetary incentives. I look at factors such as domestic and foreign GDP per capita and marriage remittances. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### January 29, 2015

 Title: Technical Writing with LaTeX Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: The document preparation system LaTeX is a powerful program for typesetting based on TeX. LaTeX was developed over 30 years ago to aid in document preparation. Like TeX, it is a markup language that takes control sequences and converts them into symbols and instructions having no normal key. It is particularly useful in creating documents with mathematical text, such as formal papers, theses, and textbooks. This talk will be interactive, allowing students to work with LaTeX on simple exercises. Location: Palenske 231 Time: 3:30 PM Citation Click for BibTeX citation

### February 5, 2015

 Title: Big Data and the Divide & Recombine (D&R) Statistical Methodology in AutoRegression Integrated Moving Average (ARIMA) Modeling Speaker: Jeremy Troisi '08 PhD Candidate Statistics Purdue University West Lafayette, IN Abstract: Big Data is highly touted by big industry, but the skill set required to handle such complicated problems is both very advanced and diverse. My research group has been investigating optimal Divide & Recombine (D&R) statistical methods for various types of data. Personally, I am seeking to find the optimal application of D&R methods to massive univariate time series data, such as a stock price recorded over time, in AutoRegressive Integrated Moving Average (ARIMA) Model estimation. In this talk, I will discuss the long standing current ARIMA model estimation method, how it works, and why it is intractable for Big Data, i.e. the purpose of my research. I will then discuss how our method both succeeds in ARIMA model estimation in the Big Data framework, while the current method does not, and how our method is vastly more efficient computationally. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 12, 2015

 Title: Triangle Mystery Redux Speaker: Michael A. Jones Associate Editor Mathematical Reviews Ann Arbor, MI Abstract: To celebrate the tenth anniversary in 2012 of the Baltic Centre for Contemporary Art in Gateshead, England, Steve Humble designed a hands-on activity to demonstrate concepts from an exhibit on hidden order in apparent random processes. The activity involves placing playing cards in a triangular lattice based on some rules. It may not be too surprising that Pascal's triangle makes an appearance, but what about fractals making an appearance, too? We'll construct mysterious triangles and talk about the mathematics behind the activity, as well as some of the order that arises in the process. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 19, 2015

 Title: Increasing Forests in Graphs Speaker: Josh Hallam Graduate Student Department of Mathematics Michigan State University East Lansing, Michigan Abstract: A combinatorial graph is a collection of vertices and edges between them. A generating function is a tool used to keep track of combinotorial data. Using generating functions, we will discuss an unexpected relationship between counting certain types of graphs, vertex colorings and acyclic orientations. No prior knowledge of combinatorics will be assumed. This is joint work with Jeremy Martin and Bruce Sagan. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 26, 2015

 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. Slides from the talk are available at http://zeta.albion.edu/~dreimann/talks/careers/careers.html. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### March 5, 2015

 Title: Constraint profit optimization in pricing an established national brand in the presence of a local generic. Speaker: Stavros Christofi Associate Professor Mathematics Western Connecticut State University Danbury, CT Abstract: In my talk, I will describe our model for pricing an established national brand in the presence of a local generic. We utilize multivariable calculus and regression techniques to solve the two-component problem: The analytical and the empirical models. The analytical one entails nonlinear optimization with equality constraints, which we show can be solved by the method of Lagrange multipliers. The model's complication depends on the form of the demand function assumed and the precise industry structure. The empirical model is based on regression (method of least squares) and requires specific market data. An interesting problem for future research that derives from the one we have considered is its game-theoretic version. The way I will present the problem and its solution allows undergraduate students who know at least the notion of derivative for a function of one variable, and perhaps the notion of vector, to follow my talk. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### March 26, 2015

 Title: Decision Models for Logistics Management Speaker: Hakan Yildiz Assistant Professor Supply Chain Management Michigan State University East Lansing, MI Abstract: Logistics management is the detailed coordination of a complex operation involving people, facilities, or supplies in order to meet the requirements of customers. In this talk, we will look at a variety of logistics problems, ranging from umpire scheduling to facility network design and show how mathematical models help managers make better decisions. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 2, 2015

 Title: f(Mathematical Thinking) = Creativity Speaker: Eric Mann, 74 Assistant Professor of Mathematics Education Mathematics Hope College Holland, Michigan Abstract: Mathematics is a discipline that embraces creativity and beauty yet often students are immersed in classroom activities where these attributes are hidden by an overemphasis on algorithms and computational speed. Creativity exists in all fields but the nature and manifestations differ based on the values and objectives within the discipline. While artists, authors, and musicians seek to invoke an aesthetic or emotional response, STEM disciplines focus on creating solutions to problems; a functional view of creativity. Yet creativity is often limited in K-12 classrooms where students mimic established algorithms to construct, as opposed to create, solutions to known problems. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 16, 2015

 Title: Making Calculus Easy the Hard Way Speaker: Andrew Livingston Department of Mathematics Eastern Michigan University Ypsilanti, MI Abstract: You probably haven't heard of the p-adic numbers, but they are full-fledged number systems on par with the real numbers—and given there's a p-adic number system for every prime p, they outnumber ℝ infinity to one! They're also weird and wild landscapes for which Alice's Adventures in Wonderland provides a better guide than common sense does: big becomes small, short becomes long, and geometry can be described but not easily drawn. In this talk we'll meet the p-adics and see how p-adic calculus makes short work of testing for convergence of infinite series in a way calculus students only dream about. We'll also see how the nice properties of p-adic numbers led to them conquering number theory in the 20th century (spoiler: they played a part in Wiles' proof of Fermat's Last Theorem). Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 30, 2015

 Title: The Foundation of Catastrophic Insurance Pricing Speaker: Kyle Albrecht, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: There are many different types of insurance plans, but larger companies sometimes opt to be self-funded. A self-funded insurance plan is any plan where the company itself pays out for claims instead of a designated insurance company. However, since an individual could have a huge claim (upwards of a million dollars), it is a good idea to limit potential losses. A self-funded company can elect to have stop-loss coverage, which will cover larger than usual claim amounts. There are a few different ways that insurance companies cover insurance plans, and my talk will focus on the different aspects of each. Specific stop-loss coverage looks at each individual and pays for a portion of claims above a pre-determined amount. Aggregate stop-loss looks at the group's total claims and pays any amount above a pre-determined amount. Finally, aggregating-specific stop-loss coverage sums the amount above a specific deductible on an individual basis, and then applies that amount to an aggregating deductible; the insurance company will cover amounts above both of these deductibles. In my talk I will cover the details of each type of coverage along with an analysis of what factors affect a company's rates. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 30, 2015

 Title: Mathematics and the Outcomes of Sporting Events Speaker: Jonathon Lorenz, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: For most casino games, the probabilities of outcomes are fairly straightforward to estimate. But what happens when we try to predict the outcome of a sports game? This talk explains the ins and outs of sports betting, and how gamblers use math to forecast winners. We will also cover the Pythagorean Method for NBA games, as well as how casinos ensure they make a profit. We will also examine influential figures in the mathematical examination of sports, like Bill James. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 30, 2015

 Title: Mathematics of creating and modeling bowling balls Speaker: Matt Prosniewski, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: Bowling is a game that most people have tired at least once in their life. Since it is such a simple game, many people underestimate the amount of mathematics involved in the game. In recent years bowling ball companies have started to design balls that are meant to hook more, turn sharper and hit harder. To do this they changed from solid plaster balls to using advanced core systems. The designs of these cores take into account many mathematical factors including center of mass, axis of rotation, radius of gyration and many more. In this talk I will describe how these factors are calculated with respect to bowling balls. I will also explain how these can be used to create bowling balls that react a certain way on the lane and how these reactions can be modeled. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 30, 2015

 Title: Group Theory of Molecules Speaker: Stephanie Sanders, '15 Senior Mathematics Major Albion College Albion, Michigan Abstract: Group theory is the study of algebraic structures called groups. By employing the concepts of group theory, chemists can study the symmetry of molecules. The possible symmetry elements and their matrix representations will be examined. Every molecule has a set of symmetry elements that make up a group. The symmetry groups of molecules and the relationship between chemistry and math terminology will be explored. Group theory and the symmetry of molecules have many practical applications in chemistry, such as understanding vibrational spectroscopy and crystallography. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation