Digital Commons Network^™

Solution Of Wave Equation By Linear Regression Artificial Neural Network, Nahdh S. M. Al-Saif, Mahmood A. Shamran, Samah Mohammed Ali, Saad Naji Al-Azzawi

Baghdad Science Journal

Wave partial differential equations are one of the most important topics that model, for example, the wave motion of ground vibrations. Hence, finding approximate solutions to such equations with high accuracy and speed faster than difficult and complex analytical solutions has become possible through the use of artificial intelligence and machine learning methods. This research has three goals. The first is to transform the problem of the initial value of the wave equation into its legal form and find its accurate solution. The second is to write a linear-regression neural network algorithm. The third result is applying this algorithm to …

Analysis Of Multiple Working Vacations Queuing System With Encouraged Arrival Using M/M (A,B)/1 Model, P. Prakati, K. Julia Rose Mary

Baghdad Science Journal

Generally, it is very common in our daily life to meet up with queuing systems. This study examines the concept of encouraged arrival in M/M (a,b)/1/Multiple Working Vacations queuing model that follows the General Bulk Service Rule. The considered queuing model consists of three states namely idle, working vacation and regular busy period. The single server available in the system usually goes on vacation whenever the system is idle, that is, when it is empty. This model deals with multiple working vacations of the server which are exponentially distributed and the concept of encouraged arrival of the customers is examined …

On En-Prime Compactly Packed Acts Over Monoid, Samira Naji Kadhim, Uhood S. Al-Hussani, Muna Jasim Mohammed Ali

Baghdad Science Journal

This work studies the concept of En-prime compactly packed (𝐸𝑛−𝒫.𝒸.𝒫) modules. Some properties and characterizations have been studied. Put ₩ is an Я-module and every submodule is En-pure , then ₩ is 𝐸𝑛−𝒫.𝒸.𝒫 if and only if each proper submodule Ϣ of ₩ is cyclic, If ₩ is 𝐸𝑛−𝒫.𝒸.𝒫. ₩ which has at least one maximal submodule then ₩ satisfies the ACC on En-p-radical submodule. The generalization of this idea has been given for S-Acts. if for each family {Pα}α∈λ of En-prime subact of Д with Ѫ ⊆⋃Pαα∈λ, Ѫ⊆Pβ for some β∈λ. An S-Act Д is 𝐸𝑛−𝒫.𝒸.𝒫, if every subact …

A New Algorithm For Finding Initial Basic Feasible Solution Of Spherical Fuzzy Transportation Problem With Applications, K. Hemalatha, Venkateswarlu. B

Baghdad Science Journal

In operation research, a specific area being analyzed in great depth is the transportation problem (TP). The key objective of this problem is to find the lowest total transportation costs for commodities to meet consumer requirements at destinations incorporating resources acquired at their points of origin. In this work, the spherical fuzzy transportation problem (SFTP) determines the lowest cost of carrying items from origin to destination. Most of the time, accurate data has been used, but these variables are actually inaccurate and ambiguous. According to the literature, several generalizations and expansions of fuzzy sets have been proposed and investigated. One …

Stationary Distribution Of Stochastic Seirs Epidemic Model With Saturated Incidence Rate And Saturated Treatment Function, S. Saravanan, C. Monica

Baghdad Science Journal

This investigation aims to enhance and broaden the mathematical model that governs a dynamic stochastic SEIRS (Susceptible, Exposed, Infective, and Recovery) epidemic. This complex model integrates crucial components, including a saturated incidence rate and saturated treatment function, which are fundamental in molding epidemic dynamics. The objective is to explore the presence and uniqueness of a positive global solution through the application of a meticulously designed Lyapunov function, facilitating a more profound analysis of the intricacies of the systems. This analytical framework enables us to uncover the interactions among disease transmission, treatment dynamics, and stochastic influences. This theoretical framework assumes that …

Exploring Elementary Mathematics Teachers’ Use Of Learning Analytics For Educating Black And Hispanic Students In Low Socioeconomic Schools: A Multiple-Case Study, Eboni Nichols

Doctoral Dissertations and Projects

The purpose of this case study was to understand the role of learning analytics with teachers who develop the mathematics skills of Black and Hispanic elementary students in Title I schools. The theory that guided this study was Mezirow’s transformative learning theory, as it provides a framework for how new information can transform adults' thinking and actions. The central research question that guided the study was: How do elementary teachers in Title I schools use learning analytics to develop the mathematics skills of Black and Hispanic students? The study was conducted using a multiple-case study design. Purposive sampling and snowball …

Setting Up Students For Success: Analysis Of Effectiveness Of Mathematics Placement, Jeff Carvell, Jason Ho, David Klanderman, Sarah Klanderman

University Faculty Publications and Creative Works

How do we e!ectively and equitably place students into math classes in a way that provides them the best chance of success? As many higher education institutions veer away from placement based on standardized testing, many departments are seeking placement alternatives that will properly support students. Additionally, math placement determines not only a student’s mathematics courses but also influences their progress in related fields, including physics, chemistry, engineering, and more. This paper will describe three di!erent existing placement systems at each of our liberal arts institutions as well as the a!ordances and constraints of each approach. Further, we analyze data …

Independent Vs. Signed Musicians: Does Thier Status Affect Their Success?, Zachary Vincent

Honors Projects in Mathematics and Economics

As technology has advanced and become more widely available, and as the public learns more about the recording industry and its workings, more musicians are choosing not to sign with record labels, becoming independent musicians. This now raises the question: does a musician’s status of independent or signed determine their level of success? It has been previously found that independent musicians have a more difficult time competing with signed musicians due to the resources provided by record labels and the way labels negotiate with large streaming platforms, giving signed labels more opportunities to be seen in the public eye, but …

Exploration Into Homotopy Equivalence And Vietoris-Rips Complexes, Alexander J. Mobley

Honors Theses

An important question in discrete topology and geometry is how to recover the structure and characteristics of a manifold when only given a finite set of points sampled from that manifold. Thus, if mathematicians have a point cloud of data which induces a discrete metric space, they look for some structure to these points. Understanding the structure of these points often gives needed insight to solve this problem. One such way to determine structure to these points is to use these points to construct a Vietoris-Rips complex. In abstract, Latschev shows that this allows us to recover the homotopy type …

Integrating Music Content Into The Secondary Mathematics Classroom: Facilitating The Process Of Designing Interdisciplinary Lessons, Denae Bumpus

Honors Projects

Many people enjoy music, and music has a multitude of connections to mathematics, so it makes sense for a mathematics classroom to incorporate musical elements into the instruction, but the literature has shown that many math teachers do not have a strong enough musical background to feel confident in incorporating music into the math class. Therefore, this research sought to provide a resource to help secondary mathematics teachers integrate age-appropriate musical applications to their mathematics lessons which connects standards of mathematics into standards of music. Specifically, the paper connects the Ohio Standards of Mathematics for Geometry with the course objectives …

Preparing To Bridge The Deaf Math Gap: Exploring Preparation Materials For Asl Interpreters In Math Education, Taylor Victor

Undergraduate University Honors Capstones

The gap in performance between hearing students and their mainstreamed deaf and hard of hearing (D/HH) peers who use ASL interpreters expands throughout various grade levels and is not a new issue, especially in mathematics. This delay in mathematical development has been prevalent for many decades, and it is still being determined at what level it begins and what the causes are. D/HH students' academic success is often connected to high-quality academic sign language interpreting (Jones, 2017). However, there are still many college-level American Sign Language (ASL) interpreting programs that are not focused on educational interpreting. This lack of focus …

Transformations Of Bound Quivers, Ari Pincus-Kazmar

Mathematics, Statistics, and Computer Science Honors Projects

A quiver Q is a directed multigraph. Representations of Q are assignments of vector spaces and linear maps to the vertices and arrows of Q; these are categorically equivalent to the modules over the path algebra kQ. The indecomposable representations of a given quiver and the irreducible morphisms between them are summarized combinatorially in the Auslander-Reiten quiver which, in the case of algebras of finite representation type, gives almost complete information about the category of representations. We introduce an intuitive transformation from a family of bound quivers to a family of A-type quivers which preserves properties of the Auslander-Reiten quiver.

Bibliography Of Christianity And Mathematics Update, Calvin Jongsma

Faculty Work Comprehensive List

This was a banquet talk given at the Twenty-fourth Biennial Conference of the Association of Christians in the Mathematical Sciences held at Dordt University on May 28-June 1, 2024.

It provides an update on the progress being made in the author’s project of producing a second edition of Bibliography of Christianity and Mathematics. This work is now being developed as a Zotero database with a slightly broader focus on Religious Faith and the Mathematical Sciences and with a much expanded list of books, articles, and blog posts on the topic. The author hopes to make the database public sometime …

Insight And Illumination In Mathematical Learning: Exemplars Of Transitions To Understanding In The Classroom From Elementary To Graduate School, David Klanderman, Sarah Klanderman, James Turner

University Faculty Publications and Creative Works

Jacques Hadamard describes a four-stage epistemological process: preparation, incubation, illumination, and verification. Hadamard developed this scheme based upon Henri Poincaré’s reflections on the process that led to his discovery of Fuchsian functions (i.e., automorphic functions) which he described in his wonderful paper La Genese de la Creation Mathematique (Mathematical Discovery in English). Philosopher and theologian Bernard Lonergan builds on the writings of Aquinas to develop his theory of insight which elaborates the transition from incubation to illumination. Insight and illumination provide an analytical lens for transitional moments as students learn ever more abstract mathematical concepts. We offer exemplars of these …

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …

High School Students’ Sense Of Belonging In Math, Marie Louise Stevenson

Electronic Theses, Projects, and Dissertations

A student’s sense of belonging in math describes the extent to which a student feels that they are a member of their math community. It is important to study math sense of belonging because it is believed that when a student feels that they are a valued and respected part of their math community, they are more likely to exhibit higher participation and performance in their math class and take more math courses in high school and college. They also have an increased chance of pursuing a STEM career. In this study, we investigated the math sense of belonging of …

The Effects Of A Two-Way Dual Language Program On The Educational Trajectory Of Hispanic Emergent Bilingual Students During The Impact Of The Covid-19 Pandemic: A Mixed-Methods Study, Jesus Jacob Villa

Open Access Theses & Dissertations

This explanatory mixed-methods study examines the impact of Dual Language Bilingual Education (DLBE) and Transitional Bilingual Education (TBE) programs on the academic achievement of Hispanic emergent bilingual students during and after the COVID-19 pandemic. With the U.S. Hispanic student population growing significantly, and emergent bilingual students historically underserved, this study addresses critical gaps in educational equity. Conducted in two school districts along the U.S. and Mexico border in Texas and New Mexico, the research explores how DLBE and TBE programs mitigated the pandemic's adverse effects on learning. This study analyzed quantitative data from standardized mathematics and language proficiency assessments for …

Learning Intentions, Success Criteria, And Metacognition: The Influence Of A Professional Development For Grades Three To Five Teachers, Jason Hart

All Graduate Theses and Dissertations, Fall 2023 to Present

Formative assessment is a strategy that teachers use to improve student learning. This study explored how professional development focused on assessment for learning practices (AFL), with the main emphasis on learning intentions and success criteria, influences teacher use of those strategies and changes in teacher and student metacognition. The overarching research question was: How does professional development on AFL practices influence teachers' reported use of AFL practices and teacher and student metacognition? This study utilized a mixes-methods research design and provided professional development on AFL practices to 16 in-service elementary mathematics teachers and measured changes to their AFL practices and …

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …

The Effects Of Implementing A Mindfulness Program In Two Elementary School Math Classrooms, Sara Lilley

Theses and Dissertations

This action research study examined the effects of utilizing trauma-informed social-emotional learning (SEL) teaching practices in two elementary math classrooms located in a Title 1 public school in North Carolina. The classrooms consisted of one third-grade classroom with 18 students and one fifth-grade classroom with 22 students. These classrooms integrated 10 minutes of mindfulness practice which included direct instruction on calming strategies and breathing techniques. This study worked to help foster a learning environment that supported the academic and mental health needs of the student participants and looked at potential relationships between calming strategies and math assessment data. This study …

ممارسات معلمات رياض الأطفال في تعليم العلوم والرياضيات بمساعدة الحيوانات الأليفة: ممارسات معلمات رياض الأطفال في تعليم العلوم والرياضيات بمساعدة الحيوانات الأليفة, آمنه حمدي, شذى الفايز

Journal of King Abdulaziz University: Educational and Psychological Sciences

هدفت الدراسة إلى التعرف على ممارَسات معلمات رياض الأطفال في تعليم العلوم والرياضيات بمساعدة الحيوانات الأليفة، ومعرفة ما إذا كان هناك فروقًا في ممارستهن تبعًا لمتغيرات: (سنوات الخبرة، نوع الروضة)، ولتحقيق ذلك اعتمدت الدراسة على المنهج الوصفي المسحي، حيث أعدَّت الباحثة استبانة طُبِّقت على عيِّنة من معلمات رياض الأطفال بمنطقة جازان، بلغ عددهن (269) معلمةً، بواقع (226) معلمةً في الروضة الحكومية، (43) معلمةً في الروضة الأهلية، وتوصلت الدراسة إلى أن تعليم العلوم والرياضات بمساعدة الحيوانات الأليفة ككل يمارَس (دائمًا) من قِبَل معلمات رياض الأطفال، وبصفة خاصة جاء تعليم العلوم بمساعدة الحيوانات الأليفة يمارَس (دائمًا) من قِبَل المعلمات، فيما يمارَس (غالبًا) …

Stability Analysis Of Excessive Carbon Dioxide Gas Emission Model Through Following Reforestation Policy In Low-Density Forest Biomass, Furqan Nezar, Shireen Jawad, Matthias Winter, Anwar Zeb

Baghdad Science Journal

Carbon dioxide is the main greenhouse gas contributing to global warming risk. Forest biomass is crucial for the sequestration of atmospheric carbon dioxide; however, the rate of decline in worldwide forest biomass is concerning and can be attributed to anthropogenic activities. Reforestation is essential in this situation to decrease the amount of C O₂ in the atmosphere. Efforts at reforestation can be evaluated according to the financial investment required for their execution. This work presents a nonlinear mathematical model that examines the impact of reforestation and the implementation of reforestation initiatives on regulating atmospheric CO₂ levels. The critical …

Prime Theta-Curves From Torus Knots, Sam Nieman, Jack Calcut

Research Symposium

Classical knot theory is the placement problem for a circle in Euclidean 3-space or in the 3-sphere. That problem has been generalized in numerous ways. Knotted graph theory replaces the circle with a graph. Knotting of certain graphs has been well-studied. That includes the theta-graph consisting of two vertices connected by three edges---a copy of the letter theta. A theta-curve is an embedding of the theta-graph in 3-space or in the 3-sphere. Connected sum of knots yields the notion of a prime knot. Similarly, one may sum two theta-curves at a vertex and one may sum a theta-curve and a …

Mathematical Skills, Rhonda Douglas Brown

Essays in Developmental Psychology

Mathematical Skills are essential for understanding how the world works and for solving problems that are important to human survival and prosperity.  They are used in everyday living in societies across the world.  The most basic mathematical skills involve estimating the amount of small sets of items without using symbols, called number sense, and tracking a small number of individual objects through space and time, called parallel individuation.  These skills are thought to be present at birth or early in life and to increase in precision into adulthood.

Basketball Jump Shot Correction Using Computer Vision, Matthew Moran

Mathematics & Computer Science Student Scholarship

Matthew Moran ’25, Computer Science major

Faculty mentor: Dr. Martin Hellwig, Mathematics and Computer Science

Basketball has evolved significantly over the years, with players continuously striving to improve their shooting accuracy and efficiency. As the game becomes more data-driven, advancements in artificial intelligence and computer vision have provided new methods for analyzing and correcting shooting mechanics that allow players to improve their game. Using deep learning, this research aims to fill a gap in these advancements, which is looking at the position of the shooters fingers relative to the ball. Doing so can improve stability and overall shooting performance.

The Significance Of Symmetry: Exploring T-Numbers And Their Role In Virus Survival And Behavior, Jenna Franco, Taylor Ligozio

Mathematics & Computer Science Student Scholarship

Jenna Franco ’25, Biology major

Taylor Ligozio ’25, Biology major

Faculty mentor: Dr. Su Jeong Kang, Mathematics and Computer Science

We studied the symmetry of different structures in common viruses and their T-numbers. We related these T-numbers with characteristics of the virus. Next we researched how the T-number of each virus was optimal for its survival and reproduction in its environment. We can use this information to infer or predict the behavior of viruses in the future based on their T-numbers.

Finite Dimensional Convex Fuzzy Normed Space And Its Basic Properties, Hawraa Yousif Daher, Jehad R. Kider

Baghdad Science Journal

Here the notion of convex fuzzy absolute value space is represented with an example which shows that the existence of such space. The reason behind introducing the definition of convex fuzzy absolute value and does not using the ordinary absolute value is the main definition in this paper will be not correct with ordinary absolute value. After that the main definition of convex fuzzy normed space is recalled with example which shows that the existence of such space. Then other definitions and theorems is recalled that will be used later in the section of main results such as the convex …

Gerrymandering And How To Find It: A Mathematical Approach, Nicholas Small

Mathematics & Computer Science Student Scholarship

Nicholas Small ’25, Mathematics and Computer Science major

Faculty mentor: Dr. Liam Donohoe, Mathematics and Computer Science

Gerrymandering is a phenomenon that has plagued American politics for over 200 years. This process, which involves redrawing congressional and legislative district boundaries to favor one group over another, has become a fact of life in the past few decades. This project explores the history of gerrymandering and some of the algorithms proposed to combat it. The two main strategies of Gerrymandering are packing—or limiting the other group’s influence by making them the extreme majority in a few districts—and cracking—or splitting up a …

Minimizing The Total Waiting Time For Fuzzy Two-Machine Flow Shop Scheduling Problem With Uncertain Processing Time, K. Ranjith, K. Karthikeyan

Baghdad Science Journal

Scheduling involves assigning resources to jobs within specified constraints over time. Traditionally, the processing time for each job was considered a constant value. However, in practical scenarios, job processing times can dynamically fluctuate based on prevailing circumstances. In this article, a novel approach is presented for the two-machine fuzzy Flow-Shop Scheduling Problem (FSSP) in a fuzzy environment, where job processing times are represented by trapezoidal fuzzy numbers. Additionally, a novel algorithm based on Goyal's approach for the two-machine FSSP with fuzzy processing times has been proposed and developed. Simultaneously, an existing algorithm has been enhanced to improve its performance in …

A Novel Approach To CExp Average Assignments On Chain Graphs, A. Rajesh Kannan

Baghdad Science Journal

In general, the exponential average of two positive numbers does not have to be an integer. Because of this, the exponential average needs to be an integer that takes into consideration the flooring or ceiling function. It has been defined that graphs can be labeled with an exponential average, where the flooring function or the ceiling function can apply labels to the edges. To establish the exponential average assignment on graphs, consider the edge labels that arise from the ceiling function alone. The vertex assignment function 𝛿 and edge assignment function 𝛿∗ are called a Cexp average assignment of the …