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Looking At The Workplace Through Mathematical Eyes, John Keogh

Doctoral

This thesis is concerned with the idea that people may know more about mathematics than they think they do and rely on it more than they realize, especially in work. That they more readily account for what they ‘do’, dismissing what they ‘know’ as ‘commonsense’ or ‘part of the job’, seems to extend a self-perception of not ‘being a maths person’ and permits it to be transmitted within families, across generations and throughout communities. At the same time, the pervasiveness of modern technology, and the proliferation of information represented in mathematical shapes, patterns, relationships, quantities and chance, would seem to …

The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour

Senior Independent Study Theses

Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole

Theses and Dissertations

Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.

The Underrespresentation Of Hispanic Women In The Science, Technology, Engineering, And Mathematics Fields: What Can Be Done To Curie The Problem., Elky Almaraz

The Scholar: St. Mary's Law Review on Race and Social Justice

Hispanic women comprise approximately eight percent of the United States’ population and represent the largest group of minority women. However, Hispanic women only make up approximately two percent of the science and engineering workforce. In contrast, Caucasian women form approximately one-third of the United States’ population and eighteen percent of the science, technology, engineering, or mathematics (STEM) workforce. Hispanic women begin a post-secondary education in STEM fields with a proportional interest to other gender or racial groups. However, they are far less likely to continue the coursework and ultimately earn a degree than their non-minority classmates. Schools and education officials …

Geometric Algebra: An Introduction With Applications In Euclidean And Conformal Geometry, Richard Alan Miller

Master's Theses

This thesis presents an introduction to geometric algebra for the uninitiated. It contains examples of how some of the more traditional topics of mathematics can be reexpressed in terms of geometric algebra along with proofs of several important theorems from geometry. We introduce the conformal model. This is a current topic among researchers in geometric algebra as it is finding wide applications in computer graphics and robotics. The appendices provide a list of some of the notational conventions used in the literature, a reference list of formulas and identities used in geometric algebra along with some of their derivations, and …

Mathematical Inequalities, Amy Dreiling

Master's Theses

In this thesis, we discuss mathematical inequalities, which arise in various branches of Mathematics and other related fields. The subject is a vast one, but our focus is on inequalities related to complex analysis, geometry, and matrix theory.

We investigate recently proven trigonometric and hyperbolic inequalities. This includes Katsuura's string of seven inequalities for the sine and tangent functions and Price's Inequality (with new proofs derived by Katsuura and Obaid). We also discuss complex hyperbolic inequalities and inequalities from infinite products.

We then establish geometric inequalities, including those relating parts of the triangle as well as conic sections and their …

Galois Theory And The Hilbert Irreducibility Theorem, Damien Adams

Master's Theses

We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theory and Hilbert's Irreducibility Theorem: given any irreducible polynomial f(t₁, t₂, …, t_n, x) over the rational numbers, there are an infinite number of rational n-tuples (a₁, a₂, …, a_n) such that f(a₁, a₂, …, a_n, x) is irreducible over the rational numbers.

We take a preliminary look at linear algebra, symmetric groups, extension fields, splitting fields, and the Chinese Remainder Theorem. We follow this by studying …

Exploring Student Perseverance In Problem Solving, Angelique Renee (Treadway) Duncker

LSU Master's Theses

ABSTRACT Many high school Geometry students lack the perseverance required to complete complex and time-consuming problems. This project tests the hypothesis that if students were provided with a means of organizing their problem solving work they will be less apt to quit when faced with complex and time-consuming mathematical problems. This study involved students enrolled in 10th grade Geometry and 10th grade Honors Geometry in two similar high schools. After trying unsuccessfully to implement methods adapted from an engineering workshop, I designed a graphic organizer that was simple to use and acceptable to the students. Ultimately, I did not detect …

Effect Of Personalized Instruction On The Achievement Of Solving Mathematical Word Problems, Danica Vukmirovic

Wayne State University Dissertations

Graduation rates are negatively affected by college learners' inability to demonstrate proficiency in mathematics. The purpose of this research study was to determine the effect of individual personalized mathematical instruction on the achievement of solving mathematical word problems by undergraduates enrolled in a college mathematics course. As well, the effect of individual personalized mathematical instruction on undergraduate motivation to solve mathematical word problems was also examined.

The research undertaken was a true experimental post-test only, control group design that took place over three consecutive weeks. Participants were randomly assigned to either the experimental group or the control group. The experimental …

Mathematical Tasks Without Words And Word Problems: Perceptions Of Reluctant Problem Solvers, Sydney Margaret Holbert

Electronic Theses and Dissertations

This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data were gathered from problem-solving sessions, in the form of session transcripts, written reflections, and interviews to determine how the reluctant problem solvers perceived the problems presented in each session. Participants' views of the problems before and after working were recorded and thick descriptions of the sessions including quotes from …

Metacognition And Its Effect On Learning High School Calculus, Bonnie Sue Bergstresser

LSU Master's Theses

The following paper discusses the effect of metacognitive training sessions on students’ calculus retention. Students in two high school classes participated. The students in both classes were then given lessons on a chapter without metacognitive training and lessons on a subsequent chapter with training in a set of metacognitive skills. After the latter chapter students scored higher on a post-test and expressed desire to incorporate the skills they learned into their other classes.

Joint Entropy Of Continuously Differentiable Ultrasonic Waveforms, M S. Hughes, John E. Mccarthy, J N. Marsh, S A. Wickline

Mathematics Faculty Research

This study is based on an extension of the concept of joint entropy of two random variables to continuous functions, such as backscattered ultrasound. For two continuous random variables, X and Y, the joint probability density p(x,y) is ordinarily a continuous function of x and y that takes on values in a two dimensional region of the real plane. However, in the case where X=f(t) and Y=g(t) are both continuously differentiable functions, X and Y are concentrated exclusively on a curve, γ(t)=(f(t),g(t)), in the x,y plane. This concentration can only be represented using a mathematically "singular" object such as a …

A Comparison Of Students' And Parents' Mathematics Attitudes And Achievement At A Private Historically Black University, Kristopher Childs

Electronic Theses and Dissertations

The focus of this research was to compare students’ and their parents’ mathematical attitudes using the Attitudes Towards Mathematics Instrument (ATMI). The sample consisted of 476 newly-enrolled students and 263 parents attending the New Student Orientation and Leadership program at a private historically black university. The sample was predominantly African American, with 96% of the students and 95% of the parents identifying themselves as African American. The ATMI total score and subscale scores of self-confidence, value, enjoyment, and motivation were explored to determine if there was a relationship between the mathematics attitudes of students enrolled at a private historically black …

The Machete Number, David Freund

Senior Independent Study Theses

Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.

Connected Mathematics Learning And Gender Equity In Predominantly Latino/A High Schools: Case Of Spatial Reasoning, Raymond Falcon

Open Access Theses & Dissertations

This study analyzed interventions used in improving the mathematics achievement in spatial reasoning tasks for females called connectedness. Gender achievement in mathematics has been a controversial topic because of the wide variance in research. Some research has found a difference between the genders in mathematics while others argue there is no difference in mathematical achievement. The Seven Clever Piece Tangrams were used in the mixed method study as the instrument of spatial reasoning tasks. Freshmen participants (N=719) from southwest high schools in a border town participated in one of two groups: control (n=247) and treatment (n=472). Of the participants, 379 …

Selected Research In Covering Systems Of The Integers And The Factorization Of Polynomials, Joshua Harrington

Theses and Dissertations

In 1960, Sierpi\'{n}ski proved that there exist infinitely many odd positive integers $k$ such that $k\cdot 2^n+1$ is composite for all positive integers $n$. Such integers are known as Sierpi\'{n}ski numbers. Letting $f(x)=ax^r+bx+c\in\mathbb{Z}[x]$, Chapter 2 of this document explores the existence of integers $k$ such that $f(k)2^n+d$ is composite for all positive integers $n$. Chapter 3 then looks into a polynomial variation of a similar question. In particular, Chapter~\ref{CH:FH} addresses the question, for what integers $d$ does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ with $f(1)\neq -d$ such that $f(x)x^n+d$ is reducible for all positive integers $n$. The last two chapters of …

Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman

Senior Independent Study Theses

This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …

Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati

College of Graduate Studies: Theses & Dissertations

In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.

Research Briefs: Improving College Students' Attitudes Toward Mathematics, Georgia Southern University

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Connectivity And Spanning Trees Of Graphs, Xiaofeng Gu

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation focuses on connectivity, edge connectivity and edge-disjoint spanning trees in graphs and hypergraphs from the following aspects.;1. Eigenvalue aspect. Let lambda2(G) and tau( G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of tau(G), Cioaba and Wong conjectured that for any integers d, k ≥ 2 and a d-regular graph G, if lambda 2(G)) < d -- 2k-1d+1 , then tau(G) ≥ k. They proved the conjecture for k = 2, 3, and presented evidence for the cases when k ≥ 4. We propose a more general conjecture that for a graph G with minimum degree delta ≥ 2 k ≥ 4, if lambda2(G) < delta -- 2k-1d+1 then tau(G) ≥ k. We prove the conjecture for k = 2, 3 and provide partial results for k ≥ 4. We also prove that for a graph G with minimum degree delta ≥ k ≥ 2, if lambda2( G) < delta -- 2k-1d +1 , then the edge connectivity is at least k. As corollaries, we investigate the Laplacian and signless Laplacian eigenvalue conditions on tau(G) and edge connectivity.;2. Network reliability aspect. With graphs considered as natural models for many network design problems, edge connectivity kappa'(G) and maximum number of edge-disjoint spanning trees tau(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G. Let kappa'(G) = max{lcub}kappa'(H) : H is a subgraph of G{rcub}. We present: (i) For each integer k > 0, a characterization for graphs G with the property that kappa'(G) ≤ k but for any additional …

Bit Error Rate Estimation In Wimax Communications At Vehicular Speeds Using Nakagami-M Fading Model, Biswojit Bose

Theses: Doctorates and Masters

The wireless communication industry has experienced a rapid technological evolution from its basic first generation (1G) wireless systems to the latest fourth generation (4G) wireless broadband systems. Wireless broadband systems are becoming increasingly popular with consumers and the technological strength of 4G has played a major role behind the success of wireless broadband systems. The IEEE 802.16m standard of the Worldwide Interoperability for Microwave Access (WiMAX) has been accepted as a 4G standard by the Institute of Electrical and Electronics Engineers in 2011. The IEEE 802.16m is fully optimised for wireless communications in fixed environments and can deliver very high …

Numeracy Support For Year Two Students, Gillian Dawn Hurle

Theses: Doctorates and Masters

Research of teaching theories and intervention programs internationally and in Australia suggests that the implementation of numeracy support programs can improve student achievement levels (Fuchs, 2005; Ketterlin-Geller, Chard & Fien, 2008; Van Kraayenoord & Elkins, 2004). An intervention program was conducted for a small group of Year Two students with the aim of improving their numeracy skills over a 20 week period. Results of two mathematics assessments, together with information provided by teachers based on classroom observations and informal assessments were combined to select a group of twelve students who were considered to be at risk of developing mathematical difficulties. …

Unitary N-Dilations For Tuples Of Commuting Matrices, John E. Mccarthy, Orr Moshe Shalit

Mathematics Faculty Research

We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T) = PHq(U)|H for all polynomials q of degree at most N.

Toward Legalization Of Poker: The Skill Vs. Chance Debate, Robert C. Hannum, Anthony N. Cabot

UNLV Gaming Research & Review Journal

This paper sheds light on the age-old argument as to whether poker is a game in which skill predominates over chance or vice versa. Recent work addressing the issue of skill vs. chance is reviewed. This current study considers two different scenarios to address the issue: 1) a mathematical analysis supported by computer simulations of one random player and one skilled player in Texas Hold'Em, and 2) full-table simulation games of Texas Hold'Em and Seven Card Stud. Findings for scenario 1 showed the skilled player winning 97 percent of the hands. Findings for scenario 2 further reinforced that highly skilled …

The Mathematics Of Skateboarding: A Relevant Application Of The 5es Of Constructivism, William Robertson

Selected Works Temporary Series

lives is a challenge for educators. As part of a weeklong mathematics summer enrichment program held in the summer of 2010 at a southern university in the United States (US), eighty-five high school students participated in a unique set of activities designed to integrate mathematics concepts and skateboarding. Project leaders used a constructivist framework to design student-centered experiences implemented in the outdoor setting of a local skatepark and in campus classrooms. The activities designed for students in “The Mathematics of Skateboarding” demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school …

The Mathematics Of Skateboarding: A Relevant Application Of The 5es Of Constructivism, William Robertson

Departmental Papers (TE)

lives is a challenge for educators. As part of a weeklong mathematics summer enrichment program held in the summer of 2010 at a southern university in the United States (US), eighty-five high school students participated in a unique set of activities designed to integrate mathematics concepts and skateboarding. Project leaders used a constructivist framework to design student-centered experiences implemented in the outdoor setting of a local skatepark and in campus classrooms. The activities designed for students in “The Mathematics of Skateboarding” demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school …

Examining The Bifactor Irt Model For Vertical Scaling In K-12 Assessment, James Koepfler

Dissertations, 2014-2019

Over the past decade, educational policy trends have shifted to a focus on examining students’ growth from kindergarten through twelfth grade (K-12). One way states can track students’ growth is with a vertical scale. Presently, every state that uses a vertical scale bases the scale on a unidimensional IRT model. These models make a strong but implausible assumption that a single construct is measured, in the same way, across grades. Additionally, research has found that variations of psychometric methods within the same model can result in different vertical scales. The purpose of this study was to examine the impact of …

Collaborating To Improve Inquiry-Based Teaching In Elementary Science And Mathematics Methods Courses, Paula A. Magee, Ryan Flessner

Scholarship and Professional Work – Education

This study examines the effect of promoting inquiry-based teaching (IBT) through collaboration between a science methods course and mathematics methods course in an elementary teacher education program. During the collaboration, preservice elementary teacher (PST) candidates experienced 3 different types of inquiry as a way to foster increased understanding of inquiry based teaching (IBT). The experiences included a PST driven science inquiry and a mathematics inquiry where PSTs were learners and a science inquiry where PSTs were teachers. During and following the semester of the collaboration, data were collected to assess the impact of the inquiry experiences on the PSTs’ understanding …

Developing Mathematics Motivation Scale For The United Arab Emirates, Jalal Haj Hussien, Othman Alsawaie, Abdelaziz Alsartawi, Iman Alghazo, Sana Tibi

Journal of Educational and Psychological Studies

The objective of this study was to develop a valid and reliable mathematics motivation scale (MMS) for UAE students in grades 4 through 12 based on the self-determination theory. A total of 1,481 students (713 boys and 768 girls) from the UAE participated in this study. The process of developing the MMS involved: a) Development of an initial item pool, b) investigating the item-type of motivation membership, c) examining the appropriateness of the administration instructions and the items phrasing, d) and exploring various types of validity and reliability of the MMS. The results indicate that the MMS has acceptable levels …