Fazal Abbas and Sierra Chimene, RIT
Improving the Radius of Convergence with HAM for Higher Order Lane-Emden-Fowler Equations
Abstract: In this presentation, we construct the Lane-Emden-Fowler type equations of higher orders. We study the linear and the nonlinear Lane-Emden-Fowler type equations of the fifth and sixth orders. We use the Homotopy Analysis Method (HAM) to solve these equations. We have shown in detail that how HAM has the capability to improve the radius of convergence for these models. We confirm that the HAM provides an efficient algorithm for a convergent series solution of the model. We compare our study with the PADE approximant on the usual Taylor Series Solution.
Jon Backus, SUNY Oswego
Delving into Recreational Mathematics Through the Exploration of Board Games
Abstract: In this talk, we give a brief introduction to Group Theory, and then explore more deeply by analyzing the board game “Tsuro.” “Tsuro” is a tile laying game where players seek to create a path for themselves without crashing into others or falling off the board. The square “Tsuro” tiles have two nodes along each edge, and pairs of nodes are connected to form the “paths” that are central to the game. In our analysis, we make use of Burnside’s Lemma to count the number of unique “Tsuro” tiles. We then move on to tiles with a greater number of sides, or a greater number of nodes, in hopes of generalizing our analysis.
Franquiz Caraballo, SUNY Plattsburgh
Flight Paths of Drones, A Mathematical Model
Abstract: According to Business Insider, the drone market is currently worth about 10 billion dollars. Along with the recreational uses of drones, such as filmography and photography, rest more business and security related uses, such as surveillance and quick delivery of goods. For these reasons, it is important to understand the behaviour of a drone’s flight under different wind conditions. For this purpose, a mathematical model is developed to describe the system.
Ashley Case, SUNY Brockport
When Lagrange Multipliers Fail to Get the Extrema
Abstract: We’ll show some examples when the method of Lagrange multipliers does not produce the extrema and will discuss what to do then.
Marguerite Davis, Ithaca College
Computer Modeling of a Tritrophic System
Abstract: In the natural world, there seems to be patterns that exist within ecosystems, yet our understanding of them is not perfect. For example, when trying to understand a predator-prey system, such as wolves and sheep, mathematicians try to represent a simplification of the real system to discover fundamental truths about species interactions using various methods. However, these current modeling systems have limitations and do not fully describe the interactions that exist in the given community. Here, we describe ways to try and improve our current models to be more biologically accurate so that in the future we can make more accurate predictions about how the environment will change in response to certain ecological factors. This approach will use wolves, sheep, and grass to try and model a tritrophic system. We use the Netlogo computer program to simulate a situation where wolves, sheep, and grass interact. This model also graphs the populations of each species over time. We also approached the problem using an algebraic model, which we will briefly describe. Then the models will be compared to see the similarities and differences.
Mary Di Cioccio, SUNY Fredonia
A Generalized Linear Model of Passing in Courses Taken with Peer-Led Team Learning at CSU Channel Islands
Abstract: This study of Peer-Led Team Learning at CSU Channel Islands examines the relationship between passing, defined as a C or higher, and participation in PLTL. It also examines the relationship between obtaining a graduate school grade of a B- or higher and participation in PLTL at intensity level 1. It was found that the probability of passing is significantly higher for PLTL participants. It was also found that the probability of obtaining a B- or higher is significantly higher for PLTL participants at intensity level 1.
Brittany Dyer, Ithaca College
War-Gaming Applications for Achieving Optimum Acquisition of Future Space Systems
Abstract: This presentation is on a project done at North Carolina State University that contributes to The Aerospace Corporation’s development of a Unified Game-based Acquisition Framework – Advanced Game-based Mathematical Framework and associated War-Gaming Engine models by building a framework that solves for optimum acquisition strategies and contractor parameters. The project combined game theory, probability and statistics, non-linear programming, and mathematical modeling to integrate Defense Acquisition Authority and contractor perspectives into mutually beneficial contract.
Tyler Fedoris and Robert Sulman, SUNY Oneonta
Computer Assisted Explorations of Polynomial Orbits Modulo n
Abstract: The orbit of any element of the complete residue system {0, 1, 2, 3, . . . , n − 1} modulo n under a polynomial function with integer coefficients will always be finite. We examine orbits under linear and quadratic polynomials and discover typical themes: cycles of various sizes, whiskers, and how inverse pairs (of the units of the Ring
(Zn, +n, •n)) are distributed within these orbit graphs.
We also examine how the graph of the orbits of a given f (x) evolves as the modulus progresses from n to n2, n3, . . . .
Jennifer Johannes, SUNY Brockport
Coding for Distributive Storage from Curves
Abstract: Our goal is to derive a more general expression for the maximum amount of correctable errors that can occur when trying to access information sent across channels. We will compare the error correcting capability of generalized AG codes to the Hermitian case.
Nathan Jue, Ithaca College
Generalizing the Golden Ratio
View Nathan Jue’s abstract (pdf)
Shoshanna Longo, RIT
Numerical and Convergent Series Solutions to Lane-Emden Type Equations
Abstract: In this Letter, we present analytical solutions to the Lane-Emden Initial value non-linear models which describes the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules. Convergent solutions are obtained by using the Homotopy Analysis Method (HAM). We show that the change in linear operator improves the interval of convergence than in the case of the corresponding traditional series solutions. Furthermore, the validity of the analytical solution is shown through numerical solutions using a Runge-Kutta technique.
Britney Mazzetta, Ithaca College
Predicting U.S. Childhood Obesity through Mathematical Modeling
Abstract: In the past 50 years, observational studies have shown obesity to be the most prevalent nutritional based disease in the most affluent countries of the world, including the United States. A variety of diseases, which results in a higher mortality rate, have been linked to those who suffer with obesity. This link raises concerns and has led to an increase in preventative efforts to reduce this rate through several public health programs in and out of schools to, hopefully, reverse the epidemic trend. We will provide a unique interpretation to how the trend can be modeled by focusing on the social and nonsocial factors that influence obesity and the degree to which those factors influence people by applying United States’ data to a new mathematical model. This model will adopt similar strategies that were developed by Lucas J´odar and his colleagues (2008). Interpretations of population changes in regards to obesity trends can then be made. Through these models, predictions can also be formed that will identify future childhood obesity trends in the U. S. This rate can then be used in a predictive manner. Subsequently, further implications on how the problem can be reduced and hopefully resolved can be made.
Melissa McGahan, Ithaca College
Elucidating Patterns within a Triangular Array
Abstract: Triangular arrays consist of rows in which the number of entries in each row increases as the number of rows increase, such as in Pascal’s Triangle. Rascal’s Triangle has the same first four rows as Pascal’s Triangle, but with differing entries in the rows for the remainder of the array. For Rascal’s Triangle, we will show that the sequence formed by the sums of the rows can be represented by a cubic function of the row numbers and that we can also represent the sums of the diagonals with a general formula. We now have determined, using the Method of Common Differences, that there are formulas for the sum of the rows and for the sum of the diagonals in Rascal’s Triangle. Our results demonstrate that the patterns in the sums of the diagonals of Pascal’s Triangle are not the same for Rascal’s Triangle. Pascal’s Triangle has applications in science and the golden ratio. In the future we hope to find connections between Rascal’s Triangle and other fields of math and science.
Sabrina Tomassetti, SUNY Oswego
Exploration of Bell-Ringing in Mathematics
Abstract: Math is in everything. In this talk, you will learn how Math and Music are connected through the topic of Bell-Ringing. Permutations and graph theory are the main mathematical points of this talk. There will also be connections to how this research can be used to teach mathematics in at the elementary and high school level.