Digital Commons Network^™

On Sharpest Tail Bounds For Functions Of Tail Bounded Random Variables, Stephen Harrison

Mathematics & Statistics ETDs

Consider n real/complex, independent/dependent random variables with respective tail bounds and g a measurable function of the r.v.’s. Consider f the “sharpest” tail bound of g (sharpest in the sense, if f were any less, then for some X1, ..., Xn satisfying the conditions, g(X1, ..., Xn) would not satisfy the tail f). Significant research has been done to approximate f often with high accuracy. These results are often of the form, for g in this family, and tail bounds of Xk in this family, f is bounded by some f′ with high accuracy. However, the question “what would it …

Affordability And Usability Of Digital Learning Resources In Higher Education: A Case Of Online Mathematics Tutorials For Engineering Students At The University Of Dar Es Salaam, Fatuma S. Ikuja, Idrissa S. Amour, Abdi T. Abdalla

Tanzania Journal of Engineering and Technology (TJET)

Effective learning requires engagements with both learning contents and instructor’s personalized support. Large class sizes often limit opportunities for personalized instruction and timely feedback. Digital resources offer a viable solution to enhanced engagement and independent learning. This study investigated the affordability and usability of online digital learning resources for mathematics tutorials, specifically targeting engineering students at the University of Dar es Salaam. A quasi-experimental research design was adopted, focusing on digitization of undergraduate course: Matrices and Basic Calculus for Non-Majors (MT161). The course was delivered through the Moodle Learning Management System integrating STACK to support Mathematics questions. Data was collected …

Exploring Secondary Educators’ Experiences Of Implementing Linguistic-Based Mathematics Instruction For English Language Learners: A Phenomenological Study, Adrian Pearce Martin

Doctoral Dissertations and Projects

The purpose of this phenomenological study was to describe the experiences of veteran educators with implementing linguistic-based instructional practices for English language learners (ELLs) in the secondary mathematics classroom. The theory guiding this study was Vygotsky’s sociocultural theory as it pertains to language and learning development through social exchanges with people, things, and events in a collective environment. This qualitative study took a hermeneutic, phenomenological approach which allowed the lived experiences of educators to be described, along with an interpretation of their instructional experiences with ELLs in the mathematics classroom to be made. The setting for this research was two …

Assessing The Effects Of Leaderboards On Motivation And Math Achievement Of 5th And 6th Grade Students, Michele Alfieri

Boise State University Theses and Dissertations

Traditional teacher-led instructional methods are increasingly disconnected with the learning preferences of students raised in digital environments. These learners often require information to be delivered more rapidly and engagingly, prompting educators to incorporate strategies such as gamification to maintain student motivation and interest. Gamification, which involves integrating game design elements into non-game settings, has been shown to enhance engagement. A common feature of gamification is the use of leaderboards, which are visual displays that show individual and peer performance rankings. While leaderboards can foster motivation through competition, their effect on student morale and achievement outcomes is mixed. The purpose of …

Predictors Of Math Identity In U.S. High School Students, Edwin Flores

Electronic Theses, Projects, and Dissertations

This study explored factors related to high school students’ sense of math identity. Data from the High School Longitudinal Study of 2009 was used which is a nationally representative dataset from the National Center of Education Statistics (NCES). The sample is representative of U.S. high schoolers who began ninth grade in 2009. Multiple regression analysis was performed and factors relating to students’ prior mathematics coursework and attitudes about mathematics were found to predict students’ mathematics identity.

Keywords. Mathematics, identity, high school students

Modified Artificial Neural Networks In Stochastic Differential Equations To Estimate The Occurrence Rate Of A New Process For Software Reliability Growth Modelling, Adel Sufyan Hussain, Zedan Zubair Mashikhin, Noora Taha Abduirazzaq

Baghdad Science Journal

This paper aims to utilize modified artificial neural networks under stochastic differential equations to improve the estimation of occurrence rates on models towards the growth of software reliability through such models. There has never been a time when reliable assessment methods have been more important as software systems grow ever more sophisticated. This study covers the risks arising from software bugs, security weaknesses, and the need to meet legal requirements. The authors use a new method that combines artificial intelligence techniques with classical reliability models to achieve their goal of a more efficient computational tool for predicting software reliability. It …

On Iterative Method For The Solution Of Non-Linear Equations Using Anti-Lobatto Four Point Quadrature Rule, Tusar Singh, Dwiti Krushna Behera

Baghdad Science Journal

By harnessing the classic anti-Lobatto four-point quadrature rule of degree of precision three, the order of convergence of the Newton-Raphson method has been profoundly enhanced. This newly developed iterative scheme reveals a remarkable order of convergence, reaching three and far surpassing the original Newton-Raphson method. It operates as a two-step iterative method that elevates Newton’s approach by integrating the quadrature rule. A theorem related to this innovative iterative method has been formulated, confirming that its order of convergence is indeed three. In the numerical computation section, insightful scenarios demonstrate the remarkable numerical efficiency of the new method. Through the power …

Impact Of Fear Cost And Time Lag On The Dynamics Of An Ecological System Of Two Competing Predators And One Prey, Arkan Nawzad Mustafa

Baghdad Science Journal

The aim of this paper is to discover the impact of the fear of predators in prey and time lag corresponding to the gestation period on the dynamics of a food web model including two competing predator species and one prey species. Existence, non-negativity and boundedness of the model solutions are examined. An attractive region for the model is found. The permanence of the model, under certain conditions is proved. The criteria for the existence of all biologically feasible equilibrium points of the proposed model are determined. Locally asymptotically stability as well as globally stability of the model equilibrium points …

New Local Function In Grill Topological Spaces, Alyasaa Jassim Bidaiwi, R. B. Esmaeel

Baghdad Science Journal

This Paper introduces a new local function φ_Sζ*in a Grill topological space (X˙, ζ,τ) by using a semi open set, which is a superset of the local function φ_ζ. Additionally, two equivalent operators, Ψs and Γ_Sthat define topology τ_Sζ, were devised based on φ_Sζ*, along with the presentation of various characteristics and properties of φ_Sζ* and the two equivalent operators, Ψ_s and Γ_S. Additionally, newly created sets with weakly open properties (φ_{Sζ …}

The Dynamic Of A Three Species Food Chain Model Under The Influence Of Fear And Wind, Kaherah Ibrahim Hadib, Hiba Abdullah Ibrahim

Baghdad Science Journal

This work suggests a system of ordinary differential equations (ODEs) containing a three-species food chain model incorporating wind and fear effects. The properties of the solution, like positivity and bound-ness, were investigated. All equilibrium points (biologically feasible) have been obtained, and the local stability of these equilibriums has been carried out. The global stability outcomes on the equilibrium points under specific restrictions have been established. Also, the persistence restrictions have been investigated. By utilizing Sotomayor’s theorem, the local bifurcation of the suggested model has been inspected. Furthermore, numerical analysis was carried out to ensure the theoretical results obtained by utilizing …

Principal Quandles, Jesse Parrish

Electronic Theses and Dissertations

This thesis concerns principal quandles and, as a special case, Alexander quandles. A principal quandle is a coset quandle, Q(G,H, f), in which the subgroup H is trivial. If in addition the group G is abelian, then the coset quandle is called an Alexander quandle. The isomorphism types of Alexander quandles were classified [16], and some progress was made on describing the isomorphism types of principal quandles in [14] and [13]. The first part of this thesis applies the ideas used in Holmes’ paper to give a classification of the isomorphism types of principal quandles. The second …

Promoting Tutees’ Self-Efficacy, Tutor-Tutee Relationship, And Mathematical Knowledge/Performance, Kimberly D. Theophile

Electronic Theses and Dissertations 2020 - Present

This action research study investigates how I, as a tutor, implemented affective instructional practices to support early adolescent tutees’ self-efficacy, tutor-tutee relationship, and mathematical knowledge/performance. Data were collected from multiple sources, including journal entries, video recordings, semi-structured interviews, report card evaluations, and Florida Assessment of Student Thinking (FAST) scores. These sources were used to gain comprehensive insight into how my affective instructional strategies were embedded within mathematics tutoring sessions with five early adolescent tutees between the ages of 10 and 12. A constant comparative analysis was employed to examine the data, with careful attention given to the four dimensions of …

Infographic: Pisa Insights – Encouraging Mathematical Thinking, Dominique Russell

Teacher infographics

Each cycle of the global Programme for International Student Assessment (PISA) includes a teacher questionnaire. One questionnaire topic – encouraging mathematical thinking – can help foster critical thinking, enhance problem-solving skills and allow students to see the relevance and connectedness of mathematics in their lives.

Mathematics And Growth Mindset: A Systematic Review And Meta-Analysis Of Interventions At The Post-Secondary Level, Sean E. Murphy

USF Tampa Graduate Theses and Dissertations

Growth mindset interventions have been implemented in academic settings for over three decades (C. S. Dweck et al., 1995a). One academic field where growth mindset may be most needed is mathematics, as it is not unusual for a student to claim, “I’m not a math person.” Notably, no meta-analysis of mindset interventions in post-secondary mathematics classrooms existed prior to the current study. To close this gap in the literature, the present study included a systematic review and meta-analysis, drawing on two search methods: Boolean and snowballing. The results from both methods were screened using inclusion/exclusion criteria. Snowballing search was hypothesized …

Italian Mathematics Prison Teachers’ Perspective On The Teaching/Learning Of Mathematics In Prison School, Andrea Maffia, Luca Decembrotto, Chiara Giberti, Federica Mennuni, Gabriella Pocalana, Silvia Regola, Agnese Telloni

Journal of Prison Education Research

Teaching in the prison context is characterized by a high complexity level; it is a multifaced activity influenced by several factors depending on the specific context. We present a preliminary but overall picture of schooling in Italian prisons by considering teachers’ reflections regarding their experiences in teaching mathematics in correctional facilities. To address the gap in the current literature on this issue, we conducted a SWOT analysis on the reflection provided by a group of nine Italian mathematics teachers who teach in different prisons and with different experiences and backgrounds. Their reflection allowed us to identify and describe six theory-driven …

On Perturbation Of Fuzzy Soft Κ Quasi Hyponormal Operator Generator Via A Special Class Of Operators, Salim Dawood Mohsen

Baghdad Science Journal

Hilbert space has been improved by building on a fuzzy soft vector space. It is named the fuzzy soft Hilbert space. This space has been crucial to the development of functional analysis. Interest emerged in investigating fuzzy soft operators, results and other intriguing properties of quasi-hyponormal operators are obtained, as a result, circumstances surrounding the achievement of certain analytical traits are also looked at and their more general called perturbation fuzzy soft operators, many pertinent findings in the context of fuzzy soft operator theory, which we will use in our talks of certain analytical aspects pertaining to characterizations feature. This …

Complexity Measures For Self-Similar And Chemical Graphs Using Entropies And Generalized Fractal Dimensions, J. Bhuvaneswari, D. Easwaramoorthy

Baghdad Science Journal

Nonlinear analysis finds numerous applications in understanding the intricate characteristics of generalized Sierpinski graphs or chemical graphs. It aids in discerning the fractal patterns inherent in self-similar structures, deciphering the dynamic interactions within chemical bonds, and assessing the complexity of molecular arrangements. Furthermore, it plays a crucial role in unraveling the emergent behaviors of complex systems, offering insights applicable to diverse fields such as materials science, chemistry, biology, network theory, and beyond. In this paper, the complexity of generalized Sierpinski graphs and chemical graphs is analyzed using fractal-based nonlinear measures computed iteratively. Nonlinear measures assess intricate relationships within graphs by …

Dense And Nowhere Dense Sets On Dual Soft Topological Space, Janat Y. Rasheed, L. A. Al. Swidi

Baghdad Science Journal

The concepts of dual soft sets are introduced as general mathematical tools for transactions with a lack of confidence or certainty. This work defined the dual soft topology on a dual soft set and presented its related properties. The main goal of this research is to clarify the concepts of dense and nowhere dense sets on dual soft topological spaces as density plays a very important role in general topology for solving many mathematical and engineering problems. Our research paper presented the notions of dense, nowhere dense and somewhere dense within the dual soft set theory which in specific ways. …

Numerical Solutions Of Poisson Problem By Using Finite Element Method Based On Linear, Quadratic, And Cubic Polynomials, Ali Kamil Al-Abadi, Shurooq Kamel Abd

Baghdad Science Journal

The finite element approach, which uses linear, quadratic, and cubic polynomials, can solve the elliptic form of the Poisson equation. This allows the method to provide a solution to the Poisson problem. This possibility arises from the structure within which the method operates. This work aims to provide an analysis of the technique in question and demonstrate its potential for applications in both square and circular dimensions. In conducting this investigation, a direct solution of the system of linear equations was used. Obtaining optimal error estimates in the L² and H¹ norms is possible for us if we …

Coefficient Estimates Of A New Subclass Of R-Fold Symmetric Bi-Univalent Functions Involving Ruscheweyh Derivative, Nihad H. Shehab, Abdul Rahman S. Juma, Maslina Darus

Baghdad Science Journal

In this work, the authors introduce and study a new subclass ofM^h,u_Σr(γ,η,κ,λ), which is r-fold bi-univalent functions in open-unit disk 𝔄. Using the Rushwaya derivative operator, the study investigates the properties and behavior of an analytically generalized r-fold symmetric two-monovalent function in the open-unit disk 𝔄. The analysis calculates the Taylor-Maclarin coefficients |a_r+1| and |a_2r+1|, which represent one of its key terms these estimates M^h,u_Σr(γ …

On The Statistical Variation Of Γ-Covers Controlled By The Class Of Weight Functions, Parthiba Das, Jalal Hatem Hussein Al-Bayati, Prasenjit Bal

Baghdad Science Journal

In this study, the notion of the star operator and the class of weight functions defined on the entire natural number set ℕ have been used to develop a version of the statistical cover of a topological space. In this version of statistical γ-cover, the pace of statistical convergence is mostly controlled by the selected weight function. A map g defined as g:ℕ→[0,∞)such that lim_n→∞g(n)=∞ and lim_n→∞⁄ng(n)≠0is called a weight function. Relationships between several γ …

A Comparison Of Mathematics Intervention Methods: Overcoming Learning Loss Caused By Covid-19, Adam Goosby

College of Education

The COVID-19 pandemic created unprecedented disruptions to the educational system and exposed weakness within the structures that resulted in measurable regression in student achievement across all academic domains, but most notably mathematics. The purpose of this study is to investigate the impact of two distinct methods of mathematics interventions provided to middle-grade students with the intent to begin to overcome the learning loss. Through the lens of the Expectancy-Value theory, the study emphasizes the importance of mathematics achievement and its role in building student capacity and establishing a growth mindset. The study employed a series of repeated-measures ANOVAs and a …

Threading Hmong Culture Into Math: Supporting Hmong Elementary Students Through Integrative Practices, Lisa Vang

School of Education and Leadership Student Capstone Projects

The research question answered in this capstone paper is: “How can educators integrate Hmong culture into their math instruction in ways that support both academic growth and cultural identity?” This paper focuses on the need for culturally responsive teaching in mathematics for elementary Hmong students and the convergence of cultural identity, student engagement, and meaningful learning experiences. This capstone paper includes a literature review that explores culturally responsive pedagogies and practices in classrooms, the importance of cultivating mathematical identity in Hmong students, and the integration of Hmong culture into elementary math instruction. The results of this capstone paper lead to …

The Role Of Gamified Learning In Developing Math Confidence And Procedural Fluency, Celeste Nosow

School of Education and Leadership Student Capstone Projects

This capstone project sought to answer: In what ways might a gamified math fluency resource focused on increasing math confidence facilitate learning for preadolescent students struggling in math? Research into game-based learning, motivation, and mindset revealed that students can benefit from engaging, collaborative, and low-stakes learning experiences that build fluency through games. Additionally, the environment should foster math confidence and competence in preadolescent learners. The project culminated in the development of a website offering free, low-preparation math games appropriate for grades 3–5. Designed for teachers and substitute educators, the learning materials provided emphasize social interaction, inclusivity, and equitable access. This …

Making Math Accessible: Addressing Language Challenges In 3rd Grade English Medium Math Classrooms, Salha Mohamad

Theses

The research article, Making Math Accessible: Addressing Language Difficulties in 3^rd Grade English Medium Math Classrooms, addresses the issue of how the teachers in UAE elementary schools assist a student who is to study mathematics in English rather than Arabic. In the School X, Grades 1 and 2 applied mathematics and science using the Ministry of Education (MOE) Arabic-medium curriculum. Since Grade 3, however, the school has used the American curriculum, so students are expected to study these subjects in English. This change brings major barriers in understanding basic mathematical terms, word problems, and instructions. The research applies …

Iterative Approximation Of Best Proximity Points Of M-T Cyclic Contraction Mappings, Raghad I. Sabri, Buthainah A. A. Ahmed

Baghdad Science Journal

In many instances, acquiring a solution for an operator equation by using conventional analytical techniques, even after it has been shown that such a solution exists. One has to know the approximate value of this solution to solve situations like these. In order to do this, the operator equation must first be restructured to take the form of a fixed-point equation (FP). On the FP equation, the most convenient iterative method is used, and the limit of the sequence that is created by this algorithm is, in fact, the value of the FP that is sought for the FP equation, …

Exponential Domination Of Some Chemical Structures In Reduced (A, B)-Ka Indices, Anjaneyulu Mekala, U Vijaya Chandra Kumar, R. Murali

Baghdad Science Journal

Mathematical modeling with the help of numerical coding of graphs has been used in different fields of science, especially in chemistry for the studies of molecular structures. A special type of graph invariant called the topological index is the collection of data on algebraic graphs and provides a mathematical way to understand chemical structural features. In chemical graph theory, the topological index is a type of molecular descriptor calculated based on the graph of chemical compounds. Topological indices help us collect information about algebraic graphs and give us a mathematical approach to understand the properties of algebraic structures. With the …

A New Strategy For Solving The Initial Basic Feasible Solution Of The Transportation Problem Using Exponential Distribution And A New Penalty Model, M. Amreen, Venkateswarlu B

Baghdad Science Journal

One of the key concepts in operations research (OR) is the transportation problem (TP). The transportation problem involves distributing products from several sources to different destinations while minimizing shipping expenses. To achieve minimum transportation costs, the transportation problem is examined in two phases. An initial basic feasible solution (IBFS) is the first phase for achieving the lowest price, with the help of IBFS, one can calculate the optimal solution derived as the second phase. The literature review indicates that the authors developed a novel algorithm for the IBFS, incorporating several mathematical tools and some new models yet possessing certain limitations. …

Laplacian Energy And Eccentricity Based Energy For Cross Monic Zero Divisor Graph Associated With Commutative Rings, Sarathy Raja, Ravi Sankar Jeyaraj

Baghdad Science Journal

For a commutative ring, a cross monic zero divisor graph is discussed, whose vertices are nonzero zero divisors of the commutative ring, then the two vertices x and y are adjacent if and only if xy = 0. Sum of absolute auxiliary eigenvalues of Laplacian matrix of a simple graph is known as Laplacian energy of a simple graph. Eccentricity sum matrix of a graph is a positive matrix, whose entries are sum of the eccentricities of two vertices and 0 for diagonals of the eccentricity sum matrix. Then the sum of absolute eigenvalues of eccentricity sum matrix is known …

A Numerical Approach To Time-Space Fractional Stochastic Diffusion Equation, Archana Mourya, Kalyanrao Takale, Shrikisan Gaikwad

Baghdad Science Journal

The primary objective of this paper is to propose a Crank-Nicolson scheme tailored to analyze a time-space fractional stochastic diffusion equation subject to additive noise. Using the Caputo definition for time fractional derivatives and the shifted Grunwald-Letnikov definition for space fractional derivatives, a fractional order Crank-Nicolson finite difference scheme is devised to obtain a numerical solution. Considerable attention has been paid to examining the stability and convergence properties of this fractional order Crank-Nicolson method. To validate the effectiveness of the developed method, a comprehensive investigation using a test problem is conducted to assess its accuracy. The study harnesses the power …