Special Representations, Nathanson's Lambda Sequences And Explicit Bounds,
2014
CUNY Graduate Center
Special Representations, Nathanson's Lambda Sequences And Explicit Bounds, Satyanand Singh
Dissertations, Theses, and Capstone Projects
{Let $X$ be a group with identity $e$, we define $A$ as an infinite set of generators for $X$, and let $(X,d)$ be the metric space with word length $d_{A}$ induced by $A$. Nathanson showed that if $P$ is a nonempty finite set of prime numbers and $A$ is the set of positive integers whose prime factors all belong to $P$, then the metric space $({\bf{Z}},d_{A})$ has infinite diameter. Nathanson also studied the $\lambda_{A}(h)$ sequences, where $\lambda_{A}(h)$ is defined as the smallest positive integer $y$ with $d_{A}(e,y)=h$, and he posed the problem to compute $\lambda_{A}(h)$ and estimate its growth rate. …
Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams,
2014
Gordon College
Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman
Journal of Humanistic Mathematics
This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.
Promoting Active Studying: The Study Challenge,
2014
Adelphi University
Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry
Journal of Humanistic Mathematics
We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.
What Is So Negative About Negative Exponents?,
2014
Gannon University
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada,
2014
Morgan State University
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Journal of Humanistic Mathematics
Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.
Improving Equity And Education: Why And How,
2014
Montclair State University
Improving Equity And Education: Why And How, Patricia Clark Kenschaft
Journal of Humanistic Mathematics
Progress is possible. When I graduated from college, only 5\% of the new U.S. doctorates in mathematics went to women; now it is about 30\%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and …
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools,
2014
University of Borås
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Journal of Humanistic Mathematics
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …
Galileo And Aristotle's Wheel,
2014
SUNY Geneseo
Galileo And Aristotle's Wheel, Olympia Nicodemi
Journal of Humanistic Mathematics
At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results …
A Modeling Study Of The History-Dependence Of Conduction Delay In Unmyelinated Axons,
2014
New Jersey Institute of Technology
A Modeling Study Of The History-Dependence Of Conduction Delay In Unmyelinated Axons, Yang Zhang
Dissertations
Conduction delay in an axon is the time required for an action potential to propagate between two positions. It is a function of the axon’s passive membrane properties, voltage-gated ion channels and the Na+/K+ pump, and can be substantially affected by neuromodulators. The conduction delay of action potential, generated by the pyloric dilator (PD) neuron unmyel i nated motor axon in the stomatogastric nervous system, shows significant variability with ongoing bursting or Poisson stimulation. When the axon is stimulated, the mean value (Dmean) and coefficient variation of conduction delay (CV-D) slowly increase with time (slow timescale effect), and the relationship …
Particle Filtering For Frequency Estimation From Acoustic Time-Series In Dispersive Media,
2014
New Jersey Institute of Technology
Particle Filtering For Frequency Estimation From Acoustic Time-Series In Dispersive Media, Nattapol Aunsri
Dissertations
Acoustic signals propagating in the ocean carry information about geometry and environmental parameters within the propagation medium. Accurately retrieving this information leads us to effectively estimate parameters that are of utmost importance in environmental studies, climate monitoring, and defense. This dissertation focuses on the development of sequential Bayesian filtering methods to obtain accurate estimates of instantaneous frequencies using Short Term Fourier Transforms within the acoustic field measured at an array of hydrophones, which can be used in a subsequent step for the estimation of propagation related parameters. We develop a particle filter to estimate these frequencies along with modal amplitudes, …
Mathematics In Rural Mexico: Motivations And Barriers For Adult Women Learners,
2014
Brigham Young University
Mathematics In Rural Mexico: Motivations And Barriers For Adult Women Learners, Janel Wilson Williams, Dr. Jacqualine Taylor Voyles
Journal of Undergraduate Research
Math educators have long realized that women in general have shied away from involvement in the mathematical world. Current research in the mathematics education field studies the motivations and barriers women have to studying math. My research extends this topic to a small village in Mexico: La Estancia. By studying factors that encourage or discourage adult Mexican women from studying math in rural settings, important influences can be identified. The identification of these elements can lead to the development of important intervention programs targeted at minimizing negative influences while capitalizing on and strengthening the existing positive influences.
Pre-Service University Math Education Programs In Japan,
2014
Brigham Young University
Pre-Service University Math Education Programs In Japan, Vonn R. Christenson, Dr. Blake Peterson
Journal of Undergraduate Research
For years the United States has lagged behind the international community in mathematical performance at the elementary and secondary education levels. In the Third International Mathematics and Science Study (TIMSS), differences between the teaching style in Japan and the United States were studied, identified and recorded. Through this study, it was discovered that students in the United States “encounter mathematics that is at a lower level, is somewhat superficial, and is not as fully or coherently developed” as the mathematics in Japan.i
Weighted Inverse Weibull Distribution: Statistical Properties And Applications,
2014
Georgia Southern University
Weighted Inverse Weibull Distribution: Statistical Properties And Applications, Valeriia Sherina, Broderick O. Oluyede
Mathematical Sciences: Faculty Publications
In this paper, the weighted inverse Weibull (WIW) class of distributions is proposed and studied. This class of distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Fr´echet distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, R´enyi entropy and Fisher information are presented. Estimates of the model parameters via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.
Solving Laplace’S Equation On A Personal Computer,
2014
Brigham Young University
Solving Laplace’S Equation On A Personal Computer, Michael Higley, Dr. Peter Bates
Journal of Undergraduate Research
Laplace’s equation is a differential equations that describes many physical properties in steady state systems. It can be used to describe heat distributions, displacements in elastic media, or electrostatic fields. My interest is in solving an electrostatics problem where the domain—the area in which the equation has physical meaning—is irregular enough that the only way to solve the problem is to use some sort of numerical approximation.
Ratios Of Positive Definite Matrices,
2014
Brigham Young University
Ratios Of Positive Definite Matrices, Dena Plant, Dr. Wayne Barrett
Journal of Undergraduate Research
As our research began we focused on proving the hypothesis that for a 4 x 4 Positive Definite matrix A, the ratio
Length Minimizing Network For N Points On The K-Torus,
2014
Brigham Young University
Length Minimizing Network For N Points On The K-Torus, W. Lauritz Petersen, Dr. Denise Halverson
Journal of Undergraduate Research
Our project consisted of several components with the end goal being: given n points on the ktorus (a donut with k number of holes), what would the shortest path network be to connect all the n points (network meaning a network of paths connecting each of the n-points).
Optimal Energy Recovery In Finite Time For Linearly Dissipative Systems,
2014
Brigham Young University
Optimal Energy Recovery In Finite Time For Linearly Dissipative Systems, Mark Meilstrup, Dr. Scott Glasgow
Journal of Undergraduate Research
Many physical processes involve the loss or dissipation of energy. For example, when pushing a box across the floor, some of the energy that is spent will be lost to frictional forces. Our research is concerned with the study of the energy which is lost, and also the energy which is recoverable, in the more complex setting of a linearly dissipative optical system. We consider some electromagnetic pulse, such as a laser beam, entering and interacting with an absorbing medium, such as glass or some gas. When the pulse exits the medium, some of the energy has been absorbed, and …
Orca Research Report,
2014
Brigham Young University
Orca Research Report, Jeanna Chilton, Dr. Gary Lawlor
Journal of Undergraduate Research
The work I was able to do for the research on the minimal surface area of the octahedron was time consuming, but unfortunately did not bring about any profound knowledge for anyone besides myself.
On Cubic Multisections Of Eisenstein Series,
2014
The University of Texas Rio Grande Valley
On Cubic Multisections Of Eisenstein Series, Andrew Alaniz, Timothy Huber
School of Mathematical & Statistical Sciences Faculty Publications
A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. We prove that the resulting series are rational functions of η(τ) and η(3τ), where η is the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations. These operators exhibit properties that mirror those of similarly defined quintic operators.
Algebraic Detection Of Flexibility Of Polyhedral Structures With Applications To Robotics And Chemistry,
2014
Fordham University
Algebraic Detection Of Flexibility Of Polyhedral Structures With Applications To Robotics And Chemistry, Stephen Fox Fcrh '11, Robert Lewis
The Fordham Undergraduate Research Journal
Many problems arise in biochemistry, robotics, and other fields in which flexibility of a polygonal or polyhedral structure plays an important role. In biochemistry, the flexibility and folding of molecules is an important factor in drug design and is a subject of ongoing research (Erickson et al. 2004). In robotics, stable configurations of manipulators (e.g., a mechanical arm grasping) as well as mechanical joints for locomotion (e.g., walking) must be calculated for safe, smooth movement.
