Mathematics & Computer Science
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Speaker: Dr. Edwin O'Shea
Assistant Professor of Mathematics
James Madison University
Title: Divisibility Tests Unified: Stacking the Trimmings for Sums
Abstract: Divisibility Tests are algorithms that can quickly decide if one integer is divisible by another. These tests first appeared in the Babylonian Talmud and have drawn the affections of such mathematical luminaries as Fibonacci, Pascal, Lagrange and many others. Our first aim in this talk is to introduce divisibility tests to the uninitiated by drawing on familiar tests like the last-digit test for 2 and 5, and the summing-the-digits test for 3 and 9. Less familiar tests include the trimming test for 7. Our second aim is to discuss the many other tests beyond the well known cases and show that, at their heart, most tests are either of the "trimming'' or "summing'' variety. The trimming and summing families of tests are thought of as two distinct techniques but we will show that they are effectively the same.
We introduce the notion of "stacking'' and use only the most basic of divisibility properties to achieve our aims. With this being the first colloquium of the academic year, this talk will be especially suitable for freshmen and sophomores and everyone else is welcome too.
Bio: Edwin O'Shea is an assistant professor of mathematics at James Madison University. His scholarly expertise is in geometric and algebraic combinatorics with a general interest (but little expertise) in number theory and the history of mathematics. Professor O'Shea has supervised nine REU students in the past three years and teaches courses across the curricular spectrum; he has a particular vocation for courses with non-STEM majors and future high school math teachers. He lives in Staunton, Virginia with his wife and their young family and likes to walk, chat, bake and read in his spare time. He has recently become a student again, currently taking a workshop class in woodworking and cabinet making.
Speaker: Dr. Brian Heinhold
Associate Professor of Mathematics
Mount St. Mary's University
Abstract: The number e ≈ 2.718 is familiar to Calculus students everywhere, but how much do you really know about it? We will see where e comes from, who discovered it, and some of the surprising places it shows up.
Bio: Brian Heinold graduated from Montclair State University in 2001. He earned a PhD from Lehigh University in 2006 and has been a faculty member at Mount St. Mary's in Emmitsburg, MD since 2006. There he teaches a variety of math and computer science courses. His research interests include graph theory and mathematical imagery.
Speaker: Dr. Caren Diefenderfer
Professor of Mathematics
Abstract: The #MegaMenger project culminates during the week of this colloquium. We will build some smaller parts of Menger cubes and discuss the fractals surrounding them.
Bio: Caren Diefenderfer is a Professor of Mathematics at Hollins University. She is currently Governor of the Maryland-DC-Virginia Section of the Mathematical Association of America.
Speaker: Dr. Susan Goldstine
Associate Professor of Mathematics
St. Mary's College of Maryland
Title: You can never have too many bracelets: Adventures in mathematical beading
Abstract: Sometimes, when opportunity knocks, it comes bearing jewelry.
Six years ago, I embarked on an unexpected journey into the realm of mathematical beading. Along the way, my colleagues and I uncovered fascinating connections between mathematics and art, and I will show you a few of the highlights of our travels into the realms of geometry, number theory, topology, and abstract algebra. Together, we will look at how geometry and modular arithmetic intersect in bead crochet, the structure of symmetry, the aesthetic principles of jewelry design, and bracelets. Lots and lots of bracelets.
Bio: Susan Goldstine received her A.B. in Mathematics and French from Amherst College in 1993 and her Ph.D. in Mathematics from Harvard University in 1998. She joined the faculty of St. Mary’s College of Maryland in 2004, where she is currently Associate Professor of Mathematics and Chair of the Department of Mathematics and Computer Science. Her joint and individual artworks have appeared in Math Horizons, the Journal of Mathematics and the Arts, and various art exhibits including the 2013 Exhibition of Mathematical Art at the national Joint Mathematics Meetings, where she received the Honorable Mention for Tessellation Evolution, a framed bead crochet necklace with over 4300 beads. Her guiding principle is that a professor’s office can never have too many toys.
Speaker: Dr. David Clark
Associate Professor of Mathematics
Title: Japanese Temple Geometry: A Tale of Math, Art, Religion, and History
Abstract: What is Japanese mathematics? During the Tokugawa Period (1603-1868), Japan was almost completely isolated from the West, including the products of the Western revolutions in math and science. At the same time, the Japanese witnessed a cultural renaissance in the visual and performing arts, music, fashion, and ceremony … and mathematics. New problems and solutions found surprising applications to the traditional Buddhist temples and Shinto shrines that pervade the Japanese landscape. By the end of the talk, I hope you’ll understand a bit of what makes a piece of mathematics Japanese, and how wasan ("wa" = Japanese, "san" = mathematics) became so delicately folded into 18th century Japanese culture.
Bio: David Clark received his PhD from UC San Diego, where he studied knot theory and quantum topology. He has won the Art Conway Teaching Award at RMC, and among the courses he's taught are two topology-related freshmen seminars: "Untangling DNA: Knot Just Genetics" and "Imagining the Shape of the Universe." He recently become interested in 18th century Japanese mathematics. As a result, he took 11 students to Japan in a January travel course.
Speaker: Ms. Elizabeth Creath '09
University of North Carolina Wilmington
Title: Highest-Weight Representations of Quantum sl2
Abstract: Representation theory is a branch of mathematics that studies abstract algebraic structures, such as Lie algebras and associative algebras, by representing their elements as linear transformations of vector spaces. Representation theory depends upon the type of algebraic object, the nature of the vector space (finite or infinite-dimensional) on which the algebraic object is represented, and the type of field over which the vector space is defined. In this talk, the algebraic object we investigate is Uq(sl2), the quantized universal enveloping algebra of the Lie algebra sl2. Because highest-weight representations are of special interest in the representation theory of Uq(sl2), we focus on Verma modules in category O(Uq(sl2)). The main result of this talk is an explicit computation of highest-weight vectors in the tensor products of Verma modules in category O(Uq(sl2)).
Bio: Elizabeth Creath graduated from Longwood University in 2009 with a degree in Mathematics and Secondary Education. She obtained her Masters in Mathematics from the University of North Carolina Wilmington in 2011, and soon after began her career teaching collegiate students. Elizabeth joined the Math Department at UNCW in 2012 as a Mathematics Lecturer. She teaches a variety of general mathematics courses, as well as math education courses for elementary and middle grades prospective teachers.
Speaker: Dr. Paul Hemler
Professor of Mathematics & Computer Science
Title: ERG and ERL at HSC
Abstract: Over the past two years I have been working to construct a new type of building on the Hampden-Sydney campus. The building is quite unusual, in that it is primarily made of concrete mixed with a stainless-steel twisted fiber called helix. The helix replaces much of the rebar that is needed to make conventional concrete rigid. The helix also allows the concrete to be more flexible that is standard counterpart. We theorize the building will not only withstand an F5 tornado and powerful earthquakes, but it will also stand for 1000 years. We also theorize the building can be heated and cooled using completely renewable resources and therefore reducing its carbon footprint. To prove the heating and cooling theory we are developing an embedded device system to remotely monitor temperatures and electrical power usage. The measurements are stored in an SQL database and visualized with a dynamic web page and an Android app. In this talk I will discuss the Energy Research Group (ERG) and the Energy Research Laboratory (ERL) and the computer based systems we are developing.
Speaker: Dr. David Taylor
Associate Professor of Mathematics
Title: Mathematics in Board Games: Making Better Decisions
Abstract: Mathematics plays an ever-increasing role in today’s world, whether it be modeling complex processes in the body, predicting winners for March Madness, or showing that a particular chemistry study has statistical validity. It can also be applied to many games, providing a way to make better decisions in your quest to win. As the owner of over 70 board, card, and dice games, I’ve had a lot of experience playing games and over the last few years I’ve studied the mathematics and probability that goes into these games. The result of my studies is my very own textbook on "The Mathematics of Games" and this very talk. This conversation series event will focus on the two games of Yahtzee and Monopoly, looking into the mathematical framework that can be used to answer interesting questions about these games. Let’s have some fun!
Bio: Dr. David Taylor is currently an Associate Professor of Mathematics along with Chairperson of the Department of Mathematics, Computer Science, and Physics at Roanoke College. He received his undergraduate degree in mathematics and computer science from Lebanon Valley College in 2002 and his doctorate in mathematics from the University of Virginia in 2007. Recently he has published his first book, "The Mathematics of Games: An Introduction to Probability," with CRC Press, and he has been praised with bringing mathematics to students in fun and energetic ways, winning the Dean’s Exemplary Teaching Award at Roanoke in just his fifth year there. In his spare time, he enjoys home improvement projects, going out to dinner and drinks with friends, and playing games; at the moment, you can find over 70 games in his closet at home.