# Coffee Time

Coffee Time is a series of presentations geared toward students and designed to engage students and faculty in discussions of mathematical and statistical topics. Talks in the series are generally brief in order to allow time for questions and conversations afterward. Coffee and snacks are available before each presentation.

For more information, please e-mail Dr. Lisa Kay at lisa.kay@eku.edu.

**Department of Mathematics and Statistics Coffee Time Series**

**Fall 2017**

**Dr. Shane Redmond**

Eastern Kentucky University

*Gerrymandering, Math, and the Supreme Court*

November 17, 2017 @ 2:30 p.m., Wallace 446

Abstract:

Gerrymandering, the practice of drawing voting districts in a way that favors one party or interest group, has been in the news quite a bit lately and was the subject of a Supreme Court case last month. We’ll briefly discuss what Gerrymandering is and look at some examples. Then, we’ll examine three mathematical measures associated with Gerrymandering: the efficiency gap, partisan symmetry, and the “winner’s bonus.” This talk has lots of examples and only a few minutes of deep mathematics, so it should be accessible to almost anyone.

**Sierra Chugg, Dalton Hopper, Claire Crouch, Zachary Morgan, & Jenna Johnson**

Eastern Kentucky University

*Student Panel: Academic Enrichment Activities*

October 9, 2017

Abstract:

Looking for applied activities or research opportunities to complement your academic experience? Searching for something exciting to do next summer? Come and talk to our panel members about their experiences with internships and summer programs.

**Dr. George Cobb, Professor Emeritus of Statistics**

Mount Holyoke

*Why look for an antiderivative when your laptop can just play Monopoly?Markov Chain Monte Carlo as the second revolution in the 2500-year history of calculus*

September 22, 2017

Abstract:

The * ideas* of calculus go back 2500 years, to the paradoxes Zeno of Elea, to Pythagoras and Euclid, and to Archimedes. How to put their ideas to work has a much shorter history. Over the thousands of years since Zeno, there have been just two big breakthroughs, both computational. You know the first: In the late 1600s, the Fundamental Theorem of Calculus made it possible for scientists to compute definite integrals (area, distance traveled, etc.) by finding antiderivatives. Newton used this calculus to derive Kepler’s three laws of planetary motion from the single law of gravitation. His use of calculus opened the door to what we now call The Enlightenment

You may not know the second breakthrough: In the 1940s a chance-based method, now known as Markov Chain Monte Carlo, or MCMC, made it possible for scientists to compute integrals that had defeated old approaches. Even with electronic computers, those old approaches sagged and buckled under the burden of new scientific challenges. If you have tens of thousands of unknowns, Newton’s calculus collapses. MCMC was the second revolution in the history of the integral.

If you have taken first semester calculus you know what an integral is. If you have played Monopoly you know what a Markov chain is. My goal in this talk is to invite you to figure out how modern science depends on putting these two powerful ideas together.

(I assume you have taken a one-semester course in calculus.)

**Spring 2017**

**Dr. Pat Costello**

Eastern Kentucky University

*A Few of My Favorite Things*

April 28, 2017

Abstract:

In this talk, some of my favorite natural numbers, their definitions, their sizes, and their properties will be discussed. Even a proof that all natural numbers are inherently interesting will be given. In 1959, Disney and Donald Duck helped to popularize some of the numbers mentioned. A few EKU students have done some excellent research on a several of the different types of numbers. Their results will be mentioned.

**Jason Rollins**

Eastern Kentucky University

*Minesweeper—NP or Not NP? That Is the Question*

March 29, 2017

Abstract:

In his paper, "Minesweeper is NP-Complete" (*Math. Intelligencer*, 22(2):9-15, 2000), Richard Kaye proved that the game *Minesweeper* is in the computational complexity class NP-Complete. He did so by basically showing that it is possible to build a computer out of *Minesweeper* board configurations. In this presentation, I will show both how he was able to accomplish this task as well as how I was able to use his research to build a full adder circuit capable of performing addition on two 1-bit numbers.

**Dr. Rachel Bishop-Ross, Dr. Jason Gibson, Dr. Jeff Neugebauer, & Dr. Michelle Smith**

Eastern Kentucky University

*Graduate School Panel*

February 27, 2017

Abstract:

Considering going to graduate school? Come and talk to our panel members about their experiences with graduate school. Get advice about how to choose a school and how to make your applications look good. Join us for this unique Coffee Time presentation!

**Fall 2016**

**Dr. Shane Redmond, Dr. Patti Costello, & Dr. Lisa Kay**

Eastern Kentucky University

*The Modern Master’s Degree in Mathematics: What Does It Look Like?*

November 11, 2016

Abstract:

Inspired by regular reports on the state of undergraduate and doctoral education, the authors undertook a nationwide survey of master’s degree programs in the mathematical sciences. We believe this to be the first comprehensive study of the master’s degree in mathematics in over 100 years! The authors will share some of the highlights of their 2013 survey on the nature, practices, and composition of master’s degree programs across the United States. If you are interested in graduate school, come hear about the different types of master’s programs that are out there.

**Dr. Noah Aydin**

Kenyon College

*The Legacy of Medieval Islamic Math and Science in the Modern World*

October 7, 2016

Abstract:

Some of the most fundamental notions of modern mathematics and science are a legacy of the medieval Islamic civilization. Although current research is far from giving us a full account of their contributions, we know that this legacy includes the number system that we use today, the fields of algebra and trigonometry, the concept of algorithm, foundations of optics, the scientific method, and important works in astronomy that played a crucial role in the Copernican revolution. Yet, these contributions are generally not known, not only in the West but in the Islamic World either. In this presentation, we will highlight a sample of such contributions and briefly introduce a few of the great scientists from that period. We will also discuss some of the reasons behind the lack of awareness on this topic and the role of religion in the remarkable rise of mathematical sciences in the medieval Islamic civilization.

**Nathan Russell**

Eastern Kentucky University

*The Mathematics of My Life and Industry*

September 23, 2016

Abstract:

Sometime during the 1980s (no need for exact dates), I was born to a family with a long history in the logistics industry. I always felt like I had a strong familiar sense of the industry. It was not until I stepped into the brokerage office building that I realized how complicated it is to get something moved from point A to point B. Starting from preteen years I developed my programming skills which later inspired a love for mathematics and economics. This talk will demonstrate how I have used mathematics and computers to optimize load selections, prevent and predict diesel engine failures, identify dangerous driver behaviors, and gain a solid foothold in an industry known for breaking dreams. My personal live load board, live truck tracking data, and routing invoices will be provided to demonstrate the mathematics. Come listen! I believe you will be entertained and surprised at the technical level of the industry. Planned guests include a vice president of operations for a regional distributor and the regional manager of the northeast region for the largest refrigerated logistics company.

**Spring 2016**

**Dr. Jeff Neugebauer**

Eastern Kentucky University

*Fractional Calculus*

April 20, 2016

Abstract:

Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary order. After some historical background is given, we will introduce the concept of fractional integrals and fractional derivatives. We will start by looking at fractional derivatives of power functions and exponential functions. Then the definitions of the Riemann-Liouville fractional integral and the Riemann-Liouville fractional derivative will be developed. Finally, some applications and different definitions of fractional derivatives will be given.

**Rebecca Thiem, Dr. Michelle Smith, & Dr. Lisa Kay**

Eastern Kentucky University

*Do Study Halls Produce Valedictorians?*

March 30, 2016

Abstract:

One of the greatest honors a graduating high school senior can receive is the title of "Valedictorian." Many students set this goal prior to high school and will forgo taking a study hall or free period in order to enroll in more weighted classes and useful electives. However, not taking a study hall may be causing these students to lose the "Number 1" ranking. This project compares prevalent methods for calculating high school GPAs and demonstrates the paradox of lowering class ranking by taking more classes. We will provide suggestions and options for school administrators to improve their ranking methods in order to ensure that the top student receives their due honor.

**Dr. Benjamin Braun**

University of Kentucky

*Information about Applying to Graduate Programs in Mathematics*

February 4, 2016

Abstract:

One goal of the mathematical community is to increase the number of students who study mathematics at all levels. However, applying to graduate school in mathematics can seem like a daunting task for many students. In this presentation I will discuss basic information about the application process and provide helpful suggestions and tips for students considering graduate school in the mathematical sciences. There will be plenty of time to discuss questions from students.

**Fall 2015**

**Dr. Atilla Sit**

Eastern Kentucky University

*Geometric Buildup Algorithm with Applications to Molecular Modeling*

October 27, 2015

Abstract:

When coordinates of points in 3D space are known, the distances among them can be computed using the distance formula. How about the inverse problem? If the distances are given, can we find the coordinates of the points satisfying the given distances? The latter problem is called the distance geometry problem in mathematics. It requires the solution of a system of equations, and it has applications such as protein structure determination and sensor network localization. We seek the solution of the problem using a geometric buildup algorithm. Central to this approach is the idea that the algorithm determines one point at a time, with available distances from the determined points to the undetermined ones. We present the general algorithm and review its recent development. We show the results from applying the algorithm to some problems and explain its use in protein modeling.

**Dr. Kari Everett**

Eastern Kentucky University

*Fractal Geometry: Geometry of Nature*

September 16, 2015

Abstract:

Have you ever looked around and wondered how you would describe a leaf or a tree in terms of shapes to someone who had never seen one? The geometry of nature helps us to do that. We will explore the origins of fractals and how computers revived the study of fractals. The geometry of nature is explored through applications in areas such as banking, literature, and art. Also, chaos theory and its connection to fractals will be explored with the use of spreadsheets and applets.

**Spring 2015**

**Deanna Pelfrey, Chris Phillips, & Chris Sears**

Bluegrass Community and Technical College, Somerset Community College, & Maysville Community and Technical College

*Panel Presentation: Teaching Mathematics at a Community College*

April 21, 2015

Abstract:

Do you think you might want to teach at a community college someday? Come and talk to our panel members about their job experiences. Join us for this unique Coffee Time presentation!

**Dr. Jeff Neugebauer**

Eastern Kentucky University

*An Introduction to Time Scales*

March 11, 2015

Abstract:

In this talk, we will introduce the field of time scales, a field that was developed to unify integral and differential calculus with the calculus of finite differences. Key concepts of time scales calculus, including the forward jump, backward jump, graininess, derivative, and integral operators will be defined. Many examples and applications will be discussed. Bring a pencil and paper to work along with the examples!

**Dr. Kirk Jones**

Eastern Kentucky University

*Exploring Complex Power Series with Gaps*

February 12, 2015

**Fall 2014**

**Dr. Rachel Bishop-Ross, Dr. Kirk Jones, Dr. Jeff Neugebauer, Dr. Shane Redmond, Dr. Michelle Smith, & Dr. Steve Szabo**

Eastern Kentucky University

*Graduate School Panel*

November 21, 2014

Abstract:

Considering graduate school? Come and talk to our panel members about their experiences with graduate school. Get advice about how to choose a school and how to make your applications look good. Join us for this unique Coffee Time presentation!

**Dr. Guy Brock**

University of Louisville

*Beyond the t-test: Lessons Learned in the Life of One Humble Biostatistician*

October 24, 2014

Abstract:

The world is awash with data. This talk will focus on several anecdotal lessons learned during my experiences as a collaborating biostatistician. These stories cover shortfalls of commonly applied approaches to analyzing public health/biomedical data and discuss application of more appropriate methodology in each case. Covered topics include how to compare response “curves,” the practical importance of missing data imputation, modeling response heterogeneity (and getting away with it), the need to account for trends in time series data, and how to handle mortality when considering other time-dependent outcomes.

**Dr. Rachel Bishop-Ross**

Eastern Kentucky University

*Euler’s Theorem and Related Results*

September 24, 2014

Abstract:

In this talk, Dr. Bishop-Ross will give the necessary background to understand Euler's Formula for planar graphs (V − E + F = 2), including the Handshaking Lemmas. She will give a proof of the theorem and proofs of some immediate important results. Time permitting, she will introduce vertex coloring on graphs and prove the Five Color Theorem for simple connected planar graphs.

**Spring 2014**

**Josh Sparks**

Eastern Kentucky University Alumnus

*Hyperpower to the Max! An E-Z Look at Tetrations and Their Maximization*

March 3, 2014

Abstract:

Just when you just felt safe with exponents . . . here comes the hyperpower. Also known as the tetration or the repeated exponent, the hyperpower takes a number, x, and forms a chain x^(x^(x^(x^ . . .) that, if extended to an infinite tower, tends to blow up pretty darn often. We will first explore a common math competition problem using this concept, and then look at graphical and calculus-based solutions to maximizing the function. From there we'll discuss the creation of Lambert's W function and the range of what values these infinite hyperpowers actually exist, overall showing that these crazy expressions are Easier than they appear!

**Dr. Don Greenwell**

*The Odd Ball Problem and Mastermind*

January 22, 2014

Abstract:

This talk will present similar solutions to two of my favorite problems: The Odd Ball Problem (aka Counterfeit Coin Problem): and the game of Mastermind. In the Odd Ball Problem, we are allowed to use a balance scale to find the odd ball among twelve balls, and determine if it is lighter or heavier than the other eleven. Mastermind is a game where one player (the codeguesser) is trying to guess the code selected by the other player (the codekeeper). The code is a sequence of four colors selected from six colors (repetitions are allowed).

We will discuss a common strategy of minimizing the worst possible outcome for each step in finding the answer, and also present solutions for each problem that uses the same steps every time (no thinking required).

**Fall 2013**

**Nathan Russell**

Eastern Kentucky University

*A Few Real Abnormalities*

November 18, 2013

Abstract:

Emile Borel made several contributions to mathematics in the areas of probability, measure theory, set theory, etc. This talk will focus on a particular set of numbers that have some interesting properties from a probabilistic and statistical point of view. This particular set of numbers is a subset of the irrational numbers that includes both algebraic and transcendental numbers. Defining the properties for elements in this set is fairly simple, but actually proving whether a specific number belongs to this set is nearly impossible. The interesting aspect of this research is not whether a number is a member of this set, but the circumstances where these numbers are present or not present and the inferences we can make about numbers that belong to this set. For example, it is easy to prove that the Cantor set will not contain any number belonging to this interesting set. In fact, if the conjecture posed by Borel about this set of numbers is true, then the irrationals in the Cantor set must be transcendental. So how rare are these numbers? Borel proved that nearly every real number will be an element of this set. By "nearly every" we mean that elements that are not a member of this set have Lebesgue measure zero. Should we call those elements outside the set “abnormal”? This talk will explore numbers believed to be elements of this set through the use of computer programs.

**Dr. Lisa Kay**

Eastern Kentucky University

*This Ain’t Your Grandmother’s P-Value: Using Randomization-Based Methods to Introduce Inference*

October 30, 2013

Abstract:

In order to utilize traditional inferential procedures, students must first study background material that includes a variety of topics. Randomization-based methods are more intuitive and allow students to get to the heart of inference quickly. We will explore the use of these methods via applets that perform simulations. Attendees are encouraged to bring laptops or other electronic devices on which to run the applets.

**Dr. Shane Redmond**

Eastern Kentucky University

*How I Tried to Beat Vegas: An Exercise in the Right and Wrong Ways to Use Probability*

September 23, 2013

Abstract:

Can you go to a casino and manipulate the odds so they are in your favor? Dr. Redmond talks about a strategy that appears to do just that and the trip he took to Las Vegas to test it out. Was it success or is there a better way of looking at the probabilities involved that shows the house always has the edge? Come share in a story about getting kicked out of casinos, with a little bit of simple math thrown in.

Anyone who has taken MAT 105 or any introductory statistics class should have no problem working through the strategies with us.

**Spring 2013**

**Dr. Xiang-dong Hou**

University of South Florida

*Sums of Reciprocals of Polynomials Over Finite Fields*

April 2, 2013

Abstract:

After a brief introduction to finite fields, we consider the sum of the reciprocals of all monic polynomials of a given degree over a finite field each raised to the power of *k*. When *k*≤*q*, the sum has a surprisingly simple result due to mysterious cancellations that occur in the sum. We discuss this interesting phenomenon and its connection to a deeper problem.

The talk is based on a recent paper in the MAA Monthly: K. Hicks, X. Hou, G. L. Mullen, Sums of reciprocals of polynomials over finite fields, Amer. Math. Monthly, 119 (2012), 313–317.

**Dr. Steven Dougherty**

The University of Scranton

*Japanese Ladders and Games*

February 28, 2013

Abstract:

We shall describe a visual representation of permutations as Japanese ladders and use this representation to make a series of interesting mathematical games. These games have interesting mathematical aspects but can be played by anyone. The ladders have applications to the Braid group in Topology.

**Dr. Jeff Neugebauer**

Eastern Kentucky University

*Introduction to Fractional Calculus*

January 31, 2013

Abstract:

For a suitable function *f(x)*, anyone that has taken Calculus I is familiar with finding the *n*th derivative of *f*, *f ^{(n)}(x)*, as long as

*n*is an integer. Similarly, someone who has taken Calculus I could integrate a function

*n*times. However, the concept of finding

*f*or taking

^{(α)}(x)*α*integrals of a function, where

*α*is any real number, is foreign to most. In this talk, we will introduce the idea of fractional calculus, which involves taking derivatives and integrals of arbitrary order. Unlike the standard derivative and integral, these ideas do not have a nice geometric interpretation. However, we will see that fractional calculus is a natural extension of the calculus everyone is familiar with. Some applications of fractional calculus will be given as well.

**Fall 2012**

**Dr. Yong Wang**

Eastern Kentucky University

*R and Introductory Data Mining*

November 12, 2012

Abstract:

R is an integrated suite of software facilities for data manipulation, calculation and graphical display. It is a choice for many statisticians for data analysis and statistical method development. It is also a good choice for data mining, which involves statistical methods to extract important patterns and trends from data.

This talk is intended to provide students with a general idea of the new course STA 580/780 offered in Spring 2013. We will introduce how the software package, R, should be put to work and conduct statistical analyses. Similarities and differences between R and some other popular statistical software, such as SAS and Minitab, will be discussed. We will also give a brief introduction of some of the concepts and methods of data mining. Students will see how we can make transitions from an applied statistical course to data mining.

**Dr. Shawn Clift**

Eastern Kentucky University

*Twin Primes*

October 25, 2012

Abstract:

The topic of the day is Twin Primes, and we will be exploring two ideas. First, how do we find twin primes? Second, how do we estimate the number of twin primes less than a given integer without actually finding all of them? We will also talk about some seemingly useless theorems for testing whether or not two numbers are twin primes.

**Dr. Daniel Mundfrom & Dr. Michelle Smith**

Eastern Kentucky University

*The Effect of “Freebies” on Winning in Baseball*

September 21, 2012

Abstract:

Former Major League Baseball player and current broadcasting personality Morgan Ensberg has developed a statistic to measure the impact of “freebies” on the outcome of a baseball game. The Morgan Ensberg Index (MEI) is a composite of walks, errors, stolen bases allowed, wild pitches, and hit batsman. This research extends the MEI to include balks, passed balls, and catcher’s interference and investigates the relationship between “freebies” and runs allowed and games won. The analyses were performed using NCAA Division I baseball statistics from the 2011 and 2012 seasons.

**Spring 2012**

**Dr. Kirk Jones**

Eastern Kentucky University

*How Much Wiggle Ya Got?*

The Final Coffee Time Talk of the Year

April 24, 2012

**Dr. Steve Szabo**

Eastern Kentucky University

*An Introduction to Algebraic Coding Theory*

March 28, 2012

Abstract:

A general introduction to coding theory will be presented along with a description of algebraic coding theory. Then some basic ideas of linear binary block codes will be given so that finally the double error correcting BCH code of length 15 can be presented.

**Dr. Daniel Mundfrom**

Eastern Kentucky University

*The Game of Mousetrap: A Problem in Permutations*

February 28, 2012

Abstract:

The Game of Mousetrap, first introduced in the mathematical literature by Arthur Cayley in 1857, involves permutations of *k* cards numbered consecutively from 1 to *k*. The cards are laid out in some order and the game is played by counting on the cards, beginning the count with 1. If at any time the number of the count matches the number on the card, this is called a ‘hit’ and the card is thrown out. The counting begins again with 1 on the next card and returns to the 1^{st} card when the *k*^{th} card is reached. Each time a card is ‘hit,’ the card is thrown out and the counting starts over at 1. The game continues until all cards have been hit (the player wins) or until the count reaches *k* with no cards having been hit (the cards win). Some examples and underlying theory will be presented.

**Dr. Cheryll Crowe**

Eastern Kentucky University

*KenKen®*

January 31, 2012

Abstract:

The popularity of Sudoku puzzles has increased dramatically in the United States over the past few years. Also gaining momentum in the mathematics and mathematics education communities is the logic puzzle, KenKen®. Originating in Japan, KenKen extends the enjoyment of Sudoku by utilizing a mixture of logical, simple arithmetic and combinatorial skills. This coffee time talk will include an overview of KenKen as well as interesting mathematical extensions of the puzzle.

**Fall 2011**

**Dr. Shane Redmond**

Eastern Kentucky University

*Backgammon Quiz*

December 7, 2011

Abstract:

Backgammon is a classic game that is easy to learn, but takes a lifetime to master. While luck and strategy are key elements to winning, using some elementary rules of probability can elevate your game to the next level. We'll present a "quiz" on some very basic probability problems that come up in backgammon games. A prize will be awarded to the student with the highest score on our quiz.

**Dr. Pat Costello**

Eastern Kentucky University

*Breaking Up (Integers) Is Hard to Do, But Not for Euler*

October 26, 2011

Abstract:

We will look at the partition function which gives a count of the number of ways to break up an integer into integer parts. We will then focus on restricted partitions which satisfy certain conditions. We show an amazing proof by Leonhard Euler of an equality between two such restricted partitions.

**Dr. Mathew Cropper**

Eastern Kentucky University

*Cook’s Paradox*

October 5, 2011

Abstract:

Many are familiar with Simpson’s Paradox. This talk will introduce Cook’s Paradox. This is named after Lyle Cook, who spent three days computing grades for a class of twenty-five students one term and, in the process, found an interesting math problem.