“Changing Perceptions of Computer Science” Computer
science is misrepresented as a science and such misperceptions may
contribute to students’ negative views and reluctance to join this field
of study. The Laboratory for Computer Science creates interactive
online lessons for high school students. This study examines how
students’ perceptions of computer science change upon completion of
these labs. Identifying whether the stigmas or stereotypes are present
with the students that experience these lessons and whether a deeper
knowledge of the underlying theories in computer science will change
these views is the goal.
Benedict, Alex & Gordon, Jeffrey "Fast Waveform Extraction on Short Computational Domains" An overview of the method of Alpert, Greengard, and Hagstrom for implementing radiation boundary conditions for the ordinary flat-space wave equation and its extension to the Regge-Wheeler equation, which describes axial perturbations of a Schwarzschild black hole, followed by a brief discussion on how the method can be used to extract the asymptotic waveform from a time series recorded at a finite radius. “Wynn's ρ-algorithm for sequence acceleration using high precision arithmetic” In this study we explored several variants of Wynn's ρ-algorithm for sequence acceleration using high precision arithmetic both in Matlab and Mathematica. The results were compared to Osada’s theoretical error estimates. We found that Matlab's implementation of high precision still has limited number of significant digits, this problem was not seen in Mathematica. Applications to several standard sequences and Jacobi Theta function will be used to illustrate the results.
“Time-Fractional Heat Equation" SUnMaRC presentation of an application of Fractional Calculus to solve the Heat Equation when the time derivative is not necessarily an index of one.
“Higher Dimensional Perfect Bricks” A numerical semigroup S is a subset of nonnegative integers such that S contains 0, S is closed under addition, and its complement is finite. This presentation considers a subset of numerical semigroups, namely perfect bricks, which have additional properties. We will also show the existence of an infinite family of perfect bricks.
“A Comparative Survey of Graceful and Harmonious Labelings” A graph labeling is an assignment of integer labels to the edges and vertices of a simple connected graph subject to specified conditions. First investigated by Rosa in 1967, his “graceful labeling” now has several variants. This presentation will compare various forms of graph labelings as well as provide examples of families of graphs that have these labelings. No prior knowledge of graph theory is needed.
“Princes and Dragons” In Dragon Territory, any two countries are connected by a dragon flight in exactly one direction. A country where a prince is searching for a bride is called a royal country, and for the princes' convenience, any other country can be reached from a royal country by a maximum of two dragon flights. In this talk, we will examine the number of royal countries that can exist for different values of n where n is the total number of countries in Dragon Territory.
“A brief introduction to pseudoreplication” Experimental studies often have to address the issue of pseudoreplication, which can be thought of as experimental replication that is nested within replications of the true variable(s) of interest. Our research is focused on evaluating competing methods for estimation under different experimental scenarios in order to understand which method should be used in a given analysis.
“A simulation analysis of competing methods for addressing pseudoreplication” Experimental studies often have to address the issue of pseudoreplication, which can be thought of as experimental replication that is nested within replications of the true variable(s) of interest. Our research is focused on evaluating competing methods for estimation under different experimental scenarios in order to understand which method should be used in a given analysis.
"Evolutionary
Games on the Lattice" My advisor and I worked on a set of seven spatial, stochastic processes that combine evolutionary game theory (EGT) and interacting particle theory. By placing EGT players on a lattice and limiting interactions only to neighbors, we get a model that more accurately represents ideas from EGT, since evolutionary systems are almost always in some kind of spatial context. I also wrote a program that simulates these processes with an animation, so I have something neat to put in the slideshow, too.
“Viewing Mathematics Linguistically” The study examines how native language can affect one's mathematical abilities.
“An Introduction to Numerical Semigroups” A numerical semigroup is a nonempty set of nonnegative integers that contains 0, is closed under addition, and has a finite complement. Although motivated by deep problems in ring theory, they are interesting to investigate in their own context. This talk will present the basic notation and properties of numerical semigroups, and will lay the foundation for the next talk.
“An Introduction to Theory and Application of Evolutionary Games” Evolutionary game theory is a relatively new but rising field that is a branch-off of traditional game theory. In traditional game theory, developed by the Hungarian mathematician John von Neumann, one looks at the players of a game, their strategies, and then tries to make a prediction on the outcome of the game. One of the key tenets to traditional game theory is that the players always make rational decisions (that is, decisions that serve to maximize their expected utility).
“Evolutionary Dynamics and Strong Allee Eﬀects" The program is an REU, i.e. Research Experience for Undergraduates, in the Mathematics Department at the University of Arizona. In the program, I was introduced to the basics of conducting a research project. Furthermore, this program gives me the opportunity to meet peers interested in similar topics as well as get published.
“Lagrangian Transport of Radioactive Particles after Fukushima”
“Trees of Irreducible Numerical Semigroups” A recent paper by Blanco and Rosales describes an algorithm for constructing a directed graph of irreducible numerical semigroups with ﬁxed Frobenius number. After presenting background information, we will explain the algorithm, construct speciﬁc examples, and present some open questions associated with these graphs. “Cloaking Against Thermal Imaging” There has been a lot of recent interest in cloaking and invisibility in the mathematics and science communities, and in fact physically plausible mechanisms have been proposed (some built) for cloaking an object against detection using a variety of electromagnetic methods. The ideas are very general, however, and should allow one to design cloaks that work against other forms of imaging.
Muniz, Abigail Damaris & Loya, Jesus “Matrix Product Application to Fibonacci Sequence” We will discuss a procedure that leads to the computation of the “nth” Fibonacci number applying matrix product. We will discuss matrix product connection to Fibonacci sequence and we will look at diagonal matrices and the power operation on them. At the end of our talk, we will reveal how matrix product and power operation on diagonal matrices allow one to calculate any value in the Fibonacci Sequence. We will need a projector and a computer for our power point presentation.
“A Pilot Study on Inverted Pedagogy” There is currently a growing disconnect between students’ technological engagement with the world around them and their largely traditional experiences in school. This study in Inverted Pedagogy analyzed the effects of using Screencasting technology to invert traditional pedagogy on student affect and achievement in a business mathematics course at N.A.U. This pilot study was used to identify key variables and concerns that will guide the development of future full-scale studies. The pilot study provided both critical feedback to consider when moving to a full-scale study and positive written feedback from the students in the experimental class.
“What is Mathematics Education Research?” Unlike research done by many mathematics contemporaries, the process of Mathematics Education research includes both quantitative and qualitative analysis that covers a wide variety of topics. This presentation is designed to expose traditional mathematics undergraduates to the motivations and processes of mathematics education research, and highlight similarities and differences between traditional Mathematics research and Mathematics Education Research. An overview of the process used during Mathematics Education Research will be given as well as the key motivations that drive the research, the process used to analyze data and the way research findings affect the mathematics education community.
“Symmetric Latin Squares and Their Properties” A brief overview of Latin squares, focusing on symmetric Latin squares. I will discuss isotopy and isotopy classes as well as the properties of symmetric Latin squares. Sudoku will be discussed as specific examples of Latin squares.
“Confirming the scaling factor of the distribution of bridge heights of a self-avoiding walk” We numerically confirmed the scaling factor of the distribution of bridge heights of a self-avoiding random walk in the upper half of the complex plane. Our results match the conjectured result of 4/3 within a few hundredth of a percent.
“The artificial phase transition for perfect simulation of repulsive point processes” We examine the critical intensity value for a birth-death Markov chain model, above which the expected run-time of the process becomes infinite. An analytic improvement of a previous lower bound on this value is introduced, and data from computer simulations provide a more precise estimate of the critical value.
“L^p Norms on Eigenfunctions of the Spherical Laplace Operator” Special Functions arise in mathematics as solutions to specific, important differential equations. One example, the Legendre polynomials, leads naturally to the well-known set of spherical harmonics. The spherical harmonics form an infinite, orthonormal basis for the function space of all square integrable functions living on the sphere. In addition, they are eigenfunctions of the Laplace Operator restricted to the sphere. I have been studying the L^p norms of the spherical harmonics. Such an endeavor gives us information about the size and concentration of our eigenfunctions over the sphere. We can also observe quantum behavior converging to classical behavior in the limit of large quantum numbers.
“Short and Long Range Population Dynamics of the Monarch Butterfly” We are primarily concerned with the effect that herbicide usage has on the long-term population dynamics of the monarch butterfly. First, we explore the life-cycle of the monarch. Then, we analyze its annual migratory cycle. Finally, we also examine the effect of herbicidal spraying of milkweed on the long term stability of the monarch butterfly population, throughout its annual migratory cycle.
“Analytic Continuation of the Riemann Zeta Function“ The Riemann zeta function defined to be the sum from n=1 to ∞ of n^(-s) for a complex number s appears to be defined in the half plane Re(s) >1. Riemann proved however, that zeta is analytic throughout the complex plane with only a simple pole at s=1 by demonstrating that zeta satisfies the functional equation ζ(s)=ζ(1-s). I will outline this proof using some basic Fourier analysis and complex variable theory. Then, time permitting; I will discuss a potential discrete analogue of zeta over the finite field Fp.
“An introductory Look at the Abelian Sandpile Model” Have you ever wondered what type pf amazing graphs you could make with sand grains? This introductory presentation will take a look at the Abelian Sandpile Model. We will learn what it is, how it “works”, and how to construct such model, through definitions and visuals.
“Statistics and Chem-Cam” Chem-Cam is a set of instruments on the Mars Science Laboratory rover that will land on Mars in August 2012. For the past 5 months I have been working with Professor Horton Newsom on several statistics questions about Chem-Cam’s ability to detect, with significant probability, small scale sedimentary layers on Mars. My talk will focus on the issue of properly phrasing the questions, an elegant solution using Poisson distributions, and a rough outline of procedural suggestions that could help the Mars rover team use statistics to make real time decisions about which sediments to measure. “Honeywell and its dependence on C/C++” Provide examples of Honeywell's progress and innovations using C/C++.
“Maintaining an Engaged Classroom: Demonstrations for Provoking and Maintaining Mathematical Curiosity” This presentation will explore the physical implications of certain mathematical models and how they can be used to create curiosity among young students of mathematics. Topics covered include Chladni patterns, ferrofluid structures, and non-Newtonian fluids with brief discussions on the mathematics behind them. The emphasis will be on framing mathematics not only as tool for solving problems, but also as a means of understanding complex and aesthetically captivating phenomena.
“Analysis of Environmental Particles Through Holistic Approaches” [View Presentation] Most of the main determinants of water quality either consist of, or are controlled by, particles. Previous water quality research has focused on particular particles in isolation or in binary combinations. In this project, we are taking a holistic approach to the characterization of the particle load in water, focusing on the collective properties of the particles rather than individual components. Because the characterization of particles is often time-consuming, applying an informatics-based approach could speed up the evaluation of water quality and the assessment of treatment effectiveness.
“Application of Continuous Wavelet Transforms to the Study of Short-Term Variability in Methanol Masers” Observations of 53 methanol masers at 6.7 GHz were taken by the Allen Telescope Array between July 2010 and January 2011. We found short timescale variability on the order of minutes or less in 3 of our observations. To analyze the structure of this variability we are applying Continuous Wavelet Transforms (CWTs) to the two-dimensional time series of each variable maser observation. In this talk, I will outline the data, the problems that we need to address to apply CWTs to the data, and some preliminary results.
“Visualization of Chaos and Legendre Polynomials” I will be discussing the visualization of chaotic and non-linear systems. There are a variety of methods of analyzing these systems visually, which includes the evolution of the paths in systems like the Lorenz attractor, Poincare' sections, and bifurcation surfaces. A demonstration of the advantages of these representations and how to analyze them will be presented. There will also be a discussion of the Legendre Polynomials and their application to the Spherical Harmonics. Some interesting behavior in the plots of these systems will also be shown.
“Snell’s Law Application to Light Waves in Optical Fiber Technology” This project is research in its initial stages of which is currently under the supervision of Dr. Virgilio Gonzalez from the electrical engineering department, and by Dr. Hamide Dogan-Dunlap from the Mathematics Department at the University of Texas at El Paso. This project is also undergraduate research directed by the National Aeronautics and Space Administration (NASA).
“Recovery of Fourier Transforms Using Edge Information” The reconstruction of piecewise smooth functions from non-uniform Fourier data is an important problem in applications such as sensing (e.g. Magnetic Resonance Imaging). In this talk we present a new method of approximating the Fourier transform $\hat{f}(\omega)$ of an underlying piecewise smooth function $f$ as an asymptotic expansion of mapped Chebyshev polynomials. This research leverages recently developed edge detection methods from non-uniform Fourier data in the recovery of the Fourier coefficients. The method is shown to converge exponentially in the (finite) Fourier transform domain given the exact edge locations, and in particular can be approximated on uniform modes. When the exact jump locations are not known, an optimization procedure is used to improve edge estimates and accuracy of the representation.
“Modeling Renminbi / U.S. Dollar Exchange Rate Based on Time Series Analysis” Since June, 2010, the Chinese currency, Renminbi (RMB) has appreciated against the U.S. dollar by more than 6 percent. The appreciation of the RMB catches worldwide attention. This paper evaluates the performances of basic time series models for modeling the daily yield rate of the RMB over 100 U.S. dollars. After analyzing the dataset and comparing different models, the autoregressive model with lag 1 (the AR(1) model) is chosen as the most appropriate. Simulation results show the selected model meets the expectation of forecasting the exchange rate. |

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