An OpenMath Content Dictionary for Finite Quandles
Georgi Smilyanov, Bard College
Faculty Sponsor Name: Robert McGrail
Abstract: We create an OpenMath Content Dictionary for finite quandles and explain the design decisions made along the way. OpenMath Content Dictionaries provide a standard way for describing mathematical objects with their properties. Moreover, they can enable applications to easily communicate mathematics to each other. Quandles are of great importance to Bard’s Laboratory for Algebraic and Symbolic Computation. We hope that this work might provide insights for developing Content Dictionaries for a host of algebraic theories.
Dynamical Analysis of the Quadratic Function "Q(x) = x2 + c"
Joseph Ruotolo, SUNY New Paltz
Faculty Sponsor Name: Richard Halpern
Abstract: This experiment analyzes the orbits generated by successive iterations of the quadratic function "Q(x) = x2 + c", paying special attention to the value "c = -2". The experiment will illustrate why this value is critical, and explain its importance in determining the eventual orbits of of "Q(x) = x2 + c".
Effects of alpha-pinene on the Musca Domestica
Angela Acevedo, SUNY New Paltz
Faculty Sponsor Name: Dr. Aaron Haselton
Abstract: Musca Domestica, commonly known as the house fly, has been known to transmit various diseases to humans. Recent research has demonstrated the repellency of terpenoid compounds on mosquitos that contain α- and β- pinene. Due to the success of these experiments attention is now focused on its effects on the house fly. Our hypothesis is that α- and β- pinene will have similar effects. To test our hypothesis different percent solution of α- and β- pinene were tested using a fly repellometer. The repellometer is a plastic tube made where the fly remains until the solution has been set up. Analysis of the results will help us determine whether or not the flies are repelled by the α- and/or β- pinene.
Enhancement of Understanding Algebraic Concepts using Cryptographic Algorithm
Casey Kondelka, Mayra Avila, Stephanie Bann and Jose Valerio, Mercy College
Faculty Sponsor Name: Dr. Sanju Vaidya
Abstract: The main objective of this project is to study the underlying mathematical concepts in cryptography and incorporating these concepts into a lesson that teachers will use in their classroom. With today’s culturally diverse world language greatly influences substitution ciphers. With the different amounts of letters and characters in each language a cipher for one language may not be the same for another. Today cryptography can be used for entertainment purposes like puzzles, riddles and games in many languages. Applying the idea of cryptology in mathematics can make learning more exciting for students from all levels as well as bilingual students.
Euler Circuits
Kyle Bryant, Stephanie Delgado and Pedro Hernandez, SUNY New Paltz
Faculty Sponsor Name: Diego Dominici
Abstract: These circuits get their name form the great eighteen-century mathematician Leonhard Euler, who first studied them and was the founder of graph theory. Euler invented the idea of a graph in 1736 when he solved a problem in “recreational mathematics”. He showed that it was impossible to stroll a route visiting the seven bridges of the German town of Königsberg exactly once.
Modeling the Energy Usage of Cell Phones
Sebastian McDaniel, Jennifer Goldfuss, and Daniel Radil, Southern Connecticut State University
Faculty Sponsor Name: Ross Gingrich
Abstract: We present our solution to Problem B from the 2009 Mathematical Contest in Modeling. The problem asked us to compare the energy usage of cell phones to landline phones and other alternatives. We then were to project our results over the next fifty years. We constructed an algorithm to estimate the total amount of energy each device consumes and wastes per year. This model led us to develop a practical and more energy-conscious recommendation in providing phone service.
New Paltz Waltz
Jessica Mandia, SUNY New Paltz
Faculty Sponsor Name: Natalie Cartwright
Abstract: SUNY New Paltz is having an open house in several of its buildings on campus. Each building will have refreshments and exhibits. Is it possible to find an optimal route where you can get to each exhibit? Come and play the game, winners will be entered in raffle for a prize
Planning and Scheduling
Natalie Teresa Medrano and James Vazquez, SUNY New Paltz
Faculty Sponsor Name: Diego Dominici
Abstract: In a society as complex as ours, everyday problems such as providing services efficiently and on time require accurate planning of both people and machines. Although many planning problems are often solved on an ad hoc basis, we can also use mathematical ideas to gain insight into the complications that arise in scheduling.
QuanDLe
Jackie Bow and Bella Manoim, Bard College
Faculty Sponsor Name: Robert McGrail
Abstract: Quandles are of increasing interest to the mathematics community. However, there lacks a comprehensive forum for mathematicians to share their discoveries in this area. To open the lines of communication, we propose a dynamic digital library, QuanDLe, to support the storage and sharing of finite quandles. By providing a cache of discoveries and ideas, it will facilitate further progress in the field. QuanDLe will extend the success of Knot Atlas, MathWorld, and PlanetMath through semantic web technology. The technologies we will employ for QuanDLe include SWiM, OMDoc, OpenMath, MathML and Mathematica.
Visualizing Quandles in Mathematica
Aleksandar Chakarov, Adina-Raluca Stoica and Petar Stojanov, Bard College
Faculty Sponsor Name: Robert McGrail
Abstract: Quandles are a collection of algebras that have arisen as part of the classification of 3-dimensional knots. They have since become important to some general algebraists and theoretical computer scientists. The goal of this project is to design the interface for a visualization of the following features of finite quandles: operation tables, subquandles, cycle structure and right Cayley graphs. A major issue in this research has been overcoming the difficulty of extracting only the relevant portions of information from large quandles.
Voronoi Diagrams Face and Flag Vectors
Liz Jimenez, Bard College
Faculty Sponsor Name: Lauren Rose
Abstract: A Voronoi diagram consists in the partitioning of a plane with n-points into regions such that each region contains exactly one generating point and every point in a given region is closer to its generating point than to any other.
And, the number of i- dimensional faces of a polytope P is written fi, and f (P)=(f0,…,fd-1) is called the f- vector of P. The flag f-vector of a polytope Q counts all chains of faces according to their corresponding sets of dimensions.
This poster will introduce some basic properties of Voronoi Diagram’s flag f- vectors.
