Current Issue : October-December Volume : 2026 Issue Number : 4 Articles : 5 Articles
Large Language Models (LLMs), as a core technology in the field of artificial intelligence, rely heavily on fundamental mathematical theories for their underlying architecture, training optimization, inference mechanisms, and performance improvement. This article systematically summarizes the advanced applications of basic mathematical branches such as linear algebra, probability theory and mathematical statistics, functional analysis, optimization theory, information theory, topology, etc. in large language models. It deeply analyzes the implementation principles of mathematical theory in key links such as word embedding, attention mechanism, model training, inference optimization, and interpretability analysis. Combined with the international cuttingedge research results in the past five years, it elaborates on the core role of basic mathematics in breaking through the performance of large language models, improving theories, and expanding scenarios. At the same time, summarizing the bottlenecks currently faced by the application of mathematical theories, and looking forward to the research direction of deep integration between basic mathematics and large language models in the future, providing mathematical theoretical references and technical ideas for the theoretical research and engineering practice of large language models....
Integrating computational thinking (CT) and artificial intelligence (AI) to foster interdisciplinary learning has received muchneeded attention worldwide in educational research, though less emphasis has been placed on simultaneously developing CT and AI learning outcomes in disciplinary (e.g., mathematics) classroom contexts. CT and AI are closely linked to mathematics, where knowledge of data practices, mathematical modelling, and generic skills such as problem-solving are highly emphasized. This paper reports on a design-based research study with four design cycles, aiming to generate empirically grounded design principles for curricular and instructional innovations in school mathematics contexts that simultaneously support CT and AI learning. Drawing upon the theoretical perspectives of CT as modelling and programming as whiteboxing, and taking exemplary tasks developed from our design-based study, we detail four design principles: (1) Encourage tinkering with computational artefacts; (2) Leverage CT as modelling for authentic problem-solving; (3) Consider tool-based developmental trajectories; and (4) Exploit the white-box effect to foster mathematical and AI literacy. From this, we conceive mathematics, CT, and AI as interconnected disciplines, where learning outcomes are not treated separately but rather as translatable across different disciplinary boundaries. We conclude by discussing the opportunities and challenges of implementing the curricular and instructional designs, offering insights to inform how CT and AI concepts and processes can be meaningfully embedded in mathematics education....
CTMath is a five-phase learning model that integrates computational thinking (CT) into elementary mathematics through Scratch. Developed using ADDIE, the model was expert-validated and then examined in a limited pilot, a field trial, and a quasi-experimental comparison with a control class. Mathematics achievement showed moderate improvement based on normalized gain (N-gain) (pilot = 0.375; field = 0.587; quasi-experimental CTMath = 0.487 vs. control = 0.224), and the CTMath class outperformed the control class at post-test in the quasi-experimental stage, t (41) = 3.247, p = .002, mean difference = 2.89/20, Hedges’ g = 0.97. In addition to cognitive outcomes, students’ Scratch projects and classroom observations suggested strengthening in CT practices such as decomposition, algorithm design, and debugging, alongside critical-thinking-related classroom performance. The main contributions of CTMath are: (i) a replicable instructional syntax (Problem Initialization → Solution Design → Implementation → Evaluation → Refinement and Support), (ii) an implementation package consisting of student worksheets (LKPD), a teacher guide, and Scratch projects, and (iii) a multidimensional assessment framework that captures process, digital product, and learning outcomes. Overall, these findings suggest that structured and gradual CT integration may support stronger mathematical understanding and CT-related classroom performance under the conditions of this study and warrant further replication across other topics and contexts....
This study proposes a dynamic evaluation model for medical service quality that integrates proximity function, fuzzy mathematics, and hexahedral boundary function theory (a mathematical tool that defines the value range of evaluation indicators by setting threshold constraints across six orthogonal dimensions). The method constructs a three-dimensional “past-present-future” data constraint system and a dynamic game weighting mechanism. Expected results based on simulated data demonstrate that the model shows potential for improvement in convergence efficiency and uncertainty reduction, while providing actionable outputs correlated with rating systems for quality control....
Modular arithmetic units for friendly moduli are crucial for residue number system (RNS) applications. Choosing a moduli set of the 2n −1 form is expected to provide maximum benefits for modular arithmetic performance. In this respect, this paper proposes a hardware architecture for the moduli set {2n+1 −1, 2n −1, 2n−1 −1} (with n even), in particular an efficient architecture for the reverse conversion, which is often the bottleneck of RNS processors. The main idea is to remove the CRT multiplicative inverse from the reverse conversion stage, achieving scalable hardware with reduced complexity. We show that the modular multiplication of the multiplicative inverse can be transferred to the arithmetic channels with minimal overhead while reaching outstanding gains in the scalable reverse conversion stage. Furthermore, the presented method enables the utilization of recent hardware reutilization strategies to attain further improvements. Results show that the proposed reverse converter outperforms the state of the art by 17.48% in delay and 53.47% in area for n = 20. Advantages become even more substantial for larger values of n....
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