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Local-Global Results On Discrete Structures, Alexander Lewis Stevens

Electronic Theses and Dissertations

Local-global arguments, or those which glean global insights from local information, are central ideas in many areas of mathematics and computer science. For instance, in computer science a greedy algorithm makes locally optimal choices that are guaranteed to be consistent with a globally optimal solution. On the mathematical end, global information on Riemannian manifolds is often implied by (local) curvature lower bounds. Discrete notions of graph curvature have recently emerged, allowing ideas pioneered in Riemannian geometry to be extended to the discrete setting. Bakry- Émery curvature has been one such successful notion of curvature. In this thesis we use combinatorial …

Topics In Moufang Loops, Riley Britten

Electronic Theses and Dissertations

We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on …

Banach Spaces On Topological Ramsey Structures, Cheng-Chih Ko

Electronic Theses and Dissertations

A Banach space T₁(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T₁ defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T₁(d, θ) is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where d ∈ ℕ with d ≥ 2, …

Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler

Senior Independent Study Theses

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …

Elementary Teachers’ Perspectives Of Direct Instruction With More Rigorous Mathematics Standards, Sharon Denise Taylor

Walden Dissertations and Doctoral Studies

AbstractMajestic County Schools (pseudonym), a large southeastern school district, has implemented changes in instruction to align with more rigorous state and national mathematics standards. The rigor of the new standards has led to changes in instruction to help students master the standards with evidence from the state-wide standardized test. Although the district has made curricular changes, over one-third of the students in Grades 3-5 at Flint Elementary are not mastering grade-level standards. This basic qualitative study focuses on one elementary school within the district. The purpose was to understand how teachers implement direct instruction (DI) strategies in the classroom to …

Fourth-Dimensional Education In Virtual Reality, Jesse P. Hamlin-Navias

Senior Projects Spring 2022

This project was driven by an interest in mathematics, visualization, and the budding field of virtual reality. The project aimed to create virtual reality software to allow users to interact and play with three-dimensional representations of four-dimensional objects. The chosen representation was a perspective projection. Much like three-dimensional shapes cast two-dimensional shadows, four-dimensional shapes cast three-dimensional shadows. Users of the software developed in this project could interact and experiment with these three-dimensional shadows using hand controlled inputs. The hypothesis put forward is that virtual reality is currently the best medium to teach three-dimensional and four-dimensional geometry.

An Investigation Of Mathematics Self-Efficacy, The Sources Of Mathematics Self-Efficacy, And Mathematics Achievement Among Primary School Students In Trinidad And Tobago, Ronald Sinanan

Dissertations

Purpose of the Study

This dissertation addressed two problems in the literature. Firstly, while many study findings have highlighted the critical role of self-efficacy in students' achievement, additional research was needed about the four hypothesized sources that influence the improvement of students' mathematics self-efficacy. Many studies on self-efficacy sources were conducted with measures not closely tied to social cognitive theory and have not demonstrated sufficient reliability. Using the Sources of Mathematics SelfEfficacy Scale, Usher and Pajares (2009) addressed this problem. They suggested several recommendations for future research (Usher & Pajares, 2008b, 2009), including exploring the validity of their scale in …

Grade K-5 Teachers’ Perceptions Of Professional Development That Supports Mathematics Instruction, Shannon Annette Manley

Walden Dissertations and Doctoral Studies

Many Grade K-5 teachers in the United States do not receive the mathematics support they need from the professional development (PD) activities offered by their school districts. The purpose of this qualitative research was to explore the perceptions of Grade K-5 teachers on the PD activities they received from their school district to support mathematics instruction. The conceptual framework that supported this study was andragogy, an adult learning theory that takes the learner’s needs into account and values the connection to real-world situations. The research question addressed how Grade K-5 teachers perceive the PD that they were offered by their …

Charter School, Kindergarten–6, Homeschool Parents’ Perceptions, Experiences, And Strategies For Mathematics Instruction, Wendy How Fayard

Walden Dissertations and Doctoral Studies

The research problem for this study was the lack of understanding regarding parents’ perceptions of and experiences with mathematics and instructional strategies for kindergarten through sixth-grade (K–6) students in a charter school, homeschool setting. Dewey’s theory of experience and education was the conceptual framework for the study. In this basic qualitative study, charter school homeschool parents’ perceptions about providing mathematic instruction for K–6 students, experiences with instructing K–6 students in mathematics, and choices and adjustments concerning mathematics teaching strategies were examined. Twelve participants took part in semistructured interviews on the Zoom platform. Their interview responses were analyzed qualitatively using coding …

Investigating Discussion Forum Impact On Students’ Social Justice Beliefs In Online Undergraduate Mathematics Courses: A Mixed Methods Study, Ashlee Lynn Akin Matney

Theses and Dissertations--Education Sciences

While teaching math for social justice and equity has become a heavily researched topic in recent decades with Jo Boaler (2008, 2015, 2016), Rochelle Gutiérrez (2009, 2013), and Eric (Rico) Gutstein (2003, 2006, 2007, 2013) emerging as recent leaders in the charge, the focus has consistently remained on traditional classroom teaching (e.g. Boaler, 2008; Gutiérrez, 2009; Gutstein, 2003). This convergent design mixed methods study investigated the impact of teaching math for social justice in the online learning environment, specifically, the impact of discussion forums on students’ social justice beliefs in fully online undergraduate math courses.

Quantitatively, 56 students completed pre- …

Wildfire Simulation Using Agent Based Modeling: Expanding Controlled Burn Season, Morgan C. Kromer

Senior Independent Study Theses

The United States is home to many different and unique forests. Prior to the 21st century, the United States Forests Service assumed that the best way to protect these forests was to put all efforts to keeping them alive. An enemy to these efforts were wildfires, thus the US adopted a complete fire suppression approach. At the turn of the century, the US realized that wildfires are a necessary part of a forest ecosystem, as they help return nutrients to the soil and reduce ground fuels. However, after suppressing all fires for over 100 years, the forests evolved into a …

Highlights Generation For Tennis Matches Using Computer Vision, Natural Language Processing And Audio Analysis, Alon Liberman

Senior Independent Study Theses

This project uses computer vision, natural language processing and audio analysis to automatize the highlights generation task for tennis matches. Computer vision techniques such as camera shot detection, hough transform and neural networks are used to extract the time intervals of the points. To detect the best points, three approaches are used. Point length suggests which points correspond to rallies and aces. The audio waves are analyzed to search for the highest audio peaks, which indicate the moments where the crowd cheers the most. Sentiment analysis, a natural language processing technique, is used to look for points where the commentators …

The Infinity Conundrum: Understanding Topics In Set Theory And The Continuum Hypothesis, Sabrina Grace Helck

Senior Independent Study Theses

This project is concerned with articulating the necessary background in order to understand the famous result of the undecidability of the continuum hypothesis. The first chapter of this independent study discusses the foundations of set theory, stating fundamental definitions and theorems that will be used throughout the remainder of the project. The second chapter focuses on ordinal and cardinal numbers which will directly relate to the final chapter. First, there is a clear explanation of the notion of order and what it means for a set to be well-ordered. Then ordinal numbers are defined and some properties are listed and …

Environmental Socialization In College: A Survey Research And Network Analysis Of Changes In Climate-Conscious Concerns And Behaviors, Bijeta Lamichhane

Senior Independent Study Theses

Studies have established that socialization takes place in different stages of life. This study explores how political socialization occurs at The College of Wooster by examining changes in students' political identities as well as their perceptions towards a politicized issue, that is, climate change. These shifts in beliefs and concerns among students were evaluated by implementing quantitative research tools present in the Statistical Package for Social Sciences (SPSS) and constructing a similarity network using Gephi to explore similarities across students at this institution. The results revealed that students have become more liberal after joining this college. The study also found …

Gaming The System: A Game Theoretic Approach To Risk Management And Cybersecurity, Abigail Breitenbucher

Senior Independent Study Theses

In this independent study, we detail two fields of game theory, traditional and evolutionary. After establishing foundational concepts in both, we explore risk management and cybersecurity through a game theoretic lens, focusing on some current applications in both fields. The research culminates in an application case of a game theoretic model for the 2017 Equifax data breach. To conclude, we discuss the implications of this model and future work involving evolutionary game theory in cybersecurity/risk management.

The Relationship Between Engagement And Tactile Learning In A Math Classroom Setting, Mikayla Mcbride

Williams Honors College, Honors Research Projects

math setting. I will be teaching a student two similar lessons of multiplication. One lesson will be taught completely with manipulatives. The other lesson will be taught with pencil and paper. The level of engagement between the student and the lesson will be measured for each lesson. I will be using formative assessment to measure student engagement through observation. I will also use a checklist to check multiplication accuracy at the end of the lesson. My hypothesis is that the student will have a higher level of engagement when tactile learning is used. I believe the student will have a …

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

On Implementing And Testing The Rsa Algorithm, Kien Trung Le

Senior Independent Study Theses

In this work, we give a comprehensive introduction to the RSA cryptosystem, implement it in Java, and compare it empirically to three other RSA implementations. We start by giving an overview of the field of cryptography, from its primitives to the composite constructs used in the field. Then, the paper presents a basic version of the RSA algorithm. With this information in mind, we discuss several problems with this basic conception of RSA, including its speed and some potential attacks that have been attempted. Then, we discuss possible improvements that can make RSA runs faster and more secure. On the …

Mathematics Instructional Level As A Predictor Of Explicit Timing Fluency Intervention Success, Chasen Rain Dillon

Legacy Theses & Dissertations (2009 - 2024)

Various evidence-based mathematic interventions have been deemed effective in remediating skill deficits. However, despite recommendation of evidence-based intervention application within Response to Intervention (RTI) frameworks, little research has been done to differentiate intervention effectiveness, specifically Explicit Timing (ET), for students who present with varying skill proficiency prior to intervention implementation. The current study utilized secondary analysis of existing ET data that was supplemented with performance feedback as part of original intervention design (i.e. ET + Feedback). The purpose was to determine whether learning rates varied among students with differential baseline proficiency with the goal of determining proficiency’s relevance to treatment …

Decision-Making Accuracy At The Classwide Level, Alexandra Payne

Legacy Theses & Dissertations (2009 - 2024)

This study was designed to evaluate decision-making accuracy at the classwide level within the context of classwide math intervention, where decisions are made regarding whether or not a class as a whole has met the predefined mastery criterion for a specific math skill. The current study examined decision accuracy when using existing classwide decision-making practices, in which one classwide data point is compared to the mastery criterion. In addition, the current study assessed the role of three variables: class size, decision rule used, and rate of classwide growth. As part of this study, an existing data set containing progress monitoring …

An Analysis Of Educational Strategies Suited For Students With Asd, Quinn Ryan

Honors Theses

This paper will analyze several reasons why traditional educational practices are not well suited for students with ASD, and will explore multiple promising areas of research on mathematical education for these students. The project has several goals, which will be described in more detail throughout the rest of this paper. One such goal is to create a web resource for teachers that is designed to be suited towards students with ASD. The website will contain an overview of my research and analysis, as well as access to sample lesson plans. The purpose of the website is to bridge a gap …

Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of K_n contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …

Teacher Experiences And Perceptions In Implementing Instructional Strategies For Fostering Student Engagement In Upper Elementary Mathematics, Gail Willis

Theses and Dissertations

The purpose of this qualitative phenomenological research study was to investigate the factors that influence mathematical instruction of upper elementary teachers in school districts within Southern California. More specifically, this research study examined teaching strategies of upper elementary teachers’ experiences and perceptions regarding implementing student engagement in mathematics in school districts within Southern California. This qualitative phenomenological research study involves teachers who utilize instructional strategies based on their best practices that foster students engaging in upper elementary mathematics. In this research study, the participants explained their lived experiences and perceptions of utilizing their chosen strategies to engage students in mathematics …

Lay It All On The Line: The Effect Of Teacher-Student Conferencing In Middle Grades Mathematics Classrooms, Natalie Ostrander

Doctor of Education Dissertations

Increasing math achievement continues to be a commonly talked about subject in the educational setting. This case study observes one classroom teacher who implemented teacher-student conferencing in middle grades mathematics classes. The purpose of this study was to reveal the perceived impact of teacher-student conferencing on student engagement and with student achievement. Through a qualitative approach, perceptual data were collected through teacher journaling, conference logs, observations, and an interview. Research occurred in one school district in southeastern North Carolina with middle grades students in sixth and eighth grades. After the qualitative data were collected by me, data were analyzed using …

A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.

Doctoral Theses

Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …

Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.

Doctoral Theses

The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …

Linear Inverse Problems And Neural Networks, Jasjeet Dhaliwal

Master's Theses

We investigate two ideas in this thesis. First, we analyze the results of adaptingrecovery algorithms from linear inverse problems to defend neural networks against adversarial attacks. Second, we analyze the results of substituting sparsity priors with neural network priors in linear inverse problems. For the former, we are able to extend the framework introduced in [1] to defend neural networks against ℓ0, ℓ2,and ℓ∞ norm attacks, and for the latter, we find that our method yields an improvement over reconstruction results of [2].

Blue Red Hackenbush Spiders, Ravi Cho

Master's Theses

One of the goals of Combinatorial Game Theory is to find provable winning strategiesfor certain games. In this paper, we give winning strategies for certain spider positions played using the rules of Blue Red Hackenbush and a variant. Blue Red Hackenbush and its variants are played on a graph of a bLue and Red edges that are connected to a vertex called the ground. We will represent the ground as a horizontal black line. In this paper, we study spider graphs played under two different variants: Blue Red Hackenbush and Reverse Blue Red Hackenbush. Both variants are played by two …

Error Propagation And Algorithmic Design Of Contour Integral Eigensolvers With Applications To Fiber Optics, Benjamin Quanah Parker

Dissertations and Theses

In this work, the finite element method and the FEAST eigensolver are used to explore applications in fiber optics. The present interest is in computing eigenfunctions u and propagation constants β satisfing [sic] the Helmholtz equation Δu + k²n²u = β²u. Here, k is the freespace wavenumber and n is a spatially varying coefficient function representing the refractive index of the underlying medium. Such a problem arises when attempting to compute confinement losses in optical fibers that guide laser light. In practice, this requires the computation of functions u referred to as …

Numerical Cognition And Autism Spectrum Traits In Adults, Benjamin Covington

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Evidence suggests that individuals with high-functioning autism spectrum disorder (ASD) may be particularly inclined toward math proficiency, especially in adulthood. There is also evidence, however, that many of those with an ASD struggle in math as children compared to their typically-developing peers. These ostensibly inconsistent findings may indicate that individuals with an ASD struggle with number sense, a precursor to formal math, rather than with formal math per se. This account is compatible with evidence of a specific form of neural dysregulation, excitatory/inhibitory imbalance, in ASD that results in reduced signal-to-noise ratios (SNR) for processes that occur in downstream …