Welcome to SDU Institutional Repository
Communities
Select a community to browse its collections.
Recent Submissions
test
(2026) test1
Fractal dimension of exceptional sets in semi-regular continued fraction
(SDU University, 2025) Duisen S.
This thesis investigates the interplay between Diophantine approximation, continued fraction representations, and fractal geometry. We begin by exploring the classical notion of badly approximable numbers-real numbers whose continued fraction expansions have bounded partial quotients. These numbers, while forming a set of zero Lebesgue measure, exhibit full Hausdorff dimension, highlighting their rich geometric structure. Building on this foundation, we introduce and analyze a generalization known as semi-regular continued fractions, wherein a fixed sequence of signs modifies the classical expansion. For such expansions, we define the class of σ-badly approximable numbers and study their distribution and fractal properties. We demonstrate that these generalized expansions preserve many of the geometric complexities of their classical counterparts, while offering new degrees of arithmetic freedom. In the second part of the thesis, we shift our focus to Lehner expansions of real numbers and examine how the statistical behavior of the associated digit sequence (bn) influences the fractal geometry of the corresponding number sets. Specifically, we investigate the impact of the average value of bn on the box dimension-a quantitative measure of geometric complexity. Employing the box-counting method, we perform numerical experiments to estimate the box dimension and uncover how variations in the digit sequence relate to the irregularity and structure of the expansion. By synthesizing the analytical and numerical approaches, this thesis provides a comprehensive view of how modifications to continued fraction representations influence the fractal characteristics of real number sets, contributing to the broader understanding of number-theoretic and geometric interrelations.
Mitigating Bias in AI-Based Loan Approval Systems through Fairness-Centric Techniques
(SDU University, 2025) Raziyeva S.
As artificial intelligence (AI) becomes increasingly embedded in high-stakes decision-making systems, ensuring fairness in algorithmic outcomes has emerged as a critical concern. This thesis investigates bias and fairness in AI-based credit scoring systems, with a particular focus on gender disparities. Using the German Credit Dataset as a case study, the research evaluates the performance and fairness of several supervised machine learning models, including Logistic Regression, Decision Tree, Random Forest, XGBoost, Support Vector Machine, and Neural Network. The study applies fairness metrics such as Statistical Parity Difference (SPD) and Disparate Impact (DI) to assess group-level inequalities in predicted loan approval outcomes. Results reveal a consistent trade-off between model accuracy and fairness, where high-performing models like Random Forest and XGBoost demonstrate notable biases against female applicants. Even interpretable models, such as Logistic Regression, exhibit fairness issues due to historical and structural biases embedded in the training data. To address these challenges, the thesis highlights the importance of incorporating fairness-aware strategies across the machine learning pipeline, including data pre-processing, fairness evaluation, and potential post-processing mitigation. The use of tools like AIF360 and stratified sampling further strengthens the analysis. This research contributes to the growing discourse on responsible AI by demonstrating that achieving fairness is not merely a technical goal but a sociotechnical imperative. It calls for an interdisciplinary approach that combines ethical reasoning, regulatory compliance, and algorithmic transparency to ensure equitable access to financial services. The findings advocate for the development of AI systems that are not only accurate but also accountable and inclusive.
Using formative assessment by rural English teachers to improve speaking skills
(SDU University, 2025) Abdykalykova Sh.
This qualitative study explores how rural teachers employ formative assessment strategies to improve students' speaking skills in resource-constrained environments. Focusing on 12 purposively selected rural teachers, the research utilizes semi-structured interviews to investigate the types of formative assessments used, the challenges faced in implementation, and the adaptive strategies teachers develop to overcome these barriers. Key findings reveal that rural teachers rely on low-cost, interactive methods such as peer feedback, oral questioning, storytelling, and one-minute summaries to assess and enhance speaking skills. However, systemic challenges-including large class sizes, limited training, inadequate materials, and student anxiety-hinder consistent and effective formative assessment practices. Despite these obstacles, teachers demonstrate resilience by fostering collaborative learning environments and providing incremental, personalized feedback. The study emphasizes how crucial it is for rural educators to receive context-specific professional development that gives them useful formative assessment strategies adapted to their particular limitations. It also suggests legislative changes to close resource and infrastructure shortages in rural school systems. Formative assessment can become a more sustainable technique for enhancing oral communication skills among rural learners by filling in these gaps. This study adds to the larger conversation about fair language instruction by emphasizing the ability of rural educators to modify their teaching methods to meet the requirements of their students. By using mixed-methods approaches or larger-scale plans, future research could build on these findings.
Effectiveness of Hands-On Chemistry Experiments in High School Education
(SDU University, 2025) Aldenov R.
This master’s dissertation explores the impact of different instructional strategies on students’ academic performance and engagement in chemistry education, with a focus on the effectiveness of practical, laboratory-based teaching methods. The study compares two groups of secondary school students: a primary group that received instruction through traditional lecture-based methods, and a focused (experimental) group taught using systematic, hands-on laboratory activities. A total of 42 students were involved in the research, equally divided into the two groups. Both groups followed the same curriculum content and were taught by similarly qualified instructors, ensuring the internal validity of the comparative design. However, the focused group engaged in practical work, including laboratory experiments aligned with curriculum objectives, while the primary group experienced conventional instruction with minimal laboratory exposure. To evaluate the outcomes, a mixed-methods approach was utilized. Data were collected through a Chemistry Achievement Test (pre- and post-intervention), a laboratory skills assessment test, and a structured questionnaire measuring student perceptions. Descriptive and inferential statistical analyses-including independent samples t-tests, and ANCOVA-were performed to assess academic growth, control for baseline differences, and examine the robustness of instructional impact. This study concludes that practical, laboratory-based teaching methods lead to more effective learning outcomes, particularly by enhancing scientific thinking, motivation, and personalized academic growth. The findings advocate for the broader integration of experimental learning strategies in chemistry curricula and underscore the need for policy support in expanding laboratory infrastructure, teacher training, and time allocation for hands-on instruction.