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Finite Mathematics: A Course Guide, Angela West Dixon, Hillary Dosser Oct 2026

Finite Mathematics: A Course Guide, Angela West Dixon, Hillary Dosser

Faculty Publications

Finite Mathematics: A Course Guide is a supplement to Mathematics for Business and Social Sciences by Kathryn Bollinger and Vanessa Coffelt. The authors of this Course Guide, Angela Dixon and Hilary Dosser, are instructors of Mathematics at Stephen F. Austin State University in Nacogdoches, Texas. This Course Guide was developed in response to adapting MATH 1324, Finite Mathematics to a zero-cost course, using an Open Educational Resource (OER) implemented in the Fall semester of 2026. According to the Texas Higher Education Coordinating Board’s Academic Course Guide Manual (ACGM), MATH 1324 Mathematics for Business and Social Sciences concerns the application of …

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A Numerical Solution Of Parabolic Integro-Differential Equations Using The Left Rectangular Rule, Ali Kamil Al-Abadi, Shurooq Kamel Abd Sep 2026

A Numerical Solution Of Parabolic Integro-Differential Equations Using The Left Rectangular Rule, Ali Kamil Al-Abadi, Shurooq Kamel Abd

Baghdad Science Journal

This study presents a numerical technique for addressing parabolic integro-differential equations encountered in various scientific and engineering domains. The backward Euler method for temporal discretization with the left rectangular rule for estimating the memory integral term, is integrated into this proposed method. The semi-discrete and fully discrete formulations of the problem are used to obtain a finite element framework. To evaluate the accuracy of the numerical approximation, the mathematical formulation is established, and error estimates are analyzed. Numerous numerical experiments are conducted and juxtaposed with established exact solutions to assess the efficacy of the proposed method. The results show that …

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Novel Solitary Wave Solutions And Stability Analysis Of The Generalized (3+1)-Dimensional Chaffee–Infante Equation, Mostafa M. A. Khater Sep 2026

Novel Solitary Wave Solutions And Stability Analysis Of The Generalized (3+1)-Dimensional Chaffee–Infante Equation, Mostafa M. A. Khater

Baghdad Science Journal

The generalized (3+1)-dimensional Chaffee–Infante equation, a nonlinear evolution equation with dispersive, dissipative and nonlinear effects, is considered a member of the class of reaction–diffusion models. Applying the Khater III method, we obtain seventeen exact analytical solutions of hyperbolic, trigonometric and rational function forms. The accuracy of these solutions is verified by comparison with the numerical simulations obtained by He's variational iteration method. The satisfactory consistency at absolute error levels less than 10^ - 9 supports the reliability of the analytical results. The analysis shows different dynamical patterns: solitary waves, periodic structures and singular wave profiles and studies their stability properties …

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Surface Wave Propagation At The Interface Between An Inviscid Liquid Layer And A Rotating Micropolar Elastic Solid With Stretch, Somaiah Kamidi, Narsimharao Kandula, Venkateswara Rao Burugu, Gaddam Rajkumar, Srinivas Remidi Sep 2026

Surface Wave Propagation At The Interface Between An Inviscid Liquid Layer And A Rotating Micropolar Elastic Solid With Stretch, Somaiah Kamidi, Narsimharao Kandula, Venkateswara Rao Burugu, Gaddam Rajkumar, Srinivas Remidi

Baghdad Science Journal

This article investigates the impact of angular rotation on surface-wave propagation at the interface between an inviscid liquid layer and a rotating micropolar elastic solid with stretch. The surface-wave secular equation is obtained analytically using the plane-harmonic solution method after the mathematical model has been developed. It is noticed that for symmetric modes of surface waves, the liquid effects and the micro-stretch do not manifest simultaneously. Using MATLAB software, the impacts of the solid's angular rotation and the liquid layer's thickness on the symmetric mode of surface waves are illustrated for a specific model. The velocity of surface waves at …

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Approximation Of Bi-Continuous Semigroups In The Trotter-Kato Framework: Application To Diffusion Equations With Non-Local Boundary Conditions, Abdulhameed Qahtan Abbood Altai Sep 2026

Approximation Of Bi-Continuous Semigroups In The Trotter-Kato Framework: Application To Diffusion Equations With Non-Local Boundary Conditions, Abdulhameed Qahtan Abbood Altai

Baghdad Science Journal

This study develops and practically reformulates the Trotter–Kato theorem for the approximation of bi-continuous semigroups defined on Banach spaces with weaker locally convex Hausdorff topologies. This method extends the Trotter–Kato framework to semigroups with weak continuity by moving the analysis from the classical norm topology to a weaker topology. Equivalence and approximation conditions are derived without requiring explicit computation of resolvents, replacing them with T-stability and T-consistency properties. This new reformulation of the Trotter–Kato theorem provides a direct method for establishing convergence between approximating and limit semigroups, thereby simplifying both theoretical proofs and numerical analysis. The suggested framework …

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Structural And Hamiltonian Properties Of The N–Array Unit Graphs Over Finite Rings, Puguh Wahyu Prasetyo, Muhammad Ardiyansyah, Joe Repka Sep 2026

Structural And Hamiltonian Properties Of The N–Array Unit Graphs Over Finite Rings, Puguh Wahyu Prasetyo, Muhammad Ardiyansyah, Joe Repka

Baghdad Science Journal

Consider a finite ring R, and let U( R ) denote the set of all its unit elements. The unit graph G_R of R is defined as follows: the vertex set V( G_R ) consists of all elements of R. Two distinct elements a,\ b∈ \ G_R are adjacent if and only if a + b∈ U( R ). Recent research has provided necessary and sufficient conditions for the unit graph G_R to have a Hamiltonian cycle. However, the property of Hamiltonicity under direct product constructions of rings has not been fully understood. This paper addresses this gap by studying …

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Understanding Primary Level Learner Progression In Scotland: Insights From Scottish Online Formative Assessments (Sofa) Data From The Highland Local Authority, Alexander Towne, Sladana Krstic Aug 2026

Understanding Primary Level Learner Progression In Scotland: Insights From Scottish Online Formative Assessments (Sofa) Data From The Highland Local Authority, Alexander Towne, Sladana Krstic

Assessment and Reporting

This report presents findings from more than 30,000 Scottish Online Formative Assessment (SOFA) assessments completed across one Scottish local authority during the 2024-2025 academic year. It demonstrates how SOFA can be used to monitor learning progression across numeracy, reading and writing, identify attainment gaps between learner groups, and provide detailed diagnostic evidence to support classroom practice, school improvement and local authority panning. Although based on a single local authority, the study illustrates how curriculum-aligned formative assessment can complement national assessment evidence by providing richer insight into learner development.

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Ngram Data Social Media, William Zywiak Aug 2026

Ngram Data Social Media, William Zywiak

Data and Datasets

Data set for a NSF STEM grant.

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Lag Correlation Variance, William Zywiak Aug 2026

Lag Correlation Variance, William Zywiak

Data and Datasets

Data set for a NSF STEM grant.

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Locating-Chromatic Number Of Bipartite Graphs, Dian Kastika Syofyan, Edy Tri Baskoro, Hilda Assiyatun, Ira Apni Purwasih, Zata Yumni Awanis, Arga Febriantoni Aug 2026

Locating-Chromatic Number Of Bipartite Graphs, Dian Kastika Syofyan, Edy Tri Baskoro, Hilda Assiyatun, Ira Apni Purwasih, Zata Yumni Awanis, Arga Febriantoni

Baghdad Science Journal

The locating-chromatic number of a graph combines proper vertex coloring with vertex identification through distances to color classes. Although this parameter has been studied for many graph families, general results for bipartite graphs remain limited. Bipartite graphs contain structural symmetries, especially within each partite set, making it difficult to obtain distinct color codes. This paper establishes lower and upper bounds for the locating-chromatic number of bipartite graphs using neighborhood equivalence classes in the two partite sets. The bounds describe the effect of identical neighborhoods on the number of distinguishable color codes. They are shown to be tight, and regular complete …

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Dynamical Properties Of Proximal Group Spaces, Najlaa Adnan Hadi Aug 2026

Dynamical Properties Of Proximal Group Spaces, Najlaa Adnan Hadi

Baghdad Science Journal

In this paper, we introduce a new class of dynamical systems, Proximal Dispersive Group Spaces (PDG - spaces), to study the structure of topological group actions. In these spaces, we observe a mixture of two different behaviors: points come close to each other (proximal convergence) under some group elements, while remaining separated (dispersive separation) under others. This framework generalizes the classical theory to allow for selective convergence without global asymptotic collapse. We give a formal definition of PDG - spaces and study some of their basic properties, like invariance under group actions and incompatibility with equicontinuous systems. Our results show …

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Analytical Study On Unsteady Flow Of A Hyperbolic Tangent Fluid In Existence Of Porous Media Of An Exponentially Stretched Sheet With Heat Transfer, Nidhal M. Abd Alameer, Sundos Bader, Fatima K. Abdullah Aug 2026

Analytical Study On Unsteady Flow Of A Hyperbolic Tangent Fluid In Existence Of Porous Media Of An Exponentially Stretched Sheet With Heat Transfer, Nidhal M. Abd Alameer, Sundos Bader, Fatima K. Abdullah

Baghdad Science Journal

The unsteady flow of a tangential hyperbolic fluid with temperature in the presence of a sublimation medium and an exponential surface was discussed in this article. The law of conservation of mass, energy, and momentum is essential to the model of matter. To make it easier to identify solutions, the partial equations were converted into ordinary equations. We refer to this approach as the homotopic method. To explain the results, the Mathematica program was used to find the solutions and graphically depict them. The impact of the parameters on velocity, temperature was discussed, which are Random motion factor (Nb …

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Performance Analysis Of Bulk Queueing Systems With Inspection, Two Rework Cycles And Multiple Vacations, R. Lokesh, S. Karpagam, Gopal Kumar Gupta Aug 2026

Performance Analysis Of Bulk Queueing Systems With Inspection, Two Rework Cycles And Multiple Vacations, R. Lokesh, S. Karpagam, Gopal Kumar Gupta

Baghdad Science Journal

In a production system, rework plays a key role in reducing waste and efficiently managing manufacturing costs. The proposed model addresses a system with batch arrivals, a single server, and a two-stage bulk service with inspection, two rework cycles, and multiple vacations. First, batches are processed in stage 1, some of which may require rework during the same cycle, albeit with a certain probability, while others proceed to stage 2. After stage 2, batches are inspected, and if evidence of nonconformities is found, they are reworked with a certain probability. After inspection or rework, batches are processed according to the …

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The Ranking Function With Trapezoidal Membership And Fuzzy Parameters Of The Inverse Exponential Rayleigh Distribution, Rehab Noori Shalan, Ali T. Mohammed, Maysaa J. Mohammed, Iden H. Al-Kinani Aug 2026

The Ranking Function With Trapezoidal Membership And Fuzzy Parameters Of The Inverse Exponential Rayleigh Distribution, Rehab Noori Shalan, Ali T. Mohammed, Maysaa J. Mohammed, Iden H. Al-Kinani

Baghdad Science Journal

This study aims to investigate the estimation of the parameters of the inverse exponential Rayleigh distribution using the Maximum Likelihood Estimation (MLE) and Ranked Set Sampling (RSS) methods, on account of their importance in modeling across lifespan and reliability data. The model is used on empirical data representing the fracture stress of carbon fibers for both single and saturated fibers, in order to determine the accuracy of the estimation methods in given applications. In addition, the classical model is expanded to a fuzzy model to focus on inherent uncertainty in real-world applications. This is realized by designing fuzzy numbers using …

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Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan Aug 2026

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

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From Reluctance To Resilience: The Link Between Attitude And Growth Mindset In Calculus Students, Olivia Valente, Kathryn E. Pedings-Behling, Amy N. Langville Aug 2026

From Reluctance To Resilience: The Link Between Attitude And Growth Mindset In Calculus Students, Olivia Valente, Kathryn E. Pedings-Behling, Amy N. Langville

Journal of Educational Research and Practice

Many postsecondary students enter general education mathematics courses with negative attitudes, shaping their willingness to engage with the content. This study explores the relationship between students’ attitudes towards mathematics and their growth mindset, revealing effective strategies to enhance learning experiences, particularly for students who are reluctant learners. The research investigates two questions: (1) How do students’ Attitude Toward Mathematics Inventory (ATMI) scores and Growth Mindset Scale (GMS) scores relate? and (2) Do gender or course modality affect this relationship? This study addresses a gap in literature by examining how enjoyment, motivation, self-confidence, and perceived value connect with growth mindset. The …

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Supporting Students’ Self-Efficacy And Motivation In The Mathematics Classroom, Audrie H. Cox Aug 2026

Supporting Students’ Self-Efficacy And Motivation In The Mathematics Classroom, Audrie H. Cox

Masters Projects

This project examines the role of mathematics self-efficacy in supporting student motivation, engagement, and achievement in secondary mathematics classrooms. Through a review of current research, the project identifies instructional practices that strengthen students' confidence in their mathematical abilities, including formative assessments, meaningful feedback, supportive teacher-student relationships, and opportunities for productive struggle. Drawing on these findings, a professional development workshop session was developed to equip secondary mathematics teachers with practical, research-based strategies that promote positive mathematics self-efficacy and improve overall classroom instruction. By translating research into actionable teaching practices, this project aims to support more confident, motivated, and successful mathematics learners.

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Student Attitudes And Perceptions Of Proof In Mathematics, Emelin G. Sibrian Marquez Aug 2026

Student Attitudes And Perceptions Of Proof In Mathematics, Emelin G. Sibrian Marquez

Electronic Theses, Projects, and Dissertations

Traditionally, mathematical proof is viewed primarily as a tool for validation or verification. However, proof holds many other important roles such as discovery, reasoning, explanation, and justification. For many students, these other roles are not always obvious. Those encountering rigorous proof for the first time often find the process abstract, intimidating or disconnected from their previous learning. This disconnect can lead to negative attitudes as students transition from computational mathematics to advanced proof-based mathematics. Utilizing a mixed-methods approach, this study examined undergraduate and graduate mathematics students at a Hispanic-Serving Institution (HSI) in Southern California. We investigated what students perceive the …

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An Investigation Of The Use Of Self-Regulated Strategy Development With A Mnemonic On The Fraction Computation Performance Of Students At-Risk For Emotional/Behavioral Disorders, Melissa D. Hullett Aug 2026

An Investigation Of The Use Of Self-Regulated Strategy Development With A Mnemonic On The Fraction Computation Performance Of Students At-Risk For Emotional/Behavioral Disorders, Melissa D. Hullett

All Dissertations

Interventions that help students organize their thinking can reduce cognitive load and support academic, behavioral, and social success. Self-Regulated Strategy Development (SRSD) is an evidence-based instructional framework that combines strategy instruction with self-regulation to promote student independence and improve student confidence. A mnemonic has been shown to help scaffold support across all content areas to the level of mastery required by Stage 4 of the SRSD framework ("Memorize It"). In mathematics, where executive functioning demands are high, interventions to scaffold content must provide the metacognitive support needed for a diverse student population. This study used a multiple-baseline design to examine …

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Music And Middle School Mathematics, Cheryl L. Hawkins Aug 2026

Music And Middle School Mathematics, Cheryl L. Hawkins

All Graduate Reports and Creative Projects, Fall 2023 to Present

The purpose of this project was to see if music playing in the background while learning essential mathematics skills would make a difference in the learning process of middle school students. For nine weeks I collected data on the scores of the special education students relearning skills they had been previously taught in a general education mathematics class. The students took a baseline assessment, then had 30-40 minutes of instruction spread across two days. They then took another assessment to see what the change was. During the lessons and assessments there was one of three conditions happening, one was silence, …

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My Journey To Mathematics, Thao Thuan Vu Ho Jul 2026

My Journey To Mathematics, Thao Thuan Vu Ho

Journal of Humanistic Mathematics

No abstract provided.

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The Urysohn Lemma: Munkres Variation, Irida Altman Jul 2026

The Urysohn Lemma: Munkres Variation, Irida Altman

Journal of Humanistic Mathematics

There is a tradition of Mathematics contributing to the understanding of Music. This article sets out to contribute in the other direction. It uses musical sensibilities to feel its way through a piece of mathematics called the Urysohn Lemma, suggesting the presence of rhythmic, melodic, and harmonic elements within standard proving practices of contemporary Western mathematics. This article employs a literary-philosophical technique of viewing a text in one discipline (mathematics) through the conceptual lens of another (music). As such, this article reports on no experiments—reading the article is the experiment. Each reader performs it for themselves.

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An Exploration Of Mathematical And Musical Connections, Jeffrey Pair, Egypt Pannell, Dani Rodriguez, Jerico Sarmiento Jul 2026

An Exploration Of Mathematical And Musical Connections, Jeffrey Pair, Egypt Pannell, Dani Rodriguez, Jerico Sarmiento

Journal of Humanistic Mathematics

In this paper, we present an introduction to some of the mathematical principles underlying music and mathematically develop a connection between the twelve musical notes and the group of integers modulo twelve. Our discussion touches on the simple mathematical ratios used to calculate consonant musical tones on the length of a string, the frequencies of tones and the method by which the twelfth root of two provides the foundation of equal temperament tuning, some algebraic connections to musical concepts like the euphonious circle of fifths, and a curious connection to twin primes.

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Reducing Unreliability Of Complex Systems By Numerical Optimization: A Hybrid Approach, Fouad Hamza Abd Alsharify, Ahmed Hasan Alridha, Zahir Al-Khafaji Jul 2026

Reducing Unreliability Of Complex Systems By Numerical Optimization: A Hybrid Approach, Fouad Hamza Abd Alsharify, Ahmed Hasan Alridha, Zahir Al-Khafaji

Baghdad Science Journal

This paper investigates the effectiveness of numerical optimization techniques in enhancing the reliability of complex systems. The main objective of the study is to reduce the unreliability of complex systems by narrowing the range of component unreliability, thereby reducing the probability of system failure and achieving stability and robustness in the reliability of complex systems. The technique for this task involves formulating the problem as a multi-objective numerical optimization problem under specified constraints using Particle Swarm Optimization and Simulated Annealing algorithms, as well as a hybrid approach combining the two algorithms. The multi-objective optimization techniques were applied to a more …

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A New Numerical Approach For Solving Caputo-Fabrizio Fractional Differential Equations, Manoj Kumar Jul 2026

A New Numerical Approach For Solving Caputo-Fabrizio Fractional Differential Equations, Manoj Kumar

Baghdad Science Journal

In this paper, we present a novel numerical scheme for solving fractional-order differential equations of the form ^CFD_t^η ψ ( t ) = f( t,ψ ( t ) ),ψ ( 0 ) = ψ 0,0 < η < 1,t∈[ 0,T ], where ^CFD_t^η denotes the Caputo-Fabrizio derivative operator. Further, we establish the stability and error analysis of the proposed scheme. We also extend this scheme for solving systems of fractional differential equations. Furthermore, we perform the several numerical simulations and present the results graphically. The obtained solutions are compared with those achieved through the well-known methods such as fractional Adams-Bashforth method and a new predictor-corrector method. It has been observed that the proposed method offers greater accuracy than these established methods. Hence, the proposed scheme can be utilized for the simulations of various fractional order differential equations, when the derivatives are considered in the Caputo-Fabrizio sense.

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A Spectral Approach To Join Based Operations On Graphs, S. Sripriya, A. Anuradha Jul 2026

A Spectral Approach To Join Based Operations On Graphs, S. Sripriya, A. Anuradha

Baghdad Science Journal

The success of Spectral Graph Theory is due to its immense applications in several fields of science and technology. The parameter `graph energy' plays a significant role in the Hückel Molecular Orbital Theory, where it is used to approximate the total π -electron energy of conjugated hydrocarbons. Several modified versions of the energy parameter have been defined by many researchers depending on the context. This study explores the spectral characteristics and energy distributions associated with selected graph operations derived from the first Zagreb, second Zagreb, and sum-connectivity matrices. When the adjacency matrix provides information only on the existence of a …

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Presentation Note Of The Manual "Elements Of Mathematics And Statistics For Economists", Fouzi Mourji Jul 2026

Presentation Note Of The Manual "Elements Of Mathematics And Statistics For Economists", Fouzi Mourji

Revue Marocaine de Droit, d'Economie et de Gestion (Moroccan Journal of Law, Economics and Management)

This paper presents a two-volume textbook on mathematics and statistics for economics students. The authors, Fouzi Mourji and Najib Mikou, emphasize that the introduction of quantitative methods in economics is a recent but irreversible phenomenon, noting that major theoretical advances in economics have often followed mathematical breakthroughs. The manual is designed to complement lectures and tutorials, helping students master basic concepts in economics curricula and understand their practical applications for economic decision-making. The presentation highlights the importance of mathematical tools for understanding economic mechanisms and rationalizing decision-making processes, while acknowledging the manual's imperfections.

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Advanced Mathematics In The Elementary School: Supporting Teachers And Students Through A Resource Compilation, Abigail Friedel Jul 2026

Advanced Mathematics In The Elementary School: Supporting Teachers And Students Through A Resource Compilation, Abigail Friedel

School of Education and Leadership Student Capstone Projects

Addressing the needs of every student within an elementary mathematics classroom is a difficult and time-consuming task that educators are charged with. The range of abilities in a general education classroom can span multiple grade levels, especially in upper elementary. Teachers are often encouraged to focus on students that are below grade level, which can lead to higher ability students being bored and disengaged when they are in the classroom (Livers et al., 2018). To address this issue, this capstone project seeks to answer the question of how can elementary classroom teachers best support their advanced learners in math after …

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Decolonizing Minnesota Mathematics: Incorporating Indigeneity Into Middle School Mathematics, Tia Ahmed Jul 2026

Decolonizing Minnesota Mathematics: Incorporating Indigeneity Into Middle School Mathematics, Tia Ahmed

School of Education and Leadership Student Capstone Projects

The invisibility of Native Americans in mainstream mathematics education has contributed to the academic underachievement and cultural disconnect experienced by Native American youth. Grounded in the frameworks of Tribal Critical Race Theory (TribalCrit), culturally relevant teaching, and ethnomathematics, this project investigates: How can the historical and current cultural contexts, mathematical understandings, perspectives, and issues relating to Dakota, Anishinaabe, and Urban Indigenous communities be incorporated into Minnesota middle school math curriculum in a way that fosters strong math identities among Native American students and supports the needs of Minnesota’s American Indian tribes and communities? Along with research on the intersectionality of …

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Sdg 4.1.1 Minimum Proficiency Levels. Definition And Blueprint For Assessment, Prue Anderson, Andrew Mannion, Ursula Schwantner, Maurice Walker, Colin Watson, Toby Simmer Jul 2026

Sdg 4.1.1 Minimum Proficiency Levels. Definition And Blueprint For Assessment, Prue Anderson, Andrew Mannion, Ursula Schwantner, Maurice Walker, Colin Watson, Toby Simmer

Global education monitoring

Sustainable Development Goal (SDG) 4 aims to ensure that, by 2030, “all girls and boys complete free, equitable and quality primary and secondary education leading to relevant and effective learning outcomes.” The primary indicator 4.1.1 concerns the proficiency of girls and boys in two learning areas (reading and mathematics) at three stages of education: at the end of lower primary, at the end of primary, and at the end of lower secondary. Large-scale learning assessments are essential tools to capture data on learning outcomes and to provide system-level evidence on education quality and equity. In the context of SDG 4, …

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