Saudi Cultural Missions Theses & Dissertations
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Item Restricted Enhancing the quality and standard of research in Saudi Arabian universities: Selection and use of research methods at doctoral level: An investigative study on the use of research into statistical methods(University of glasgow, 2024) Abohiamid, Manal; McMahon, Margeryhis study investigated the selection and use of research methodologies at doctoral level, with particular emphasis on the use of statistical practices in research and with a focus on the Saudi Arabian context. There are misapplications in certain studies when analysing the statistical data, and some of these inaccuracies come from using improper management and suitable statistical methods at the analysis stage, contributing to misleading research conclusions. A key question was ‘How do academics and PhD students from Education departments in a selected university in Saudi Arabia and a university in Scotland/United Kingdom, from different educational backgrounds, view their readiness, selection, and utilization of statistical methods in PhD research?’. The accurate use of Statistics is critical in academic research, Statistics provide a methodical and objective approach to data analysis and interpretation, allowing researchers to make meaningful conclusions and uncover noteworthy patterns. Thus, a study acquires credibility and assures the validity of its findings by using accurate statistics, allowing policymakers and stakeholders to make educated decisions and perform targeted adjustments that enhance every aspect of society. This study examined PhD students' perceptions of their preparedness for statistical analysis, as well as their statistical and mathematical skills. Currently in Saudi Arabia, a programme of development: Vision 2030, is being implemented and so an aim of this study was to show why reforms are needed in Saudi Arabia's education system and why future university students should have sufficient Mathematical understanding to maintain the PhD researcher's basic knowledge base (Mathematics and Statistics). This was accomplished by sending a questionnaire to PhD students in SA and UK and conducting interviews with Statistics lecturers for postgraduate students in Saudi Arabia. The study found there is data analysis problems, such as inaccurate statistical technique application, a lack of pre-existing Mathematical expertise, wrong data processing, and incorrect result analysis. To increase the accuracy of statistical methods employed in PhD research, the study recommends that qualified statisticians, Statistics centres, and quality Mathematics and Statistics material be developed in the KSA. Furthermore, the research showed the significance of developing educational cadres in Statistics, developing the literacy pathway in schools in Mathematics, and making advanced Statistics courses necessary for postgraduate students in order to improve the quality and credibility of research undertaken, and the significance of students having a mathematical foundation in the Kingdom of Saudi Arabia22 0Item Restricted Cubic Curves and Cryptography(University of Sussex, 2024-08) Altimani, Nuof; Hirschfeld, JamesThis dissertation investigates elliptic curve theory and its foundational role in algebraic geometry, number theory, and cryptography. At its core is the Weierstrass equation, which defines the group structure of elliptic curves—a critical property for cryptographic systems that rely on the discrete logarithm problem for secure data exchange. Additionally, this work examines the geometric and algebraic properties of elliptic curves, emphasizing their applications in cryptography. The dissertation presents core concepts, the Weierstrass equation, methods for solving discrete logarithm problems, and cryptographic applications.18 0Item Restricted Modelling the stability of ternary solid dispersions(University of Galway, 2024-08) Albaqami, Modhi; Meere, MartinThis thesis provides a mathematical analysis of the stability of some ternary solid dispersions using thermodynamic theory. Solid dispersions have been developed to improve the solubility of poorly soluble drugs. Traditional solid dispersions typically consist of two components - a drug and a hydrophilic polymer, the purpose of the polymer being to improve the solubility of the drug when administered orally. More recently, ternary dispersions (that is, systems with three components) have been developed. Ternary dispersions provide an extra degree of freedom to enable system designers to optimize both the stability and solubility properties of the dispersion. Unstable dispersions may phase separate, thereby limiting their shelf life. In this thesis, I mathematically model ternary solid dispersions with a view to identifying parameter regimes that lead to favourable and unfavourable stability properties for the dispersion. A systematic study of this kind has hitherto been lacking in the literature. The methodology used is as follows. The solid dispersions are modelled using Flory- Huggins solution theory, a well-established thermodynamic model in polymer science for polymer blends. The stability properties of the dispersions are determined by constructing phase diagrams using the Gibbs free energy of mixing. The phase diagrams determine whether a particular ternary composition is stable or unstable or metastable. The requisite numerical calculations to construct the diagrams are carried out by programs that I wrote using the mathematical packages MAPLE and MATLAB. Thermodynamic theory determines the broad character of the ultimate state of the mixture, but yields no information on how the mixture evolves to that state, or what the detailed character of the final state is for unstable compositions. To address these issues, a partial differential equations model is developed to describe the dispersion mixture evolution, and some simulations of this model are also presented. A few notable results are as follows. For polymer-polymer-drug ternary systems, it is found that for desirable stability properties to be possible, the two polymers need to be compatible (in a sense that has been described quantitatively). Also, the stability behaviour can be finely dependent on the asymmetry between how the two polymers interact with the drug. Closed loops of immiscibility are shown to be theoretically possible. For polymer-surfactant-drug ternary systems, it is shown that the stability behaviour can be sensitive to the character of the interaction between the polymer and the surfactant, and the molecular weight of the surfactant. Numerous other predictions are made.18 0Item Restricted The Role of Educational Leadership in Supporting the Development of Reading Comprehension Skills in MATHEMATICS among Primary School Student(Manchester Metropolitan University, 2024) Alsharif, Mohammed Ibrahim; Brady, CatherineThis research focuses on the role of educational leadership in supporting the development of reading comprehension skills in mathematics among primary school students. Research recommends leadership practices that improve math literacy because reading skills predict math success. The study considers issue comprehension, conceptual understanding, procedural fluency, and deductive reasoning mathematical ability. Students learn mathematical terminology and context via reading. This research analyses how educational leadership might improve math literacy and understanding through document analysis methodology. The goals included identifying mathematical understanding hurdles, leadership gaps in enhancing these abilities, and evidence-based reading-rich mathematics education. Based on the findings of the research, the paper recommends that educational leaders need to progress from operational managers to learning leaders. Studies show that gaps in math instructors' literacy approach training hinder understanding. The study also indicates that instructional leadership promotes mathematical literacy by fostering a clear and supportive atmosphere that connects leadership objectives with classroom practices. The results also reveal that educational leaders and teachers must collaborate to create great teaching models and share best practices.55 0Item Restricted Teacher Characteristics and Standardised Mathematics Achievement: Global Evidence-Based Reviews and Empirical Evidence for Saudi Arabia(University of Glasgow, 2024-08) Abotalib, Ahmad; Hermannsson, Kristinn; Wincenciak, Joanna; Anderson, SarahTeacher effectiveness has gained considerable attention in recent research, especially over the past two decades. Nevertheless, the precise teacher characteristics that drive this effectiveness remain a subject of debate. Within Saudi Arabia, there is a great interest in enhancing education quality, aligning with the nation's pursuit of Vision 2030 objectives. Teachers are considered one of the most important elements in the education process, contributing to improving student performance in the classroom and beyond. Despite their critical role, limited research has been conducted on teacher effectiveness in Saudi Arabia. This study aims to explore the relationship between various teacher characteristics – including same-gender match, types of certifications, teacher test scores, graduate degrees, experience and professional development - and standardised mathematics achievement among fourth and eighth-grade students in Saudi Arabia. Two reviews were conducted at the international level to establish a theoretical framework concerning this relationship. First, a scoping review examined the relationship between teacher characteristics and student achievement across several study designs. This was followed by a systematic review and meta-analysis focused specifically on mathematics as a subject and fourth to eighth grades. The reviews revealed a scarcity of experimental and quasi-experimental studies for most teacher characteristics, except for professional development. Furthermore, a major finding of these reviews showed that the association between these teacher characteristics and standardised student achievement varies across subjects and grade levels. Among the examined characteristics, teacher experience demonstrated the strongest positive association with standardised mathematics achievement, particularly at the peak of this relationship. Math-specific certification and professional development showed a moderate positive correlation indicating significant associations. Teacher test scores showed small but consistent positive association across various measures. Same-gender match exhibited a slight positive association, though this finding warrants caution due its small effect size. Notably, holding a graduate degree showed negligible association, suggesting no practical relationship with mathematics achievement. In addition, these reviews revealed that standardised student achievement is not fully explained by these teacher characteristics. Next, an empirical study was undertaken in the context of Saudi Arabia using secondary data from TIMSS 2019. Utilising Ordinary Least Squares (OLS) regression models, the findings of this study showed that, contrary to the literature regarding the gender gap in mathematics achievement, there is a significant gender gap in standardised mathematics achievement in favour of female students. Additionally, the results showed that teacher experience and professional development are positively correlated with standardised mathematics achievement in fourth and eighth grades in Saudi Arabia, although these associations were not always statistically significant. Furthermore, the analysis indicates that the majority of the variation in standardised mathematics achievement in Saudi Arabia is attributed to student variables such as students' absence, parental education and socioeconomic status. This dissertation extended the research by exploring further analysis in Saudi Arabia across various sub-samples to examine the heterogeneity of teacher effects. By considering different sub-groups - including school type (female vs male schools), achievement level (high-achieving students vs low-achieving students) and parental education (students whose parents have university degrees vs those whose parents do not have university degrees) - this dissertation offers a further perspective on how teacher characteristics correlate with standardised mathematics achievement among diverse student groups within the Saudi Arabian context. The findings underscore the existence of teacher effect heterogeneity in Saudi Arabia, signalling variations across sub-samples within the Saudi educational landscape. This dissertation provides valuable implications for educators and policymakers in Saudi Arabia and beyond. It offers insights into optimising teacher effectiveness and addressing diverse student needs.26 0Item Restricted Projective Curves in Algebraic Geometry(University of Sussex, 2023-12-20) Aldawsari, Abdullah; Hirschfeld, JamesThis thesis began a thorough investigation of the complicated interactions between geometric characteristics and the intrinsic algebraic structures in the world of projective curves. The focus of the inquiry was a methodical analysis of curve C' in the confined affine plane A to the power 2 (K) , on the field K, has the set of zeros (x, y) of a polynomial f (X,Y) . The curve C' present in the projective plane P to the power 2 (K has the set of zeros (x, y, z) of a polynomial which were homogeneous F (X, Y, Z). Therefore, this study investigated the singular point, inflection point, genus of C' along with the points of intersections of these two curves and produced valuable results.20 0Item Restricted Investigating Computer Aided Assessment of Mathematical Proof by Varying the Format of Students’ Answers and the Structure of Assessment Design by STACK(University of Edinburgh, 2024-03-18) Alarfaj, Maryam Khalid H; Sangwin, ChristopherStudents are increasingly being expected to use Computer Aided Assessment (CAA) systems as support for traditional courses. Assessing a full mathematical proof in an educational context and providing feedback and other outcomes to students is currently well beyond the capabilities of CAA systems. One possible approach to assessing students’ answers has been to break up larger tasks into smaller individual steps to which automatic assessment can then be applied. However, the method of marking depends on the format of a mathematical response. This thesis aims to investigate the effectiveness of different formats in computer aided assessment of mathematics. A format effect occurs when the format of an exercise affects the rate of successful outcomes of the exercise. Having established the need to study the format effect when writing mathematical arguments particularly online, I consider three formats for writing open-ended questions: two-column, typing, and Separated Concerns. The first of three studies explored the impact of the two-column format in writing simple mathematical arguments. In conducting this research, I developed a coding scheme to describe and analyse the structure of individual mathematical arguments. The second study focused on the difference and the format effects between uploading handwritten and typing in writing mathematical responses. Another outcome of this study is to provide a further application of using the coding scheme on analysing students’ arguments. The third study focused on updating STACK potential response tree based on Separated Concerns. STACK is a System for Teaching and Assessment using a Computer algebra Kernel, is an open source computer aided assessment system for mathematics, and other STEM subjects. Separated Concerns is a phrase used to describe materials in which potential misconceptions are addressed directly. In this study, I focused exclusively on students’ responses, and misconceptions in learning proof by induction using STACK. Mathematical induction is used as a vehicle to illustrate the idea of Separated Concerns. The main goal of the third study is to understand how engagement with learning materials packaged into online quizzes to replace live lectures, a “lecture quiz”, related to success on the weekly assessed quiz, and the course total. A second goal of the third study is to explore the common mistakes made by students when using online materials to prepare for mathematical induction. This study also illustrates how to use research to update the algorithms which assess students’ answers, known as “STACK potential response trees”, in questions written to support learning mathematical induction based on Separated Concerns.64 0Item Restricted Mean-field, Stochastic, and Individual-based Models of Insect Movement in the Context of Trapping and Ecological Monitoring(Saudi Digital Library, 2023-10-22) Alqubori, Omar; Petrovskii, SergeiIn this thesis, we attempt to understand the conditions that affect insects' and animals' movements in the real world. Mathematical modelling is an efficient research tool that can help to bridge this gap in our knowledge. Herein, we revisit the straightforward, yet powerful simulation framework of individual-based modelling using Brownian Motion (BM), Correlated Random Walk (CRW), and Biased Random Walk (BRW). In chapter \ref{chapter1}, we outline previous research in this area. In chapter \ref{chapter2}, we consider trapping problems, where we suppose there to be two particular traps, i.e., baited and non-baited, and we verify whether a large non-baited trap is equivalent to a small baited trap. Thereafter, we determine how the trap position affects the results, i.e., where there is a competition area between two traps. Furthermore, we verify which trap shape is more effective, circular or square. In chapter \ref{chapter3}, we then study different insects' behaviours as a response to an attraction. To this end, we consider several different response types as quantified by different combinations of turning angle and step size distributions. We show that, depending on the response type, trap counts can be counter-intuitive and misleading. Then, in the chapter \ref{chapter4}, we simulate realistic slug movement by using data on slug spatial distributions collected during a three-year project conducted in crop fields across England. In particular, we study how slugs' movements depend on their population density, reception radius, and density threshold. Our simulation results are consistent with the above field data. Finally, chapter \ref{chapter5}, summarises the results for each chapter and discusses potential future work.21 0Item Restricted Quantum Groups And Their Invariant Theory(2023) Alqahtani, Awn; Xingting, WangThe focus of this research is on algebraic manifestations of quantum symmetries, more specifi- cally from the point of view of homological algebra, representation theory, category theory, and noncommutative algebraic geometry. The notion of a group describes symmetry in mathemat- ics. In recent decades, certain “quantum” examples include subfactors, quantum groups, Hopf algebras,and topological phases of matter. These mathematical objects have applications in the diverse range of settings across mathematics and physics, including quantum invariant of links and 3-manifolds, representation theory, condensed matter physics,topological phases of matter, and quantum information.39 0