News Archive

2015-16 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 (711-1492). 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 brain-teaser 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 six-sided 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 eight-sided 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 end-game 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:

Two-Colored 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 two-colored 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

2014-15 Academic Year Colloquium Schedule

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 p.m.
Citation: 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, Michigan
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 p.m.
Citation: 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 p.m.
Citation: 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 p.m.
Citation: 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, Michigan
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: 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, Michigan
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 p.m.
Citation: 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 p.m.
Citation: 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 p.m.
Citation: 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, Michigan
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 dG(x,y)=dH(x,y) for all pairs of x,yH. 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 p.m.
Citation: BibTeX citation

November 13, 2014

Title: Tempered fractional processes
Speaker: Farzad Sabzikar
Visiting assistant professor
Statistics and Probability
Michigan State University
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 p.m.
Citation: 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, Michigan
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 p.m.
Citation: BibTeX citation

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