Digital Commons Network^™

Optimization And Forecasting Algorithms For Converter Dominated Distribution Networks Using Blockchain And Ai, Chinmay Shah

Engineering

Integration of power electronic converter-based distributed energy resources (DERs) in electric power distribution networks is growing exponentially with the recent interest in reducing carbon emissions from fossil fuel-based generation. As the contribution of renewable energy sources in the DER mix continues to increase, so does the incorporation of battery energy storage systems and other controllable loads to compensate for the high variability and uncertainty in the generation from renewable DERs and grid demand. Strategies for increasing the contribution of renewable energy sources and using reserves to accommodate for variations and uncertainty in generation and load include distributed optimal power flow …

The Impact Of Virtual Learning Modalities On The Academic Success Of Students In One Arkansas School District, Diane F. Richards

ATU Theses and Dissertations 2021 - Present

The COVID-19 pandemic changed the way Arkansas public schools’ offered students an education. While moving through this pandemic, many Arkansas schools implemented optional methods of delivery for their students. Some schools tried to maintain face-to-face classes, while others offered completely online classes. Still, others offered a hybrid format where students attended some face-to-face classes and online classes. One Arkansas school district offered all three options. School districts need guidance as to which teaching methods worked well. The long-term effects of the educational impact of COVID-19 are not known at this time. Schools could benefit from a guide with useful strategies …

Movement In Math - Integrating Movement-Based Activities Into Kindergarten Math, Katelyn Belch

Masters of Education in Teaching and Learning

Gross-motor movements have shown promising effects on student academic achievement and engagement especially in kindergarten classrooms. The purpose of this study was to examine what happens when movement-based mathematical activities are introduced into a kindergarten math curriculum and its implications on how kindergarteners engage during math time. Using surveys, observational and reflective data, and semi-structured interviews of students and my cooperating teacher, this study aimed to examine student and teacher perceptions of incorporating movement-activities. When movement activities were introduced into math time, the students were more engaged in math. The movement activities served as form of play-based learning and relied …

The Efficacy Of The Covid-19 Vaccine In Mississippi, Ilyse Miriam Levy

Honors Theses

The Efficacy of The COVID-19 Vaccine in Mississippi

(Under the direction of Dr. Xin Dang)

By tracking and analyzing fifty-three weeks of COVID-19 data, this thesis analyzes the efficacy of the COVID-19 vaccine within the State of Mississippi. Over the course of these fifty-three weeks, I have also been able to calculate the confidence intervals for vaccination efficacy and the risk reduction due to vaccination by using data regarding the correlations between deaths and vaccination status, provided to me by the Mississippi Office of Epidemiology. My analysis demonstrates that the COVID-19 vaccine is effective not only in Mississippi but also …

Causalmodels: An R Library For Estimating Causal Effects, Joshua Wolff Anderson

Computational and Data Sciences (MS) Theses

Free and open source software for statistical modeling and machine learning have advanced productivity in data science significantly. Packages such as SciPy in Python and caret in R provide fundamental tools for statistical modeling and machine learning in the two most popular programming languages used by data scientists. Unfortunately, robust tools similar to these are limited in terms of causal inference. The tools in R that exist lack consistent and standardized methodologies and inputs. R lacks a comprehensive package that offers traditional causal inference methods such as standardization, IP weighting, G-estimation, outcome regression, and propensity matching in one common package. …

Judith Shakespeare's Problem : Using Timss To Examine Contextual Indicators In Girls' Mathematics Achievement, Elizabeth Ann S. Kelly

Legacy Theses & Dissertations (2009 - 2024)

Using the Trends in International Mathematics and Science Study Data (TIMSS) 2015 dataset, this study examines 30 different contextual indicators to determine significant predictors of girls’ mathematics achievement globally. The study design employs three nested levels in the hierarchical linear model (individual, classroom, and nation) to analyze cross-national scores and responses to the contextual questionnaires. Additionally, the focus is on girls as a standalone, independent population, not in comparison to boys. This research seeks to understand at which level of society the most variability is found, as well as analyze the comparative effect sizes of various explanatory contextual predictors within …

“I Just Learn Differently”: The Experiences Of Dis/Abled Students Of Color Interpreting And Resisting Normalizing Forces In The Mathematics Classroom, Dina Mahmood

Education (PhD) Dissertations

This critical phenomenological study employs a disabilities studies in education and critical race theory (DisCrit) lens to unpack the learning experiences of seven dis/abled students of color in the secondary mathematics classroom. Based on data collected from individual and group interviews, the counter-stories presented in this study highlight the implicit and explicit ways that the normative forces of ableism and racism circulate in the secondary mathematics classroom. Through their education journey maps, the participants described forms of hyper-labeling, experiences of implicit and explicit biases from teachers and peers, and rigid conceptions of mathematics that constrained their success. The counter-stories are, …

Exploring Teachers’ Beliefs And Practices On Mathematical Discourse For Diverse Students In Inclusive Classrooms, Gloria A. Carcoba Falomir

UNLV Theses, Dissertations, Professional Papers, and Capstones

The recent implementation of rigorous standards in mathematics education has required shifts in classroom practices. Standards-based instruction places large emphasis on students’ conceptual understanding, requiring them to demonstrate high cognitive levels of mastery of the content through communication of their mathematical reasoning. Teachers and students’ mathematical discursive practices in the classroom can lead to meaningful discussions that integrate students’ explanation, justification, and arguments of ideas or claims and understanding of the content. Research on teachers’ discursive practices has shown that (a) teacher talk tends to dominate classroom instruction and (b) classroom discourse lacks frequent opportunities for teacher-student and peer interactions. …

The Executive’S Guide To Getting Ai Wrong, Jerrold Soh

Asian Management Insights

This article explores how we see AI and argues that we mostly get it wrong. In the process, it explains the reasons backed by social science research on why we tend to get AI wrong and illustrates the dangers of doing so from a managerial and law-making perspective. Some readers may also find the article useful as a guide on how and when to manipulate portrayals of AI in your favour.

Parents And The Evolving Math Curriculum: Supporting One's Student In Elementary Mathematics, Kailyn Heather Scobie

Undergraduate Honors Thesis Collection

The current-day mathematics curriculum is evidently different from the traditional means of teaching math. Due to this, there exist disparities between a child’s math education and their parent or guardian’s math education. This thesis will present firsthand evidence on how these disparities affect a parent’s perception of current-day curriculum, the extent to which parents can support their child in their learning of mathematics at home, and will strive to attend to the needs of both the parents or guardians as well as students in supporting the learning of these new concepts and strategies. With this, the research question asks: What …

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

Entrepreneurship Education Relation To Mathematical Proficiency Amongst Secondary Youth, Mariam Abdelhamid

STEMPS Theses & Dissertations

Mathematical aptitude in the United States has been a concern over the past few decades, not only from an international perspective but from a student proficiency perspective. This phenomenon is also further negatively impacted due to COVID-19 associated learning loss. Correspondingly, there are calls for students to develop entrepreneurial skills to thrive in the 21st century economy. The purpose of this quasi-experimental study was to examine whether participation in an entrepreneurship class was related to mathematical proficiency (Algebra II) in high school. Data on students from two school districts were used, consisting of 2,741 and 1,172 Algebra II students in …

Delivering On A Promise: A Longitudinal Cohort Study Of Emergent Bilinguals' Academic Achievement In A Utah Dual Language Program, J. Eric Campbell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Emergent bilingual (EB) students are a growing population in the U.S. school system currently comprising over 10% of the total population. U.S. school districts have educated EB students using a myriad of practices, including dual language immersion (DLI). Many studies have looked at the academic achievement of native-Spanish speaking EB students, yet there is a dearth of research on DLI in medium-sized school districts in rural settings. This study focused on native-Spanish speaking EB students in a DLI program in a rural Utah district. Specifically, the study compared student academic achievement in English acquisition, English language arts, mathematics, and grade …

A Computer Programming Intervention For Second Grade Math Students, Eric B. Bagley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The multiplication algorithms taught to elementary students are made to help students find answers quickly, but why the algorithm works and how it relates to multiplication is not widely known. For example, one intuitive meaning of multiplication is that of iterated, or, repeated, addition. In this paper, we look at the ways a visual, block-based, programming activity uses the concept of iteration to help second-graders learn multiplication. The results of the study observing second-grade students use visual programming and iteration to setup and solve multiplication story problems. We found that generally students enjoyed these activities and found them helpful during …

Children's Mathematical Engagement Based On Their Awareness Of Different Coding Toys' Design Features, Joseph S. Kozlowski

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Tangible coding toys have been promulgated as useful learning tools for young children to learn computer science and mathematics concepts and skills. Although research shows coding toys can support mathematics for early childhood aged children, little is known about the specific design features of coding toys that afford mathematical thinking concepts and skills to young children. The purpose of this study was to examine kindergarten-aged children’s awareness of the design features in coding toys and to understand how those design features afford children’s engagement with mathematics. The dataset used for this study was collected as part of design-based research NSF …

The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All …

Stop And Smell The Fractals: An Exploration Into Math, Poetry, And Everything In Between, Caroline Jennings

English Undergraduate Honors Theses

Stop and Smell The Fractals is a collection of poetry written during my time at The University of Arkansas. These poems highlight the connections between mathematics and poetry, focusing particularly on their emergence in everyday life.

A Case Study On Targeted Support Using Tpack Model For Newly Hired Secondary Mathematics Teachers, Kristin Leigh Mckitrick-Rojas

STEMPS Theses & Dissertations

As teachers plan for instruction, technology integration is an important factor in the planning and implementation process. This is become imperative in a virtual learning environment for instructors to be competent (Gregory & Lodge, 2015). Problems exist with integrating technology that aligns with teaching and learning in content areas. Among the many possible factors that contribute to these problems is lack of understanding of technology, lack of support for teachers with technology, everchanging technology tools, inadequate training alignment to instruction, technology training that is not content-specific, lack of support with the integration of technology, pedagogy, and content (Koehler et al., …

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science

One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.

First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …

The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres

Honors Projects in Mathematics

Professional sports teams are adored nationwide for their talents and the pride they bring to their city for their efforts. However, not all teams take this responsibility seriously and will lose on purpose, or tank, to gain a higher draft pick in the future. Although the long-term goals of tanking are to help the organization, many people take issue with athletes not putting in their best efforts in every game. Teams in both the NBA and NFL are guilty of tanking to gain better draft picks but not all have found success in this process. This leads to important questions …

Lines On A Smooth Projective Surface, Jordan Demoura

Mathematics & Computer Science Student Scholarship

Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math

This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.

Vampires And Other Diseases: Stochastic Infection Dynamics Of Small Populations, Marijn Jaarsma

Honors Projects in Science and Technology

Mathematical models are powerful tools often applied in the field of epidemiology. The type and shape of the model will differ between different types of diseases. In this study, stochastic dynamical models are applied to the entertaining example of vampires, and the results of this analysis are compared to real-life diseases with small populations of infected. The data used comes from pop-culture depictions of vampires in literature, television shows, movies, and fan pages associated with these depictions. The aim of this study is to serve as an educational tool for modeling diseases with small populations to predict and control the …

Applied Math In Introductory Chemistry, Ji Kim, Grace Pai

Open Educational Resources

Students, particularly those who are non-science majors, often struggle with college-level science courses required for graduation due to the applied mathematics needed to successfully complete the course. This resource includes four activities on the topics of units and measurements, dimensional analysis, density, and gases. These topics were specifically designed to teach the mathematics embedded in these topics in a culturally responsive way. Throughout the activities, we incorporate these four elements of culturally relevant pedagogy (Ladson-Billings, 2009) in order to engage students in successfully solving basic mathematics in chemistry while promoting their interest in learning chemistry.

Using Video Recordings To Support Meaningful Reflection Of Mathematical Teaching Practices, David Scalzo

Honors Program: Senior Projects (Public)

The practice of teaching mathematics is a skill that can be continually built upon. In order to maximize the effectiveness of one’s math lessons, it is essential that they become a reflective teacher. This project explains the importance of reflecting on mathematical teaching practices, then outlines the steps I have taken to start becoming a reflective teacher. Video recordings working with math are included as part of the project, which are used as the material I reflect about.

Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri

Student Research

• Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level.
• Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population.
• Here, we have examined the behavior of a measles-like disease[2] that is characterized by a non-constant transmission rate.

Topological And Dynamical Aspects Of Strata Of Differentials, Aaron Calderon

Yale Graduate School of Arts and Sciences Dissertations

The first part of this dissertation investigates the relationship between strata of Abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. We show that the fundamental group of a stratum surjects onto the subgroup of the mapping class group which preserves a fixed framing of the underlying Riemann surface, thereby giving a complete characterization of the monodromy group. In the course of our proof we also show that these "framed mapping class groups" are finitely generated (even though they are of infinite index) and give explicit generating sets. This work was accomplished in collaboration …

Localization And Cantor Spectrum For Quasiperiodic Discrete Schrödinger Operators With Asymmetric, Smooth, Cosine-Like Sampling Functions, Yakir Moshe Forman

Yale Graduate School of Arts and Sciences Dissertations

This dissertation addresses the question of Anderson localization for quasi-periodic discrete Schr\"odinger operators $H = \varepsilon\Delta + V$ with potential $V$ sampled with Diophantine frequency $\alpha$ from an asymmetric, smooth, cosine-like function $v \in C^2(\mathbb{T},[-1,1])$. After reviewing the known results in case $v$ is analytic or symmetric, we develop an inductive analysis on scales, whereby we show that locally the Rellich functions of Dirichlet restrictions of $H$ inherit the cosine-like structure of $v$ and are uniformly well-separated. We utilize this construction to prove almost-sure Anderson localization and Cantor spectrum in our case for sufficiently small interaction $\varepsilon \leq \varepsilon_0(v,\alpha)$.

Uniform Exponential Mixing Of Frame Flows For Congruence Covers Of Convex Cocompact Hyperbolic Manifolds, Pratyush Sarkar

Yale Graduate School of Arts and Sciences Dissertations

The main objective of this thesis is to prove uniform exponential mixing of the frame flow for congruence covers of a hyperbolic manifold $\Gamma \backslash \mathbb H^n$ with respect to the Bowen--Margulis--Sullivan measures, for some convex cocompact thin subgroup $\Gamma$ of an arithmetic lattice in $\SO(n, 1)$. In order to accomplish this, we first need to prove exponential mixing of the frame flow for a single convex cocompact hyperbolic manifold $\Gamma \backslash \mathbb H^n$ as well. The former result extends the work of Oh--Winter who established the $n = 2$ case. The theorems follow from (uniform) spectral bounds for the …