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Cantor Sets, Cantorvals, And Their Topological Structure, Ángel Adrián Agüero

Open Access Theses & Dissertations

With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.

Upper Dimension And Bases Of Zero-Divisor Graphs Of Commutative Rings, S. Pirzada, M. Aijaza, Shane Redmond

EKU Faculty and Staff Scholarship

For a commutative ring R with non-zero zero divisor set Z∗(R), the zero divisor graph of R is Γ(R) with vertex set Z∗(R), where two distinct vertices x and y are adjacent if and only if x y = 0. The upper dimension and the resolving number of a zero divisor graph Γ(R) of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs …

Optimizing Timber Harvest Value: A Dynamic Programming Investigation, Kayleigh T. Dietz

Senior Independent Study Theses

Operations research models have been and continue to be integral to the implementation of forest management strategies. Fundamental operations research models such as linear and dynamic programming have respective advantages and disadvantages when applied to any forest system. An overview of five fundamental operations research models are provided in terms of a timber harvesting system. Timber production management is a branch of forest management that seeks to optimize the economic benefits of harvesting timber. The time-stage nature of timber harvesting systems makes dynamic programming a particularly useful model for timber production management. Thus, dynamic programming is the primary model discussed …

Exploring Topics Of The Art Gallery Problem, Megan Vuich

Senior Independent Study Theses

Created in the 1970's, the Art Gallery Problem seeks to answer the question of how many security guards are necessary to fully survey the floor plan of any building. These floor plans are modeled by polygons, with guards represented by points inside these shapes. Shortly after the creation of the problem, it was theorized that for guards whose positions were limited to the polygon's vertices, the floor of n/3 guards are sufficient to watch any type of polygon, where n is the number of the polygon's vertices. Two proofs accompanied this theorem, drawing from concepts of computational geometry and graph …

Middle School Mathematics Pre-Service Teacher’S Responses To A Mathematics Content And Specific Mathematics Pedagogy Intervention, Stephen J. Norton

Australian Journal of Teacher Education

Prospective middle school pre-service teachers’ knowledge and affect in Australia has had little empirical research. In this study, 108 graduate entry pre-service teachers were surveyed for their knowledge of middle years’ mathematics, confidence, and self-efficacy at the commencement of a mathematics curriculum course. It was found that their memory of middle years’ mathematics was very poor and this was accompanied by low levels of confidence and self-efficacy. An intervention was undertaken to address these issues. The findings are discussed in the context of the “genericism” of pre-service teacher preparation. In particular, the findings call into question the justification for pre-service …

The Interview Project: A Way Of Bridging Theory And Practice In Early Childhood Mathematics Preservice Teacher Education, Doris Santarone

Georgia Educational Researcher

Twenty-nine early childhood preservice teachers (PSTs) participated in an Interview Project. The project’s goals were for the PSTs to apply their knowledge of research on children’s mathematics in their interactions with a child and to learn to listen to and learn from children. The purpose of the study was to evaluate the project and determine whether it met these goals. Pre and post data were collected, and I found that the PSTs showed a significant improvement in their ability to describe and analyze a child’s mathematics and to use their listening to make appropriate instructional decisions. In addition, I found …

Drug Repositioning Based On Bounded Nuclear Norm Regularization, Mengyun Yang, Huimin Lao, Yaohang Li, Jianxin Wang

Computer Science Faculty Publications

Motivation: Computational drug repositioning is a cost-effective strategy to identify novel indications for existing drugs. Drug repositioning is often modeled as a recommendation system problem. Taking advantage of the known drug–disease associations, the objective of the recommendation system is to identify new treatments by filling out the unknown entries in the drug–disease association matrix, which is known as matrix completion. Underpinned by the fact that common molecular pathways contribute to many different diseases, the recommendation system assumes that the underlying latent factors determining drug–disease associations are highly correlated. In other words, the drug–disease matrix to be completed is low-rank. Accordingly, …

Detecting Special-Cause Variation 'Events' From Process Data Signatures, Timothy M. Young, Olga Khaliukova, Nicolas André, Alexander Petutschnigg, Timothy G. Rials, Chung-Hao Chen

Electrical & Computer Engineering Faculty Publications

The ability to detect the special-cause variation of incoming feedstocks from advanced sensor technology is invaluable to manufacturers. Many on-line sensors produce data signatures that require further off-line statistical processing for interpretation by operational personnel. However, early detection of changes in variation in incoming feedstocks may be imperative to promote early-stage preventive measures. A method is proposed in this applied study for developing control bands to quantify the variation of data signatures in the context of statistical process control (SPC). Control bands based on pointwise prediction intervals constructed from the Bonferroni Inequality and Bayesian smoothing splines are developed. Applications using …

Teachers' Perceptions About Instructing Underachieving K-5 Students On Mathematical Word Problem-Solving, Crystal Yvette Baldwindouglas

Walden Dissertations and Doctoral Studies

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed …

Teachers' Perceptions Of The Sustainability Of Mathematics And Science Partnership Professional Development, Robert Harold Alt

Walden Dissertations and Doctoral Studies

The sustainability of improved pedagogy gained through professional development (PD) of mathematics teachers has undergone little empirical study. In a midsized urban school district in the Northeastern United States, all high school mathematics teachers attended a 3-year mandatory PD program. Although an external evaluator studied this program immediately after completion, there had been no longitudinal study of the perceptions of its participants regarding the sustained benefits of the program. This qualitative study offered a follow-up study of the participants in the Math and Science Partnership (MSP) PD program to provide insight to administrators regarding the sustainability of benefits gained through …

Eighth-Grade Teachers' And Students' Experiences With Ipads In Math Inclusion Classes, Sitembiso Maduma Ncube

Walden Dissertations and Doctoral Studies

Although educators have embraced technology in mathematics inclusion classrooms, students with math learning disabilities (MLD) still have anxiety and negative attitudes about mathematics and score lower than their counterparts. The purpose of this qualitative single case study was to investigate and describe the experiences of middle school 8th grade inclusion iPad math app users. The technological pedagogical content knowledge model, the universal design for learning model, and the experiential learning theory provided the conceptual framework of technology integration. The research questions addressed the experiences of middle school inclusion teachers and students with MLD regarding iPad use in a Common Core …

Fourth-Grade Teachers Use Of Mtss-Rti To Teach Mathematical Word Problem-Solving, Theodell Joanna Blake

Walden Dissertations and Doctoral Studies

Schools in Florida used the multitiered system of support response to intervention framework to help students achieve the state and national standards but, in the national report card, 61% of the fourth-graders assessed in mathematics failed to achieve proficiency. Research indicated that the students lacked mathematical word problem-solving skills. The purpose of the qualitative study was to discover how fourth-grade special and general education teachers used the response to intervention framework evidence-based curriculum, instruction, intervention, assessment, and student data to teach math word problem-solving skills to children who have persistent and significant difficulties. Welner'€™s zone of mediation framework and Vygotsky'€™s …

Teachers' And Students' Beliefs In Mathematics At State Senior High School 5 Semarang, Muhtarom Muhtarom, Dwi Juniati, Tatag Yuli Eko Siswono, Ismi Rahmatika

Jurnal Riset Pendidikan Matematika

The aim of this research was to discover the relationship between teachers' and students' beliefs in mathematics. The sample consisted of two mathematics teachers, twenty eight students from 10th grade natural science 6 (X IPA 6) and twenty eight students from 10th grade natural science 10 (X IPA10) at state senior high school 5 Semarang. The data were collected from questionnaires and guided interviews on beliefs about mathematics. The research results showed that both of the mathematics teachers had platonist beliefs. It was found specifically that 4.76% of students in class X IPA 6 consistently had instrumentalist beliefs, 85.71% were …

Comparing The Methods Of Vertical Equating For The Math Learning Achievement Tests For Junior High School Students, Chairun Nisa, Heri Retnawati

REID (Research and Evaluation in Education)

Developing the students' mathematical ability needs to be carried out to improve the teaching process. This is very important for continuous education. This study aimed to describe: (1) the characteristics of the mathematics achievement tests for grades VII and VIII; (2) the equity constant of the vertical equating result of the mathematics achievement; (3) the accuracy of the mean & mean method, mean and sigma, Haebara characteristics curve, Stocking & Lord characteristics curve methods in the vertical equating of the tests for grades VII and VIII. The data were the students' scores for the Higher Order Thinking tests collected with …

Search For The Rare Decay Of B+→ℓ+Νℓγ With Improved Hadronic Tagging, Belle Collaboration, R. Kroeger

Faculty and Student Publications (Open Access)

No abstract provided.

The "Mathematics Problem": A Plymouth Foundation Year Case Study, Mj Craven, J Sharp

School of Engineering, Computing and Mathematics

Research indicates the transition from school mathematics to university-level STEM courses is often problematic, leading to issues with student satisfaction and retention (the “Mathematics Problem”). An increasing number of HEIs are establishing foundation years in an effort to ameliorate this problem. Undergraduate Mathematics cohorts at Plymouth often contain a sizeable number of exfoundation year students, meaning that efforts to enhance student foundation year experience are vital to student satisfaction, retention and further recruitment. This paper is a report mid-way through a two-year project to examine a partially-flipped learning approach to improve foundation year retention and mathematical knowledge of those progressing …

Stem Superstar Women: Ada Lovelace, Pioneering Computer Programming, Erica Sonzogni

Children's Book and Media Review

When a person thinks of a scientist, they usually consider the men that dominate the field. In reality, there were many important women who made a strong contribution in this area. Ada Lovelace is one of those women. Ada’s life is chronicled from birth to death in this book. The text focuses on her many contributions to science and mathematics in a time when women were not supported in receiving an education. Ada’s mother encouraged this, her husband continued with the support, and Ada pursued her passion until her early death.

Measurement Of The Decays Λc→Σππ At Belle, Belle Collaboration, R. Kroeger

Faculty and Student Publications (Open Access)

No abstract provided.

A World Of Her Own: 24 Amazing Women Explorers And Adventurers, Leah Christopher

Children's Book and Media Review

Join twenty-four women explorers and adventurers as they dive into the deep sea, summit Mt. Everest and other peaks, discover new plants and animals, cross the world in a yacht, explore the Amazon River, catch venomous snakes, save endangered species, and venture through forest canopies. These women are diverse, coming from various countries, ethnicities, family situations, age groups, time periods, and career fields. Although each woman’s path is different, they share a love for nature and discovery—and they all have to overcome others’ doubts about their abilities. These motivating accounts can transform readers’ thinking about the great potential women have …

Edgar Allan Poe's Pie: Math Puzzlers In Classic Poems, Nicole Clark

Children's Book and Media Review

What do you get when you cross Walt Whitman with a spider whose web-spinning was disturbed by a wind which blew sixty percent of it away? Robert Frost with boxer shorts at ninety cents a pair? Shel Silverstein with a hippo-po-tah-tum eating you at four percent per bite? In Edgar Allan Poe’s Pie, children’s poet Laureate J. Patrick Lewis cleverly integrates math problems into new adaptations of classic poetry using the original rhyme and meter.

A Hundred Billion Trillion Stars, Kristie Hinckley

Children's Book and Media Review

We live in a world filled with a hundred billion stars. Our planet is covered with lots of water and trees. This book tells you exactly how many in cardinal numbers. Including the number of seconds in a year and the number of rabbits in the world, the entire world is filled with crazy numbers that make it what it is today! This book acknowledges that by the time readers are finished reading this book, almost every number in it will have changed! Try to wrap your head around that (not literally)! The book starts zoomed out from earth, and …

Analysis And Simulation Of Convolution Reverb Using City Tech’S New Auditorium, Tian Leng

Publications and Research

In digital signal processing, convolution reverb can simulate the reverberation of a real acoustic space. The acoustics of different seating areas in an auditorium can vary from each other. To determine the reverberant characteristics of City Tech new building’s auditorium, impulse response (IR) signals are recorded in five key locations of the auditorium.

Directly recorded balloon burst is chosen as the source of impulse source. An omnidirectional and a cardioid microphone with flat frequency response curves are used to record IR signals to 24-bit monophonic wav files. Each IR signal, along with a vocal, is convoluted in MATLAB through both …

Four Derivations Of Schrödinger’S Time Dependent Equation, Sydney Swanson

Essential Studies UNDergraduate Showcase

Physics and the natural world have been studied by humans since the first person wondered ‘Why?’ The Schrödinger equation is important because it attempts to describe a relatively new (to us) and unfamiliar part of our universe, behavior of subatomic particles, and helps modern scientists uncover secrets that have proven useful in technology and explaining our origins. The time dependent Schrödinger equation can be derived from various starting points in Classical such as the equation of a wave, the time independent Schrödinger equation, and Hamilton-Jacobi equations. Why Quantum mechanics exists, useful applications, and cases when it fails or is inaccurate …

Scottish National Assessments: National Report For Academic Year 2017 To 2018, Australian Council For Educational Research (Acer)

Assessment and Reporting

This report has been developed to provide a summary of outcomes at a national level on the newly established system of national standardised assessments, which has since been termed ‘Scottish National Standardised Assessments’ (SNSA) in the 2017 to 2018 academic year, the first year of the programme. A central aim of SNSA is also to provide information on the outcomes of Scottish children and young people in literacy and numeracy over time. The assessments have been available for use in publicly funded schools in Scotland since August 2017. They are administered to children and young people in Primary 1, Primary …

Algebraic Number Theory And Fermats Last Theorem, Edward Evans

The Plymouth Student Scientist

The project aims to deliver sufficient mathematical background to understand a partial proof, due to Ernst Kummer, of Fermat’s last theorem for a specific class of primes called regular primes. In doing so, we also develop some theory that is applicable to a wide range of scenarios in modern number theory, a few of which are discussed in somewhat more superficial detail in the final section.

An Evaluation Of The Psychometric Properties Of The Sf-12v2 Health Survey Among Adults With Hemophilia, Ruchit Shah, Benjamin F. Banahan, Erin R. Holmes, Amit Patel, Marie Barnard, Rahul Khanna, John P. Bentley

Faculty and Student Publications (Open Access)

No abstract provided.

The Role Of Teaching Presence On Academic Achievement In Fully Online Asynchronous And Hybrid Undergraduate Mathematics Courses, Shaghayegh Azadi Setayesh

Theses and Dissertations

This study was designed to investigate how mathematics student perceptions of teaching presence differ by course delivery mode and student achievement. Online learning has had a steady growth in higher education, and mathematics courses are also offered in fully online and hybrid modes, but the research on online mathematics learning and academic achievement is limited. In order to contribute to the body of research in this field, the focus of this study was on teaching presence and academic achievement in two delivery modes: fully online asynchronous, and hybrid.

The Community of Inquiry was the theoretical framework of this study, where …

Relationships Between Teachers' Past Experiences Learning Mathematics And Their Pedagogical Practices And Beliefs, Caci M. Jensen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This creative project centered around the cyclical pattern of mathematics anxiety currently prevalent in our schools. A high percentage of elementary teachers carry mathematics anxiety and beliefs around mathematics that effect their pedagogical practices day-to-day. This anxiety transfers to their students effecting their future choices in mathematics. This project was conducted in case studies with six teachers from a rural charter school. Journey maps, semi-structured interviews, surveys, and observations were used to collect the data.

Comparing The Predictive Power Of Executive Function Assessment Strategies On Preschool Mathematics Performance, Jacob A. Esplin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A child’s executive function (aspects: working memory, response inhibition, and set-shifting between sets of rules) capabilities have been found to strongly relate to their mathematics skills. However, while the relationship has been strongly supported by researchers, a consensus has not been reached regarding the specifics of the relationship between executive function and math skills, including which executive function aspect is most predictive of mathematical performance and the differences in said relationship that might be found when examining both numeracy, such as counting skills and basic operations, and geometry skills. The lack of consensus may be in part because researchers have …

A Case Study On How Meeting The Academic Needs Of Students Substantially Below Grade Level In Mathematics Affects Their Self-Efficacy Beliefs And Engagement, Lauren K. M. Burton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This researcher examined an alternative classroom structure for ninth-grade students substantially below grade level (SBGL) in mathematics. This researcher considered whether targeting the academic and social needs of students SBGL in mathematics in a ninth-grade class would increase their self-efficacy and engagement with the mathematics by studying four teaching effects: teacher, teacher-curriculum, peer-curriculum, and peer.

The researcher used interviews, observations, and surveys to collect qualitative and quantitative data. The case study (n = 19) employed a QUAL + quan convergent parallel mixed methods case study. Meta-inferences from the analyses of qualitative and quantitative data indicate that the structure of …