Abstracts for Contributed Papers: 2014 Section Meeting

s for Contributed Papers: 2014 Section Meeting (Note: due to scheduling constraints, some talks may be moved to other sessions) Session: Undergraduate Speaker: Tyler Gorshing Title: Center of Non-Relativistic Lie Algebras Abstract: In this talk, we use elementary multiplication of matrices to calculate the centers of some non-relativistic Lie algebras, namely the Schrödinger Lie algebra, the Galilei algebra and the Harmonic Oscillator Lie algebra. Faculty Mentor: Guy Biyogmam Speaker: Danny Somers Title: Fumble! The Unpredictable Bounce Of a Football Abstract: This paper looks into the direction and height at which a regulation sized NCAA football bounces disregarding physics. Faculty Mentor: Nicholas Jacob Speakers: Mikasa Barnes & Jonathan Yarbrough Title: Paintings of Caterpillar Continua Abstract: In the research performed, we count the number of nonhomeomorphic paintings of all caterpillar continua with n points of order greater than 2, for n= 1, 2, 3, and 4 in an effort to determine the number of paintings for a general n. Faculty Mentor: Michael McClendon Speaker: Alanna Riederer Title: A Mathematical Model of Circadian Rhythms in Drosophila Abstract: We develop a comprehensive model of Circadian rhythms by gene interaction in Drosophila Faculty Mentor: Brittany Bannish Speaker: Bryan Dawkins Title: A Mathematical Model and Analysis of the Adaptive Immune Response in Antitumor Laser Immunotherapy Abstract: We present a mathematical model composed of a system of ordinary differential equations describing the immune-mediated dynamics of tumor cell populations with exponential growth. The model includes populations of several types of immune cells and both primary and metastatic tumor populations. We will present conditions for complete tumor clearance, initial tumor clearance and eventual recurrence, and tumor escape. We will show that key parameters of our model represent the effects of immune system stimulants that greatly impact the overall success of treatment. Model results will be compared to experimental data of our collaborator to show similarity under reasonable biological conditions. Faculty Mentor: Sean Michael Laverty Speaker: Raymond Jeter Title: The Existence of a Continuous Function Whose Fourier Series Diverges at a Point Abstract: There exists a continuous function whose Fourier series diverges at a point. In fact, the set of continuous functions whose Fourier series diverges at 0 is dense in C([0,2π]) Faculty Mentor: David C. Ullrich Speaker: Jay Mayfield Title: Motion of a non-linear spring with dynamical contact Abstract: In this work, we study mathematical and numerical approaches to a nonlinear spring with dynamic contact. In our mathematical modeling, a nonlinear spring is attached to a wall. At the end of the spring, a mass is attached which may come into contact with a rigid obstacle. We also consider a lubricated surface, causing friction to be negligible. The equation of its motion with contact conditions is formulated in terms of a differential inclusion. Reformulating it into a time discretization and using the Euler methods and non-smooth Newton’s method, numerical schemes are proposed to obtain numerical results. Faculty Mentor: Jeongho Ahn Speaker: Laura Beth McKinley Title: More on “Derivative of Area Equals Perimeter”: Coincidence or Rule? Abstract: Describes how to use the Miller-Half Rule when finding the relationship between the derivative of the area and the perimeter of a shape with multiple partitions. Faculty Mentor: Dean Priest Describes how to use the Miller-Half Rule when finding the relationship between the derivative of the area and the perimeter of a shape with multiple partitions. Faculty Mentor: Dean Priest Speaker: Jaclyn Vanhook Title: How Math Shapes Your World Abstract: Eugene Wigner (Nobel Laureate – 1963) said, “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious . . . There is no rational explanation for it.” However, there have been a number of schools of thought developed in the attempt to explain this phenomenon. In this talk, we will take a brief look at three of these views on the effectiveness of mathematics in science. Faculty Mentor: Sarah Marsh Speakers: S. Gleen, A. Morales, T. Pleasant, L. Smith, T. Vaughn Title: Applications of Least Squares Problems to Intensity Modulated Radiation Therapy Planning, Part I Abstract: Brief overview of the application of Least Squares Problem (LSP) as applied to 3D-Intensity Modulated Radiation Therapy Planning (IMRT) will be presented in this part. Faculty Mentors: Andrew Bucki, Abebaw Tadesse Speaker: Khristen Anderson Title: The Flight Path of a Volleyball: An Analysis of the Drag Crisis of Volleyballs in Service Abstract: The study of the behaviors of sports balls has always been something that interests members of the scientific community. This can be seen in the extent to which tests have been done concerning soccer balls, baseballs, and golf balls. However, little attention has been given to the flight path of the volleyball. At the request of Dr. T.W. Cairns, the drag coefficient for a traditional 18 panel Wilson volleyball was determined by two aeronautical engineering students from the University of Michigan using a wind tunnel. The lift coefficient was also computed and published and so Cairns could plot pictures of serves by numerically solving the equation of motion. Subsequently, Molten and Mikasa have produced tournament approved balls with different surface patterns. The US Women’s Olympic Volleyball Team has testified that the three different balls perform differently significantly during play. A different method for analyzing ball paths is to model the surfaces of the balls and perform simulations using Computational Fluid Dynamics (CFD) software. This method has successfully been used to model the flight characteristics of soccer balls, but never that of volleyballs. The goal of our study is to discover the flight patterns of the Molten and Mikasa balls using the star-CCM+ computer package Faculty Mentor: Tom Cairns Speaker: Kodi Liddell Title: The Miller Half Rule and Its Extensions Abstract: This is an exploration of the Miller Half Rule and its extensions to higher dimensions as well as its applications in optimization. Faculty Mentor: Dean Priest Speakers: S. Gleen, A. Morales, T. Pleasant, L. Smith, T. Vaughn Title: Applications of Least Squares Problems to Intensity Modulated Radiation Therapy Planning, Part I I Abstract: In this part, MATLAB Implementation of the (LSP)-IMRT on the computational environment for Radiation Therapy Research (CERR) platform will be presented. Sample patient image data from CERR Archives will be used for demonstration purposes. Faculty Mentors: Andrew Bucki, Abebaw Tadesse In this part, MATLAB Implementation of the (LSP)-IMRT on the computational environment for Radiation Therapy Research (CERR) platform will be presented. Sample patient image data from CERR Archives will be used for demonstration purposes. Faculty Mentors: Andrew Bucki, Abebaw Tadesse Speaker: John Kreidler Title: Computational Thinking and Programming Approach in Teaching and Learning Processes Abstract: In this presentation, some ideas of the new educational program in Mathematics based on computational thinking with programming approach and supporting STEM-C are presented. Elements of basic logic serve as illustrations of these ideas. Faculty Mentor: Andrew Bucki Speaker: Bailey Sinnett Title: Successful States or Successful Schools Abstract: This research is a statistical analysis of high school graduation rates organized by states across the country and common factors often blamed for the incompletion of high school within the expected four year time frame. Faculty Mentor: Andrew Wells Speaker: Amanda Morales Title: Dynamics of HIV Infection Abstract: In this talk, compartmental model of the dynamics of HIZ infection will be presented followed by some preliminary results on estimation of HIV model parameters using interruption trial data including drug efficacy and reservoir dynamics. Faculty Mentors: Abebaw Tadesse, Andrew Bucki, Alonzo Peterson Speaker: Staci Gleen Title: How Far is a Chicken McNugget from being Prime? Abstract: Numerical monoids have long been studied for their interesting (i.e., nonunique) factorization properties. While numerical monoids of embedding dimension 2 are relatively well-understood, the presence of a third minimal generator makes these monoids more difficult and interesting to study. We provide a complete analysis of MN = < 6,9, 20 >, an embedding dimension 3 numerical monoid whose elements correspond to the amounts of Chicken McNuggets one can purchase using the traditional order sizes of 6, 9, and 20. Our analysis includes a closed formula for ω(x), the omega-primality of an element, which measures how far that element is from being prime in the monoid. Furthermore, we also develop formulae for the elasticity ρ(x) and delta sets Δ(MN), quantities which measure non-uniqueness of factorizations in MN. After presenting computational data, we will also provide conjectures for more general classes of embedding dimension 3 numerical monoids. Faculty Mentors: Andrew Bucki, Abebaw Tadesse, Alonzo Peterson Speaker: Bobby Carnes Title: Fibonacci Sequence and its Generating Function Abstract: This research includes an overview of the Fibonacci Sequence. The origin, recursive form, and its generating function are explored. A proof of its generating function is included. Faculty Mentor: Andrew Wells Speaker: Kendra Parker Title: Jacobi vs. Gauss-Seidel Abstract: This paper talks about two different numerical methods used to solve systems of linear equations, the Jacobi Method and Gauss-Seidel Method. The methods are compared by looking at the solutions, how many iterations are needed to obtain the solutions, and the relative and absolute error. Faculty Mentor: Robert Ferdinand Speaker: Stephanie Duncan Title: Curriculum Integration and the Mathematics Classroom Abstract: This research paper discussed the variety of ways local junior high and high school mathematics teachers incorporated curriculum integration into their classroom activities. Faculty Mentor: Mary Harper Speaker: Kendall Dobbs Title: Mathematics Self-Efficacy: Is Math Class Hard? Abstract: My theses research project was inspired by my many years of one-on-one tutoring in and out of the classroom. Through these experiences, I have come to realize the importance of mathematics self-efficacy and the role it plays for each individual. In order to understand mathematics self-efficacy and how it affects a student, my faculy mentor and I created a questionnaire to be disbursed to approximately 100 participants from four different undergraduate mathematics courses. The questionnaire consisted of seven questions ranging in topics from mathematics self-efficacy, mathematics anxiety, and a negative feeling towards mathematics and had a moderate mathematics self-efficacy level. These feelings and levels were found to be influenced mainly by prior experiences, such as grades, teachers, and tests. After the discussion of my findings, I also reported suggestions on how mathematics educators can boost mathematics self-efficacy levels for their sutdents. Faculty Mentor: Mary Harper Speakers: Stephanie Bayne, Matt Garner, Vikki Orso Title: A Teacher’s Perspective: The Impact of Common Core Abstract: The research is about a teacher’s perspective of Common Core. We want to know the impact on students from Common Core told from the teachers point of view. Faculty Mentor: Mary Harper Speaker: Trent A. Rogers Title: The Two-Handed Tile Assembly Model is Not Intrinsically Universal Abstract: In this paper, we show for a particular model of self-assembly, there is an infinite hierarchy of classes with increasing power. In order to accomplish this, we define notions of simulation and intrinsic universality. Faculty Mentor: Matthew Patitz Speaker: Douglas Bohlman Title: Introduction to Spectral Analysis of Graphs Abstract: Simple, finite graphs are algebraic objects that can be powerfully utilized in modeling complex networks. We explore the structure of such graphs with a variety of matrix representations and discuss the vector space interpretation of nodeand edge-sets, as well as decomposition into orthogonal subspaces. Finally, we discuss graph eigenvalues and their connection to global structure. Faculty Mentor: Edmund Harriss Speaker: Emily Coats Title: Occurrences of Sierpinski’s Triangle Abstract: This paper is about the fractal Sierpinski’s Triangle and its properties, such as self-similarity and Hausdorff dimension. Different occurrences of the pattern are explored, particularly in Pascal’s Triangle modulo 2, the Chaos Game, and a transformation from the Cantor Set. Faculty Mentor: John Akeroyd Speaker: Frederick McCollum Title: Smooth Interpolation of Data: Minimal Lipschitz Extensions Abstract: Using results from classical analysis and techniques from computational geometry, we have designed an algorithm for computing optimal interpolants in C^{1,1}(R^d). The results of this research could be used in the design of experiments in applied physics and chemistry. Faculty Mentor: Mark Arnold Speaker: Matt Lukac Title: Continuously Diagonalizing the Shape Operator Abstract: We will be investigating the curvature of surfaces in 3 using a 2 2  symmetric matrix known as the shape operator. We will see the conditions meeded to diagonalize the shape operator in a neighborhood of the origin and what this implies. Faculty Mentor: Phil Harrington Speaker: Madison Sandig Title: Origami, Surfaces and Curvature Abstract: An exploration through surfaces that can be represented through origami and the curvature of these surfaces. Faculty Mentor: Edmund Harriss Speaker: Matt Hartley Title: Using the Metropolis-Hastings Algorithm to Analyze Galaxy Morphology Abstract: A short discussion of the function Metropolis-Hastings algorithm with a description of the application of the algorithm to the specific context of analyzing the morphology of spiral galaxies. Faculty Mentor: Edmund Harriss Speakers: Chase Roberts & Sarah Zimmerman Title: Modeling in Calculus Using Approximation Curriculum: A Close Look at a Derivative Lab Abstract: We describe a research-based approximation approach to calculus to help make calculus conceptually accessible to more students while simultaneously increasing the coherence, rigor, and applicability of the content learned in the courses. In this talk we take a close look at a lab designed to support student discovery of key ideas related to the notion of derivative in the context of rates of change. Speaker: Gage Rice Title: Detecting Handwriting Forgeries Using Discrete Wavelet Transformations Abstract: Discrete wavelet transformations, used along with statistics, can be used to detect handwriting forgeries with a great degree of accuracy. The field of wavelet theory is a relatively new one that gained a footing in the mathematical community in the mid 1980’s. Work in wavelet theory, and the wavelet transformations that followed, have led to many advances in the compression, denoising, and detection of edges in images. In our work, we took handwriting samples from a handful of sources and made forgeries of the given samples. From there, all of the handwriting samples were scanned into the computer where we used Matlab to perform discrete wavelet transformations on them. After this, the weights and respective errors for the linear predictors were calculated and we used a one-way ANOVA test to compare the skewness of the samples with their associated forgeries. Faculty Mentor: Jill Guerra Speaker: Mary Jo Galbraith Title: An Exploration of Generalized Parabolas Abstract: A generalized parabola is the set of all points that are equidistant from a given point, the focus, and a given curve, the directrix. In this presentation, we explore the different generalized parabolas that result from using directrixes from many different families of curves. We look at the similarities between these generalized parabolas when the directrix remains fixed and the focus is allowed to occupy any point in the plane, as well as the patterns that develop from iterating generalized parabolas about the same focus. Faculty Mentor: Nicholas Zoller