Mathematics & Computer Science
- Undergraduate Programs
- Undergraduate Research
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- Problem of the Month
Speaker: John Berryman
Thought Box, Inc.
Title: Incorporating Semantic Search into the Solr Search Engine
Abstract: Solr is a wildly popular, open source search engine which provides fast, highly scalable, and easily maintainable full-text search capabilities. However, under the hood, Solr is really just a sophisticated token-matching engine. What's missing? A couple of things!
First, Solr lacks semantic search. If you're looking for documents about "software architecture" then it might be appropriate to retrieve documents about "programming design patterns" even if they don't explicitly contain the terms "software" or "architecture". Semantic search allows users to find documents by meaning rather than just by simple token matching.
Second, Solr lacks the ability to make rich recommendations. If most customers who purchase cameras also tend to purchase tripods, then it is a good idea to recommend tripods when a new customer is purchasing a camera! So-called "recommenders" provide users with recommendations based upon the previous behavior of other similar users.
In this fast-paced discussion I will describe the nature of token-based search and outline the need for semantic search and recommendation. Then, I will provide an audience-friendly mathematical demonstration of how token-based search can be augmented so that both semantic search and recommendation are possible. Finally I will also demonstrate our ongoing work using Mahout to equip Solr with both of these useful capabilities.
Bio: Coming from a background of Aerospace Engineering, John soon discovered that his true interest lay at the intersections of information technology and entrepreneurship (and when applicable - math). In early 2011, John stepped away from his day job to take up software consulting. Finally John found permanent employment at Opensource Connections where he currently consults large enterprises about full-text search and Big Data applications. Highlights to this point have included prototyping the future of search with the US Patent and Trademark Office, implementing the search syntax used by patent examiners, and building a Solr search relevancy tuning framework called SolrPanl.
Speaker: Dr. Minah Oh
Assistant Professor of Mathematics
James Madison University
Title: Finite Element Methods and its Applications
Abstract: When using computers to find a good approximation of the solution to a given problem, we want to use a computational method that is not only fast but also mathematically proven to give an accurate approximation. The finite element method is one of the very popular fast computational methods that also has a solid mathematical theory behind it.
We apply the finite element method to axisymmetric problems (problems defined on an axisymmetric three-dimensional (3D) domain, for example a Coke bottle, with axisymmetric data). In other words, we use cylindrical coordinates and the axial symmetry of the problem (independence of the angular variable) to reduce a 3D problem into a two-dimensional one. This is an attractive feature, since it reduces computational time significantly. In this talk, we will discuss the mathematical theory and real world applications of the finite element method used for axisymmetric problems. Furthermore, we will discuss problems defined on an axisymmetric domain with non-axisymmetric data.
Bio: Dr. Minah Oh did her undergraduate studies at Yonsei University in Seoul, Korea and at St. Olaf College in Northfield, MN. She continued studying mathematics at the University of Florida where she earned her Ph.D. Teaching mathematics is what she enjoys the most, and she also enjoys working on research projects with undergraduate students. Her research is in the field of Numerical Analysis, and she focuses on a popular numerical method called the finite element method. She is currently an Assistant Professor of Mathematics at James Madison University.
Speaker: Dr. Kerry Luse
Clare Boothe Luce Assistant Professor of Mathematics
Trinity (Washington) University
Title: Topics in Knot Theory
Abstract: Knot theory is a branch of mathematics that has historical roots in physical knots. Indeed, knots were used for record keeping in ancient civilizations as well as for decoration.
Mathematical knots differ from physical knots in the sense that they have no ends and cannot be undone. Formally, a knot is an embedding of a circle in 3-dimensional Euclidean space. A motivating problem of knot theory is how to tell if two given knots are equivalent.
This talk will introduce some of the basic concepts of knot theory and knot invariants. In particular, we will consider the Alexander polynomial of a knot.
Bio: Kerry Luse is a Clare Boothe Luce Assistant Professor of mathematics at Trinity Washington University in Washington, DC. She has a BA in mathematics from Franklin and Marshall College and received her PhD in mathematics from The George Washington University in 2008. Her research interests are in knot theory. When she is not teaching, she spends time with her two young children.
Speaker: Mr. Joseph Gills and Ms. Karen Green
Longwood Mathematics Majors
Title: LU-PRISM presentations
Abstracts: Joe Gills: The study of the geometry of curves and surfaces presented in multivariable calculus depends heavily on the geometry of Euclidean space and its ''rigid motions.'' In this talk, we view Heisenberg 3-space, Nil3, as R3 equipped with an alternative group of ''rigid motions,’’ and in the spirit of Klein, we employ the Fels-Olver moving frame method to find a complete set of differential invariants for curves and surfaces in Nil3.
Karen Green: In this talk, we will discuss action research, what it is, its purpose, and how it is used. We will also look at the action research performed in order to inform mathematics instruction in a university precalculus course.
Bio: Joe Gills is from Farmville, VA and currently attends Longwood University. He is majoring in Math and Computer Science and participates in several campus organizations including the Longwood Ambassadors, SGA, Math Club and Honors Student Association.
Karen Green is from Lunenburg County, VA. She is a senior mathematics secondary education major with a minor in coaching. She will be doing her student teaching in the spring. She is a member of Pi Mu Epsilon, and she tutors for the Center for Academic Success as well as student athletes.
Speaker: Dr. Rebecca Jayne
Assistant Professor of Mathematics
Title: Partitions and Young Diagrams
Abstract: An integer partition is a way of writing a positive integer as a sum of other positive integers. As is the case with many mathematical ideas, pictures can help us better learn about integer partitions. Here, the pictures we use are called Young diagrams. We will use these diagrams to show several combinatorial relationships between certain types of integer partitions. Finding these relationships involves a lot of (fun!) searching for patterns.
Bio: Rebecca Jayne grew up on Maryland's Eastern Shore. She received her undergraduate degree at McDaniel College in Maryland. She then moved to Raleigh, NC, where she earned a Ph.D. in mathematics from North Carolina State University. Rebecca taught at Washington College for two years and has recently relocated to Hampden-Sydney College.
Speaker: Dr. J. Todd Lee
Professor of Mathematics
Title:Forever Fractions and Forty-Eight
I want to show you some really awesome things about adding fractions the "wrong" way, but I need you to provide a couple of tools first:
1) Assuming the indicated tangencies in the figure, find some identities for the radii.
2) If given four positive integers w, x, y, z, what does w x – y z = 1 tell us?
Bio: Loving childhood-> Public School -> Eagle Scout -> Governor’s School -> Mathematics Love -> Guilford College -> Super Mathematics Love -> Texas Tech University -> More Texas Tech -> Teaching Award -> New Horizons -> Governor’s School -> Elon College -> Profile Picture -> Project NExT -> Undergraduate Research -> Elon College Fellows -> Elon University -> Marriage -> Kids -> Math Education Love -> Teaching Award ->Tech Immersion -> Longwood Talk
Speaker: Dr. John David
Assistant Professor of Mathematics
Virginia Military Institute
Title: Machine Learning in Sports
Abstract: Who’s going to win? Who’s the best team? What factors determine a good team? Who should your favorite team draft? These are just a few of the questions that sports teams are increasingly addressing using math and science, particularly a branch called data analytics.
Data analytics is one of the most rapidly growing and used areas in the mathematical sciences. Rarely does a week pass in which there isn’t a major news story about an application of data analytics. In this science, data sets are analyzed and used to build models to discover useful trends, predict future outcomes and support decision making.
In the past four years my students and I have applied these techniques to large data sets in professional and collegiate football, major league baseball and professional basketball. I will discuss the techniques we have used, the accuracy of our prediction, what factors are important in predicting these sporting events and how these predictions can be used to rank the teams.
Bio: John David received his BS in Mathematics from the University of North Carolina at Chapel Hill and MS and PhD in Applied Mathematics from North Carolina State University. He spent time at the Massachusetts Institute of Technology Lincoln Laboratory as a systems analyst and at the College of Wooster as a Visiting Assistant Professor.
He currently directs VMI’s Applied and Industrial Mathematics (AIM) Program and has advised 50 undergraduate researchers in projects sponsored by the National Science Foundation, National Security Agency, Department of Homeland Security, Department of Energy, Calabazas Creek Research Inc., Johns Hopkins University Applied Physics Lab, Goodyear Tire Company, Bekaert Steel Company, the City of Lexington and the Valley Program for Aging Services and more.
His areas of interest include mathematical modeling, computational mathematics, control, filtering, data mining and the application of mathematics and statistics to sports.
Speaker: Dr. Rebecca Nelson
Adjunct in Mathematics Education
Title: Mimi ni mwalimu: On being a math teacher in Kenya
Abstract: Have you ever wondered what it might be like to be a teacher (or student) of mathematics in another country? One way to discover this is to join the ranks of Peace Corps volunteers who teach in various countries throughout the world. The speaker will share various aspects of her experience as a secondary mathematics teacher in a Kenyan village (to include a brief overview of the Kenyan Curriculum and National Exam) and encourage all interested participants to seek "the toughest job you’ll ever love."
Bio: Rebecca Nelson, essentially a classroom teacher at heart, has taught mathematics at various levels since 1990. Most recently she taught secondary mathematics in Marereni , Kenya as a Peace Corps volunteer. Currently she works as a Project Manager with the Middle Matters Project-James Madison University and teaches as an adjunct professor for Longwood at the Southside Virginia Community College location in Emporia, Virginia. She holds a PhD in Curriculum & Instruction-Mathematics from Virginia Tech and a MEd in Mathematics from Virginia State University.