2014-2015 Academic Year Colloquium Schedule |
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September 4, 2014
| Title: |
Technical Writing with LaTeX
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| Speaker: | David A. Reimann
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 231
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
September 11, 2014
| Title: |
The Numbers Behind The Neon
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| Speaker: | Mark Bollman
Professor and Chair, Department of Mathematics and Computer Science
Mathematics and Computer Science
Albion College
Albion, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
September 18, 2014
September 25, 2014
| Title: |
Relationships between Platonic Solids and Scottish Carved Stone Balls
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| Speaker: | David A. Reimann
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
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| 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?
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
October 2, 2014
| Title: |
Bond and CDS Pricing with Stochastic Recovery
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| Speaker: | Albert Cohen
Academic Director, Actuarial Sciences Program
Mathematics (also appointed in Statistics and Probability)
Michigan State University
East Lansing, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
October 9, 2014
| Title: |
EY & Data Analytics: Building a Better Working World
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| Speaker: | Aaron Croad and Dennis O'Dowd
Data Consultants - Advisory Services
Analytics
Ernst & Young
Detroit, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
October 23, 2014
| Title: |
Rise of the Hackers
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| Speaker: | NOVA Video
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
October 30, 2014
| Title: |
Data, Data, Everywhere!
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| Speaker: | Michele Intermont
Associate Professor
Department of Mathematics
Kalamazoo College
Kalamazoo, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
November 6, 2014
| Title: |
Distance-Preserving Graphs
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| Speaker: | Dennis Ross, `08
Graduate Research Assistant
Computer Science and Engineering
Michigan State University
East Lansing, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
November 13, 2014
| Title: |
Tempered fractional processes
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| Speaker: | Farzad Sabzikar
Visiting assistant professor
Statistics and Probability
Michigan State
East Lansing, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
November 20, 2014
| Title: |
A Geometric Perspective on Counting Nonnegative Integer Solutions and Combinatorial Identities
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| Speaker: | Michael A. Jones
Associate Editor
Mathematical Reviews
Ann Arbor, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
December 4, 2014
| Title: |
The RSA Public Key Encryption System
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| Speaker: | Preston M. Arquette, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
December 4, 2014
| Title: |
Marriage: No Longer a Domestic Matter
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| Speaker: | Tram Hoang, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
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 |
| Flyer | Click for a printable flyer |
February 5, 2015
| Title: |
Big Data and the Divide & Recombine (D&R) Statistical Methodology in AutoRegression Integrated Moving Average (ARIMA) Modeling
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| Speaker: | Jeremy Troisi '08
PhD Candidate
Statistics
Purdue University
West Lafayette, IN
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
February 12, 2015
| Title: |
Triangle Mystery Redux
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| Speaker: | Michael A. Jones
Associate Editor
Mathematical Reviews
Ann Arbor, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
February 19, 2015
| Title: |
Increasing Forests in Graphs
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| Speaker: | Josh Hallam
Graduate Student
Department of Mathematics
Michigan State University
East Lansing, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
February 26, 2015
March 5, 2015
| Title: |
Constraint profit optimization in pricing an established national brand in the presence of a local generic.
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| Speaker: | Stavros Christofi
Associate Professor
Mathematics
Western Connecticut State University
Danbury, CT
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
March 26, 2015
| Title: |
Decision Models for Logistics Management
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| Speaker: | Hakan Yildiz
Assistant Professor
Supply Chain Management
Michigan State University
East Lansing, MI
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 2, 2015
| Title: |
f(Mathematical Thinking) = Creativity
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| Speaker: | Eric Mann, `74
Assistant Professor of Mathematics Education
Mathematics
Hope College
Holland, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 16, 2015
| Title: |
Making Calculus Easy the Hard Way
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| Speaker: | Andrew Livingston
Department of Mathematics
Eastern Michigan University
Ypsilanti, MI
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| 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).
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 30, 2015
| Title: |
The Foundation of Catastrophic Insurance Pricing
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| Speaker: | Kyle Albrecht, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 30, 2015
| Title: |
Mathematics and the Outcomes of Sporting Events
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| Speaker: | Jonathon Lorenz, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 30, 2015
| Title: |
Mathematics of creating and modeling bowling balls
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| Speaker: | Matt Prosniewski, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
April 30, 2015
| Title: |
Group Theory of Molecules
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| Speaker: | Stephanie Sanders, '15
Senior Mathematics Major
Albion College
Albion, Michigan
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| 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.
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| Location: |
Palenske 227
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| Time: |
3:30 PM
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| Citation | Click for BibTeX citation |
| Flyer | Click for a printable flyer |
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