Program of Activities



Program of Activities

For the 97th Annual Meeting of the

Mathematical Association of America

Ohio Section

[pic]

Spring, 2013

Denison University

Granville, Ohio

April 5-6, 2013

MAA Ohio Section

Program

 

 Friday, April 5, 2013

|12:00 - 4:00 |Registration |Herrick Hall |

|12:00 - 1:20 |Student Team Competition |Higley Auditorium |

|12:00 - 1:00 |Committee Meetings: | |

| |CENTENNIAL COMMITTEE |Olin 222 |

| |CONCUR (Curriculum) |Olin 215 |

| |CONSACT (Section Activities) |Olin 220 |

| |CONTEAL (Teacher Education and Licensure) |Olin 221 |

|1:00 - 4:00 |Vendor & Book Exhibits |Samson-Talbot Hall |

|1:30 - 1:45 |Welcome and Announcements |Herrick Hall |

|1:45 - 2:45 |Invited Address: | |

| |“Blown Away: What Knot To Do When Sailing” |Herrick Hall |

| |Sir Randolph Bacon III | |

| |(cousin-in-law to Colin Adams, Williams College) | |

|2:45 - 3:10 |Break |Samson-Talbot Hall |

|3:10 - 3:15 |Centennial Minute – Dave Kullman |Herrick Hall |

|3:15 - 4:15 |Invited Address: |Herrick Hall |

| |“Opt Art” | |

| |Robert (Bob) Bosch, Oberlin College | |

|4:25 - 6:20 |Contributed Paper Sessions |Olin 114, 221, 314 |

|4:25 - 6:20 |Executive Committee Meeting |Olin 222 |

|6:30 - 8:00 |Student Pizza Party |2nd floor Atrium –Burton Morgan |

|6:30 - 6:50 |Social Time |Welsh Hills Room – |

| | |Burton Morgan |

|6:50 - 8:00 |Banquet |Welsh Hills Room – Burton Morgan|

|8:15 - 9:15 |Stage Performance: “Pythagoras’s Darkest Hours, The Book, Lord of the Rings |Lecture Hall (115) Burton Morgan|

| |(and more)” | |

| |Colin Adams, Williams College | |

| |and the Mobiusbandaid Players | |

|9:15 |Business Meeting and Presentation of Teaching Award |Lecture Hall (115) |

| | |Burton Morgan |

Saturday, April 6

|8:00 - 10:00 |Registration |Olin 201 |

|8:00 - 10:00 |Book Vendors and Exhibits |Samson-Talbot Hall |

|8:00 - 8:50 |Coffee and Pastries |Samson-Talbot Hall |

|8:05 - 8:40 |Meeting of Department Chairs and Liaisons |Olin 222 |

|8:05 - 8:40 |Committee on Local Arrangements |Olin 220 |

|8:50 - 9:00 |Welcome and Announcements: Student Team Competition Results |Herrick Hall |

|9:00 - 10:00 |Invited Address: |Herrick Hall |

| |“Stefan Banach and the Scottish Café” | |

| |Barbara Faires, Westminster College and Secretary of the MAA | |

|10:00 - 10:20 |Break |Samson-Talbot Hall |

|10:25 - 11:40 |Contributed Paper Session |Olin 114, 221,314 |

|11:50 - 12:50 |Retiring President’s Address: |Herrick Hall |

| |“The Lady Tasting Tea: R.A. Fisher and the Statistical Revolution” | |

| |Wiebke Diestelkamp, University of Dayton | |

|12:50 - 1:00 |Closing Remarks |Herrick Hall |

Abstracts of Invited Addresses

Friday

Speaker: Sir Randolph Bacon III (cousin-in-law to Colin Adams, Williams College)

Title: Blown Away: What Knot To Do When Sailing

Abstract: Being a tale of adventure on the high seas involving great risk to the tale teller, and how an understanding of the mathematical theory of knots saved his bacon. No nautical or mathematical background assumed.

Speaker: Robert (Bob) Bosch, Oberlin College

Title: Opt Art

Abstract: Optimization is the branch of mathematics concerned with optimal performance---finding the best way to complete a task. It has been put to good use in a great number of diverse disciplines: advertising, agriculture, biology, business, economics, engineering, manufacturing, medicine, telecommunications, and transportation (to name but a few). In this lecture, we will showcase its amazing utility by demonstrating its applicability in the area of visual art, which at first glance would seem to have no use for it whatsoever! We will begin by describing how to use integer programming to construct a portrait out of complete sets of double nine dominoes. We will then describe how high quality solutions to certain large-scale traveling salesman problems can lead to beautiful continuous line drawings. We will conclude by presenting other examples of Opt Art---art constructed with the assistance of mathematical optimization techniques.

Speaker: Colin Adams, Williams College and the Mobiusbandaid Players

Title: Stage Performance: Pythagoras’s Darkest Hour, The Book, Lord of the Rings (and more!)

Abstract: This event includes a small collection of humorous short mathematical pieces that ask questions like, “How did Pythagoras discover his famous theorem?”, “Do the contents of mathematical paper have the power to lord over its owner?”, and “What would you see if you looked in ‘The Book’?”.

Saturday

Speakers: Barbara Faires, Westminster College and Secretary of the MAA

Title: Stefan Banach and the Scottish Café

Abstract: The Scottish Café, the favored cafe of mathematicians in Lvov, Poland, is now known by many through the notebook of problems produced by those mathematicians.  The notebook provides insight into problems posed as well as life in Poland at that time.  I will examine these along with one of the regulars at the cafe, Stefan Banach, who contributed 25 problems to the notebook.

Speaker: Wiebke Diestelkamp, University of Dayton

Title: The Lady Tasting Tea: R. A. Fisher and the Statistical Revolution

Abstract: Ronald Aylmer Fisher (1890 - 1962) made extraordinary contributions to statistical theory and methods, experimental design, scientific inference, evolutionary biology and genetics. He published seven books and several hundred papers in more than 80 different journals. His contributions to mathematical statistics are still relevant today. We will talk about his life, some of his ideas that revolutionized the practice of statistics and his (sometimes contentious) relationships with his contemporaries. 

Brief Biographies of Invited Speakers

Colin Adams, Williams College

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College. He received his Ph.D. from the University of Wisconsin-Madison in 1983.  He is particularly interested in the mathematical theory of knots, their applications and their connections with hyperbolic geometry. He is the author of "The Knot Book", an elementary introduction to the mathematical theory of knots, "Why Knot?", a mathematical comic book with attached toy and "Riot at the Calc Exam and Other Mathematically Bent Stories", a compendium of humorous math stories.  He is the co-author of the humorous supplements "How to Ace Calculus: The Streetwise Guide" and "How to Ace the Rest of Calculus: the Streetwise Guide” as well as the textbook "Introduction to Topology: Pure and Applied".  He also appears with Thomas Garrity in "The Great Pi/e Debate",  "The United States of Mathematics Presidential Debate" and “The Derivative vs. the Integral: The Final Smackdown”, DVD’s of humorous debates on mathematical topics that are available from the Mathematical Association of America. He has written a variety of research articles on knot theory and hyperbolic 3-manifolds. He is a recipient of the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. He is also the humor columnist for the Mathematical Intelligencer.

Robert (Bob) Bosch, Oberlin College

Robert (Bob) Bosch is Professor of Mathematics at Oberlin College. He specializes in optimization, the branch of mathematics concerned with optimal performance. Since 2001, Bosch has devoted increasing amounts of time and effort into devising and refining methods for using optimization to create pictures, portraits, and sculpture. He has had pieces commissioned by Colorado College, Western Washington University, Occidental College, Spelman College, and the organizing committees of several academic conferences. He operates a website, , from which it is possible to download free plans for several of his domino mosaics (including a 44-set portrait of President Barack Obama). His sculpture Embrance was awarded first prize at the 2010 Mathematical Art Exhibition in San Francisco.

Barbara Faires, Westminster College and Secretary of the MAA

Barbara Faires has been active in MAA since joining the faculty at Westminster College and beginning the student puzzle session for the Allegheny Mountain Section. She has received the Section's Meritorious Service and Distinguished Teaching Awards and was an initial coordinator of Section NExT.

Barbara joined the MAA Committee on Sections in 1982 and has been on the Executive Committee as Chair of committees: Sections, Audit, Budget, and as First Vice President. She has chaired nominating, awards, and search committees and served on a broad range of MAA committees and strategic planning groups.

Barbara earned her doctorate in mathematics (vector measures and Banach space theory) at Kent State University with adviser Joe Diestel and then studied computer science at Carnegie Mellon University during a sabbatical leave. Her undergraduate degree from East Carolina University is in mathematics and business. She has held visiting positions at Carnegie Mellon and Westminster College, Oxford, UK and taught in the early PA Governor's School for the Sciences. Her publications include papers in Transactions and Proceedings of the AMS. At Westminster she has chaired the Department of Mathematics and Computer Science, served as Vice President for Academic Affairs, and received both the Henderson Lecture and Distinguished Faculty Awards.

Wiebke Diestelkamp, University of Dayton

Wiebke Diestelkamp holds an M.S. and a Ph.D. in Mathematics from the University of Wisconsin – Milwaukee. She is an Associate Professor of Mathematics at the University of Dayton. She has been teaching a broad range of courses, in particular, probability and statistics courses for various undergraduate and graduate student populations. She is involved in interdisciplinary research projects with a number of colleagues in various departments. As a member of the University of Dayton team of the LEADER Consortium working to improve the recruitment, retention, advancement and climate for women STEM faculty, Wiebke serves as the Equity Advisor for the College of Arts and Sciences. (LEADER is an NSF-ADVANCE funded partnership of AFIT, Central State University, Wright State University and the University of Dayton). In the Ohio Section of the MAA, Wiebke served as co-coordinator for Ohio NExT (2005 - 2011) and as Liaison Coordinator (2006 - 2011). She is the current President of the Ohio Section. 

Contributed Paper Sessions

Friday, April 5

4:25—6:20

*denotes undergraduate student

|Time |Session A |Session B | Session C |

| |Room 114 |Room 221 |Room 314 |

| |Session Chair: Maduka Rupasinghe |Session Chair: Chandra Dinavahi |Session Chair: Flavia |

| | | |Sancier-Barbosa |

|4:25-4:40 |Data Mining and Analyzing Basic |Bessel formula for transient |Converse to Lagrange’s Theorem on |

| |Features of the State of the Union|distribution |groups |

| |Addresses |Abstract 2 |Abstract 3 |

| |Abstract 1 | | |

| |Trevor Bihl |Barbara H. Margolius |Blain A. Patterson* |

| |AFIT |Cleveland State University |Youngstown State University |

|4:45 – 5:00 |Using Livescribe Pencasts to |Exploring Properties of the Bow |Prioritizing Vacant Homes for |

| |Enhance/ |Sequence-Generating Functions |Demolition in Youngstown, Ohio |

| |Supplement Lectures |Abstract 5 |Abstract 6 |

| |Abstract 4 | | |

| |Moez Ben-Azzouz |Allison Biaglow* and Andy Miller* |Eric A. Shehadi* |

| |Sinclair Community College |Baldwin Wallace University |Youngstown State University |

|5:05-5:20 |Kramerica Returns:  The Power of |Subtriangles and Their Implications |Rubik's Cube Solving Android App |

| |Outsourcing |for Creating Subrectangles |Abstract 9 |

| |Abstract 7 |Abstract 8 | |

| | |Stacee M. King* | |

| | |Ashland University | |

| |John Tynan | |Jarrett M. Scacchetti* |

| |Marietta College | |Youngstown State University |

| | | | |

|5:25-5:40 |50 Years of Service ... and Then | Variations on the Monty Hall Problem|Prime Time Algorithms: Constructing|

| |Pffft! |Abstract 11 |a Prime Number Generator |

| |Abstract 10 | |Abstract 12 |

| |David A. Cusick |Kate Fleming* |Sarah E. Ritchey* |

| |Marshall University |Ashland University |Youngstown State University |

|5:45 – 6:00 |Ming Antu and His Work on the |Decimal Expansions Involving |Selecting the Best Primality |

| |Theory of Power Series |Fibonacci Numbers |Testing Algorithm |

| |Abstract 13 |Abstract 14 |Abstract 15 |

| |Weiping   Li |Megan Raber* |Tim Shaffer* |

| |Walsh University |Ashland University |Youngstown State University |

|6:05-6:20 |Discrete Deconvolution |Thinning Out the Primes: Convergence |The “Bigger Half”: Examining Fair |

| |Abstract 16 |of Sums of Reciprocal Primes |Division |

| | |Abstract 17 |Abstract 18 |

| |M. B. Rao |Justin N. Young |Megan J. Chambers* |

| |University of Cincinnati |Ashland University |Youngstown State University |

Saturday, April 6

10:25-11:40

*denotes undergraduate student

|Time |Session A |Session B |Session C |

| |Room 114 |Room 221 |Room 314 |

| |Session Chair: erica Whitaker |Session Chair: Don Bonar |Session Chair: Adam Parker |

|10:25-10:40 |Pi to 10,000 Digits |Parallels on parallels: on the plane, |Exploring Check Digit Error Correction|

| |Abstract 19 |sphere, and hyperbolic plane |Abstract 21 |

| | |Abstract 20 | |

| |Brian J. Shelburne |Daniel E. Otero |Ashley E. Orr* |

| |Wittenberg University |Xavier University |Youngstown State University |

|10:45 – 11:00 |Survival Analysis and Highly |Faculty Flexibility & Black Belts |Mathematical Model of the Interaction |

| |Censored Data |Abstract 23 |between Light and Photonic Crystals |

| |Abstract 22 | |Abstract 24 |

| |Shelby M. Cummings* |Daniel Baczkowski |Michael A. Baker* |

| |Wittenberg University |The University of Findlay |Youngstown State University |

|11:05-11:20 |MathJax:  Displaying mathematics on |Graph Theory and Google Maps |Necessary condition of d-bar equation |

| |the web |Abstract 26 |in Holder norm in complex 3 |

| |Abstract 25 | |dimensional Euclidean space |

| | | |Abstract 27 |

| | Barbara D’Ambrosia |Tyler Muryn* | |

| |John Carroll University |University of Findlay |Young Hwan You |

| | | |Indiana University East |

|11:25-11:40 |D. Ransom Whitney and the | Mathematics Madness: Insight on |C-z Frames M(b,n) where z is even |

| |Mann-Whitney U Statistic |Picking March Madness Brackets |Abstract 30 |

| |Abstract 28 |Abstract 29 | |

| |Thomas Hern |Alexandria R. Bishop* and Daniel J. |Chandra Dinavahi |

| |Bowling Green State University |Brooks* |The University of Findlay |

| | |University of Findlay | |

Abstracts of Contributed Papers

Friday 4:25-4:40

Data Mining and Analyzing Basic Features of the State of the Union Addresses

Trevor Bihl

Air Force Institute of Technology

Abstract 1: Changes in the Flesch-Kincaid reading level of the State of the Union Addresses over time were recently in the news; however why the State of the Union Address changed was not examined.  As a database, the State of the Union Addresses offer a relatively set of annual speeches, thus facilitating the application of data mining and statistical pattern recognition methods; this research applies statistical methods to examine changes in data features as the State of the Union Address transitioned between written, oral, televised, and prime-time delivery mediums from 1790 to 2013.  Data features examined include words per sentence, characters per word, total words, education level of president, and Flesch-Kincaid reading level. This research examines features and applies artificial neural network feature screening as a classification method to examine possible reasons for changes in the State of the Union Addresses.

In defense of the much maligned classical formula for the transient

distribution of the number in the single server queue

Barbara H. Margolius

Cleveland State University

Abstract 2: Queuing systems arise everywhere from call centers, to planes waiting to take off, waits for internet resources or cell phone bandwidth. The transient distribution for the number of customers waiting in a queue with a single server, Poisson arrival distribution and exponential service distribution is given in most introductory queuing texts.  The formula is described in these texts as difficult to evaluate, interpret and generalize.  More specifically, various authors have written of the formula that it is ugly, disheartening, complex and obscure.  In this short talk, we argue that the classical transition probability formula can be understood in a straightforward way using sample path arguments and that there are a variety of ways to evaluate it using readily available software.  Time permitting, we will also discuss how the formula can be generalized to more complex queuing systems.

Converse to Lagrange’s Theorem on Groups

Blain A. Patterson*

Youngstown State University

Abstract 3: We will take a venture into the realm of finite group theory. I will be discussing Converse to Lagrange's Theorem groups, or CLT groups for short. This includes defining what it means to be a CLT group, examples of CLT and non-CLT groups, and properties of CLT groups. My research attempts to classify these groups and discover their structure.

Friday 4:45 – 5:00

Livescribe Pencasts to Enhance/Supplement Lectures

Moez Ben-Azzouz

Sinclair Community College

Abstract 4: This will be a brief introduction to the SmartPen/EchoPen technology and how it might be used to promote learning in mathematics.

Simple Functions for Finding Normal Probabilities

Allison Biaglow* and Andy Miller*

Baldwin Wallace University

Abstract 5: This talk will explore some properties of the Bow Sequence.  The Bow sequence is a family of recursive sequences that are defined similarly to the Stern Sequence.  In particular, we are considering the case with initial conditions 0 and 1.  The main topics that will be discussed are generating functions and various properties of the crushed array.

Why Our Mathematics is Neither Necessary Nor Sufficient for Science

Eric A Shehadi*

Youngstown State University

Abstract 6 A January 2013 article in the Youngstown Vindicator noted that the city of Youngstown has historically taken a “scattershot approach” to identifying and razing vacant homes. This research focuses on creating and applying a mathematical model to prioritize vacant homes for demolition. It relies on variables including property condition, neighborhood, and also through geographical analysis of the surrounding area and homes. The model utilizes data collected by organizations within the city to assign scores to vacant properties and weigh these scores to ultimately rank vacant homes for demolition. By identifying priority demolitions, it is hoped that the model will maximize the impact of demolition funds to benefit the community and the city.

Friday 5:05 – 5:20

Kramerica Returns:  The Power of Outsourcing

John Tynan

Marietta College

Abstract 7: The most "interesting" question in Calculus I is of course to determine the maximum area that can be enclosed by a fixed amount of fencing.  Over the years I have given this question to students and asked them to consider different scenarios along with it, such as the inclusion of a barn, using shapes other than rectangles, and deciding when more work is justified.  Recently I was contacted by John Michel about using various graphical techniques to answer these questions.  This talk will show how some of the scenarios can be answered with graphical techniques making the problem even more accessible. This is joint work with John Michel.

Subtriangles and Their Implications for Creating Subrectangles

Stacee M. King*

Ashland University

Abstract 8: Given a triangle and a ratio it is possible to construct what are called subtriangles of the given triangle; which have an interesting symmetry property. Through the use of matrices and the Cartesian plane the vertices of subtriangles can be obtained. Extending this graphical approach to a given rectangle, is it possible to determine the vertices of its subrectangles and to explore if the properties of subtriangles also extend to subrectangles. 

Rubik's Cube Solving Android App: Implementation of Kociemba's Two-Phase Algorithm

Jarrett M Scacchetti*

Youngstown State University

Abstract 9: The Rubik’s Cube is a household common puzzle invented in 1974 by Erno Rubik, a Hungarian sculptor and professor of architecture. It is a puzzle that became popular in the 1980’s to kids of all ages, and even more so in the field of mathematical group theory. This Rubik’s Cube Android App takes pictures of a 3x3x3 cube, and will generate a solution with twenty-two moves or less. The solution is created by the implementation of a color recognition algorithm that changes the RGB values to a Hue-Saturation value, which maps the 3x3x3 cube and passes it into Kociemba’s Two-Phase Cube Solving Algorithm, outputting the result to a text friendly interface for the user to understand. Credit for this app goes to the team of Aaron Bishop, Michael Sammartino, and Jarrett Scacchetti.

Friday 5:25 – 5:40

350 Years of Service ... and Then Pffft!

David A Cusick

Marshall University

Abstract 10: After more than three centuries as a well-known calculation tool, the slide rule was eclipsed by electronic calculators in the 1970s.  Based on the common (base 10) logarithm, this analog device was state-of-the-art before its popularity collapsed.  The elementary slide rule aided the approximation of products, quotients, powers and roots. A variety of other models could handle more sophisticated functions.  Some rules are still in regular use even at the present time.  Virtual rules exist, and there are some apps for that. Today’s talk will just touch the basic theory and a few examples.  Logarithm laws are well represented.  If time permits, we can see a photo gallery.  Everything should be readily accessible to those at and above pre-calculus.

Variations on the Monty Hall Problem

Kate Fleming*

Ashland University

Abstract 11: The Monty Hall Problem is a classic problem that has been around since the 1960s with a very controversial beginning. The problem begins with a contestant of a game show who has the choice to pick between three doors. One door hides a car and the other two doors hide a goat. Monty then reveals the contents behind one of the doors not chosen. We will look at the probability of winning the car should the contestant choose to keep the initial chosen door or switch to the door Monty did not open. To this end, we employ Bayes Theorem and the law of total probability. We also explore modified versions of this class problem.

Prime Time Algorithms: Constructing a Prime Number Generator

Sarah E. Ritchey*

Youngstown State University

Abstract 12: Throughout history, prime numbers and their properties have received great attention from numerous mathematicians.   Easy to define and understand, these rather independent numbers surprise and confound researchers.  For example, one can easily prove that there are infinitely many primes, and more recently, one can easily determine if a given number is prime. On the other hand, although conceptually trivial, it is not easy to factor a large composite number into its prime components nor is it a trivial matter to find a practical formula for generating all the primes or even one that generates only primes.  This presentation will examine the accuracy of different prime generating algorithms like polynomial generators, the Fermat primality test, and the W. H. Mills equation. It will also take a closer look at the precision and brute computational power needed to produce prime numbers.

Friday 5:45 – 6:00

Ming Antu and His Work on the Theory of Power Series

Weiping Li

Ashland University

Abstract 13: Ming Antu (1692? – 1765?) was an outstanding astronomer and mathematician of Mongolian nationality. He was usually regarded as the first person in the history of Chinese mathematics to study infinite series. His major mathematical work is contained in the book Ge Yuan Mi Lu Jie Fa (Quick Methods for Determining Segment Areas) completed in 1774 and published in 1839. In the talk, we will present some recent studies on the book and Ming Antu’s work on the theory of power series. We will show that he used a combination of Western knowledge with traditional methods in his work. We will also discuss his influence on the development of the theory of infinite series in China in 18th and 19th centuries.

Decimal Expansions Involving Fibonacci Numbers

Megan Raber*

Ashland University

Abstract 14: We explore fractions whose decimal expansions involve sequences of the Fibonacci numbers. Using a generating function, we examine several such fractions and how they give rise in their decimal representation to the Fibonacci numbers.

Selecting the Best Primality Testing Algorithm

Tim Shaffer*

Youngstown State University

Abstract 15: While it is computationally infeasible to determine the prime factors of an integer, it is often orders of magnitude easier to determine whether or not a number is prime. There are a variety of algorithms available for this purpose, some of which run in polynomial time. Due to limitations on the hardware, however, the actual implementation can become problematic despite low time complexity. When choosing an algorithm, one must weigh running time, accuracy, storage space, implementation difficulty, etc. In this presentation several primality testing algorithms and their implementation and use considerations will be discussed.

Friday 6:05 – 6:20

Discrete Deconvolution

M. B.  Rao

University of Cincinnati

Abstract 16: Suppose X and Y are two independent Bernoulli random variables. Then the distribution of the sum S = X + Y is easy to work out. Conversely, suppose the distribution of S is known. Is it possible to figure out the distributions of X and Y individually? This problem arose in a data analysis context. We will discuss these problems and the attendant statistical issues.

Thinning Out the Primes: Convergence of Sums of Reciprocal Primes

Justin N. Young

Ashland University

Abstract 17: It is a well-known fact of elementary number theory that the sum of reciprocals of the prime numbers diverges.  A natural question is, how "large" can a subset of the primes be, such that the sum of reciprocals of primes in the subset converges?  I will discuss some appropriate measures of "largeness" for sets of primes and their relation to convergence, and then I will give some interesting examples of "smaller" sets of primes.

The "Bigger Half": Examining Fair Division

Megan J. Chambers*

Youngstown State University

Abstract 18: The Fair Division Dilemma, also known as the Cake-Cutting Problem, is a method of resource allocation used to ensure that each party sharing the resource believes that they have received at least a fair share. It is a problem that has been studied extensively by mathematicians for years and has been the topic of many mathematical papers and books. In my presentation, I examine this problem's different variations, various algorithms that can be executed to solve the problem, and an impossibility proof regarding the algorithms. The potential uses for the problem are abundant, and the mathematics behind it are beautiful, not to mention delicious!

Saturday 10:25-10:40

Pi to 10,000 Digits

Brian J. Shelburne

Wittenberg University

Abstract 19: As part of an investigation on how, in 1949, the ENIAC computed the decimal expansion of pi to 2035 digits, I had to first determine how to do the calculations on a modern computer before understanding how it could be done on the ENIAC’s very different architecture. It required high precision calculations on numbers more than 2000 digits long. This talk will present how to do the calculations to determine pi to 10000 (or more) digits – in case you might want to try it for yourself.  

Parallels on parallels: on the plane, sphere, and hyperbolic plane

Daniel E. Otero

Xavier University

Abstract 20: A standard topic in college courses in geometry is a study of parallelism in the plane and the ways in which this concept breaks down when we translate it to other surfaces, notably the sphere and the hyperbolic plane. Indeed, two common criteria are used to define parallelism of pairs of lines in the plane: nonintersection, and the existence of a transversal that makes congruent alternate interior angles. These criteria behave much differently on the other surfaces. In particular, on the hyperbolic plane only some pairs of nonintersecting lines have transversals that make congruent alternate interior angles. We discuss what goes wrong here, and exploit the resulting differences to provide a deeper understanding of parallelism between lines on all three types of surface.

Exploring Check Digit Error Correction

Ashley E. Orr*

Youngstown State University

Abstract 21: Coding theory reveals the usefulness of a single digit called a check digit.  This digit, which is not only used on commercial products, but throughout the business world, is instrumental in checking a variety of codes for errors.  Its helpfulness is limited though because while it allows a computer to recognize there is an error in the code it does nothing more.  Thus when the code encountered is identified as incorrect check digit error correction can be utilized.  This talk will investigate check digit error correction and how mathematical operations can be derived to solve the issue and fix the mistake in the code.  Furthermore this presentation will examine what variations of error correction can be used to fix a wide range of errors thus making coding, and the amending of the unavoidable mistakes, far more efficient.

Saturday 10:45-11:00

The Use of Survival Analysis Techniques Among Highly Censored Data Sets

Shelby M. Cummings*

Wittenberg University

Abstract 22: Every day, scientists and medical researchers work to develop new medicines, techniques, and surgical procedures to enhance the quality and length of the human life. But once someone has come up with a new medical technique, how can one tell that this new technique actually works better than the previous methods? This is where survival analysis comes into play.  Survival analysis is a way of measuring the survivability of patients receiving different types of treatment.  Survival analysis methods do a very good job of this when a complete data set is being used.  But many times we are dealing with an incomplete or censored data set. When the data is censored, our estimators become both higher in bias and variability.  The purpose of this research is to refine the current survival analysis techniques in order to lower the bias and variability of the estimators we gain from these studies.

Faculty Flexibility & Black Belts

Daniel Baczkowski

The University of Findlay

Abstract 23: Similar to IQ (Intelligence Quotient), EQ (Emotional Quotient) raw scores are converted to standard scores with the mean EQ score being 100 points and the standard deviation fixed at 15 points.  Recently data was collected from a varying degree of martial arts black belts.   We will describe how the sample black belt group's EQ score compared to the general public’s.

Mathematical Model of the Interaction between Light and Photonic Crystals

Michael A. Baker*

Youngstown State University

Abstract 24: In this presentation, we shall examine a matrix viewpoint of the transformations of the electric and magnetic fields. Photonic crystals are made of two thin films, A and B, that are layered n times, which shall be denoted (AB)n. Such layers are approximately parity invariant with materials that are layered as (BA)n. However, tri-layered photonic crystals have striking differences in reflection between (ABC)n and (CBA)n. An Octave program was created to perform the calculations. Results from this Octave program shall allow us to explore tri-layered films that break parity.

Saturday 11:05 –11:20

MathJax:  Displaying Mathematics on the Web

Barbara D’Ambrosia

John Carroll University

Abstract 25: MathJax provides a simple mechanism for including mathematical expressions in web pages, which can be displayed by virtually any browser, with no plugins or extra software required.  The mathematics displayed by MathJax is completely scalable, with no loss of resolution.  Best of all, there is absolutely no cost!  And did I mention that it's simple?  In this talk, I will show some examples of MathJax output and explain how to include MathJax in your web pages.

On Coincidences

Tyler Muryn*

The University of Findlay

Abstract 26: The use of computer algorithms has a tight connection with mathematics. This project demonstrates that statement through the use of concepts in graph theory integrated into a Google Maps application. The application aims to construct the safest route from point “A” to “B” using local crime statistics. In order to build a path with the least amount of crime, the principles of the shortest path algorithm are implemented except using crime as the driving force. The application incorporates many concepts within computer science as well as mathematics, and looks at how the integration of the two can result in new powerful and innovative applications.

Necessary condition of d-bar equation in Holder norm in

complex 3-dimensional Euclidean space

Young Hwan You

Indiana University East

Abstract 27: Suppose that a smooth holomorphic curve has order of contact k at the boundary point of a pseudoconvex domain in complex 3 dimensional Euclidean space. We show that the maximal gain in Holder regularity for solutions of d-bar equation is at most 1/k. This result improves the previous works by Krantz and McNeal.

Saturday 11:25 – 11:40

D. Ransom Whitney and the Mann-Whitney U Statistic

Thomas Hern

Bowling Green, Cincinnati

Abstract 28: Donald Ransom Whitney was the first chair of the statistics department when it spun off from mathematics at Ohio State in 1970.  Unlike today Whitney always believed that statistics was an applied branch of mathematics, and was meant to be used to help scientists in their research. Henry B. Mann, and Whitney published their world-famous paper introducing the Mann-Whitney U Statistic in 1947. It soon became the most widely used non-parametric statistic for two-sample tests. This is joint work with Thomas Wilke, Ohio State and Otterbein.

Mathematics Madness: Insight on Picking March Madness Brackets

Alexandria R. Bishop * and Daniel J. Brooks *

University of Findlay

Abstract 29: In this presentation, we will show the mathematics behind picking winning teams based on the teams' performance throughout the season. The method is that of paired comparisons and the AHP (Analytical Hierarchy Process) that uses matrices and eigenvectors.

C-z Frames M(b,n), where z is even

Chandra Dinavahi

The University of Findlay

Abstract 30: Let M(b, n) be the complete multipartite graph with b parts B0, ...,Bb−1 of size n. A z-cycle system of M(b, n) is said to be a cycle-frame if the z-cycles can be partitioned into sets S1, ..., Sk such that for 1 ≤ j ≤ k, Sj induces a 2-factor of M(b, n) Bi for some i ∈ Zb. The existence of a Cz-frame of M(b, n) has been settled when z ∈ {3, 4, 5, 6}. Here, we consider Cz-frames when z ≥ 8 is even. This talk will be more clear with the help of an example.

NOTES:

Reminder:

Starting this Spring, MAA members can now receive their section meeting discount on books online! The MAA is providing a coupon code that provides 35% off book purchases and is valid one week before and one week after your section meeting.

 

For the Ohio MAA, the coupon code is OHIOSPR3 and is valid from Sunday, March 31 - Saturday, April 13, 2013.  This code cannot be combined with any other offers or discounts from the MAA and is only valid at the online MAA store at .

Of course, you can still browse the books at the MAA meeting at the book table and take advantage of the discount there as well.

Happy shopping!

-----------------------

Save these Dates!

The fall meeting of the Ohio Section will be held at Cleveland State University on October 4-5, 2013. Featured speakers include

• Tim Chartier, Davidson College

• Rick Cleary, Bentley University

• Harold Putt, Ohio Northern University

• Brad Hartlaub, Kenyon College

MathFest will be in Hartford, CT, August 1-3, 2013. Registration has begun!

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download