This article is dedicated to the issue of teaching mathematical education in the training of IT specialists in higher education institutions. With the rapid growth of information technology and its implementation in various sectors such as the economy, production, education, etc., there is a constant need to update fundamental knowledge and acquire professional skills for IT graduates. The article highlights the importance of improving teaching methods for mathematical disciplines and the competencies obtained, focusing on the integration of interdisciplinary connections aimed at forming professionally-oriented training for bachelor-level IT specialists, which helps to meet market demands and employer preferences. The research methods included the main aspects of a practice-oriented approach and interdisciplinary connections among fundamental mathematical and specialized disciplines, as well as the requirements of the state educational standards of the Republic of Kazakhstan for the field of information technology training. Based on the conducted research, the authors provided an analytical review of the methods for teaching mathematics, issues of integrating mathematical disciplines with IT to develop the necessary competencies for future information technology specialists. The research revealed that the integration of disciplines, particularly the sections "Linear Algebra and Analytical Geometry" and "Programming," improves the quality of the knowledge obtained. This is achieved through the development of analytical and mathematical logic, a deep understanding of algorithmic thinking, and strengthening the connections between them. This study showed that in teaching mathematics, it is essential to emphasize its connection with professional disciplines, paying particular attention to solving practice-oriented applied problems, which will contribute to the enhancement of the required competencies for future bachelor-level IT specialists.

The sorites paradox reveals the tension between the vagueness of natural language and the principles of classical logic. It has sparked significant contemporary debates in logical philosophy. Traditional binary logic struggles to face the challenges posed by ambiguous predicates. Researchers have proposed various solutions, such as degree theory, supervaluationism, and many-valued logic, but all face interpretive limitations. This paper systematically examines the logical structure of the sorites paradox and focuses on Williamsons epistemicist theory. Epistemicism maintains that ambiguous predicates possess objective and precise boundaries, though these lie beyond human cognitive reach and remain unknowable. By introducing the notion of unknowability, this theory preserves the validity of classical logic while offering a unique framework for addressing vagueness. This paper analyzes the mathematical logic foundations of epistemicism and its applied value in natural language analysis, legal reasoning, and ethical judgment, highlighting its advantages in theoretical simplicity, interpretive consistency, and intuitive rationality. Although epistemicism still faces challenges such as boundary arbitrariness and higher-order fuzziness, it has significant importance in resolving the sorites paradox and promoting interdiscipcolinary exchange. Finally, this paper proposes that future studies on epistemicism should focus on these three aspects: formal expansion, comparative studies, and interdisciplinary integration.

ABSTRACTIndustrial automation and smart ecological monitoring are key fields of Internet of Things environments, where devices function under complex practical conditions and with restricted infrastructure. In such conditions, devices often face critical concerns in guaranteeing trustworthiness and better outcomes. In this article, we preliminarily suggest a thoughtful design that anticipates the programming complexities of Internet of Things (IoT) environments and accounts for their unpredictable conduct under practical conditions. Central to our strategy is the use of a method grounded in mathematical logic to allow their core properties to be rigorously checked through mathematical proofs. This process builds trustworthy IoT infrastructures and ensures dependability of their conduct before practical programming. Beyond theoretical design, we perform programming and field experiments, demonstrating that mathematically grounded designs lead directly to more productive environment outcomes, particularly in restricted conditions where infrastructure must be exploited judiciously. The results underscore the value of integrating our mathematically checked design not only at the design level but also in shaping concrete solutions for critical blockchain‐enabled IoT environments. Finally, the results show that applying our design translates into demonstrable outcomes and easier environment adaptation during practical programming.

1. Overview Professor John Komlos is a former chairman of the Department of Economic History at the University of Munich and also taught as a visitor at Harvard, Duke, and the University of Vienna. In his book, “Foundations of Real-World Economics: What Every Economics Student Needs to Know and Doesn’t Get in the Usual Principles Text”, he examined mainstream economics and contemporary economic policies. This book has been translated into Chinese, German, Hungarian, Romanian, Russian, and other languages are forthcoming. This can be categoriSed as a major reference book to study the hopelessness of mainstream economic thought in explaining contemporary economic issues. Professor Komlos received a PhD in history in 1978 and a second PhD in economics in 1990, both from the University of Chicago. His academic career mainly consists of research and study of the effect of economic development on human biology. This background is reflected in the contents and sub-topics of his book in which he established the links of economics with neurology, psychology, sociology, ideology, and humanism. He advocates for a new paradigm: Capitalism with a human face by differentiating humanistic and mainstream economics based on their fundamental characteristics. Humanistic economics accepts the foundational achievements of sister disciplines as well as behavioral psychology. Instead of using mathematical logic, he emphasises considering human sentiments and morality, which cannot be incorporated into mathematical equations. In his own words, “I believe that our starting point should not be Adam Smith's Wealth of Nations (1776), but his Theory of Moral Sentiments (1759), in which Smith asserted forcefully that we possess an innate empathy toward our fellow human beings.”

Evaluation of creative project production performance in mathematical logic and computational thinking skills among gifted high school students.

Chronic lymphocytic leukemia (CLL) is a common neoplasm that carries the risk of transformation into Richter’s syndrome (RS), a highly aggressive B cell lymphoma with poor prognosis. Limited availability of animal models and cell lines hinders understanding of transformation mechanisms. Addressing this gap, we established the first in silico dynamic model of the disease. Our methodology integrates mathematical logic modeling with experimental data to identify disease drivers, mechanisms, and potential therapeutic targets. We validated the model by comparing the model’s readout with experimental data from different biological levels, such as single-cell RNA sequencing analyses and a CLL/RS patient formalin-fixed paraffin-embedded (FFPE) tissue cohort. Our analyses identified BMI1 proto-oncogene and TP53 loss as key RS progression regulators. In addition, we performed an in silico target screening to identify promising target combinations in a personalized fashion. Through the synergy of mathematical modeling with experimental readouts, our model provides a complementary approach to investigate the process of CLL transformation to RS.

The article sets the task to show how the dialectical form of thinking is con­cretized in the form of a new dialectical approach to mathematical creativity. Its philosophical basis is the fundamental ontology of Martin Heidegger, from which the operation of dialectical negation, called privation, is borrowed. Pri­vation in its ultimate expression finds a place in the paraconsistent (“Imagi­nary”) logic of N.A. Vasiliev, operating with logical antinomies and revealing their difference from logical contradictions (from logical absurdity). In logical and mathematical research, a clear example of the application of privation are the well-known Gödel incompleteness theorems, which establish the existence of positive integers with properties opposite to the properties of inductive numbers (N.N. Luzin). Within the framework of the task, the descriptive set theory of Luzin and the non-Euclidean (hyperbolic) geometry of Lobachevsky are analyzed. They are united by the problem of ordering the arithmetic conti­nuum. In this context, the question is posed as to why the set of real points of the continuum is not countably ordered, and an answer is given. The answer is provided by the dialectical approach to mathematical creativity described here as part of the logical discipline of thinking called complementary-dialecti­cal logic. The dialectical approach to mathematical creativity includes the trans­formation of mathematical logic developed on the basis of classical formal logic. This transformation is presented in the article as a synthesis of the exten­sional and intensional aspects of logical thinking, which are often called (for brevity) extensional and intensional logic. Key words: fundamental ontology, privation, paraconsistent logic, descriptive set theory, hyperbolic geometry, vir­tual points.

Mathematical literacy-based problems require the ability to read, interpret and connect contextual information with mathematical concepts, which is often a challenge for students. This difficulty is especially evident in modulo congruence material which requires an understanding of number concepts and mathematical logic. This study aims to analyze students' errors in solving mathematical literacy problems related to modulo congruence material. The research subjects were ten grade XI students from one of the high schools in Gowa Regency who were selected by purposive sampling. The method used was a written test to identify the types of errors, as well as in-depth interviews to explore the causes. The results showed that students had difficulty in understanding important information from the problem, translating it into a mathematical model, and composing the solution steps systematically. The conclusion of this study shows that learning interventions are needed that focus on strengthening context understanding, practicing reading problems critically, and habituation to develop coherent solution strategies. In addition, gradual integration of mathematical literacy exercises needs to be done so that students are able to develop mathematical thinking skills as a whole. Keyword: Error Analysis, Math Literacy Problem, Congruence, Modulo

This article explores the concept of \emph{absoluteness} in the context of mathematical analysis, focusing specifically on the Riemann integral on $\mathbb{R}^{n}$. In mathematical logic, \emph{absoluteness} refers to the invariance of the truth value of certain statements in different mathematical universes. Leveraging this idea, we investigate the conditions under which the Riemann integral on $\mathbb{R}^{n}$ remains absolute between transitive models of $\mathrm{ZFC}$—the standard axiomatic system in which current mathematics is usually formalized. To this end, we develop a framework for integration on Boolean algebras with respect to finitely additive measures and show that the classical Riemann integral is a particular case of this generalized approach. Our main result establishes that the Riemann integral over rectangles in $\mathbb{R}^{n}$ is absolute in the following sense: if $M \subseteq N$ are transitive models of $\mathrm{ZFC}$, $a, b \in \mathbb{R}^{n} \cap M$, and $f \colon [a, b] \to \mathbb{R}$ is a bounded function in $M$, then $f$ is Riemann integrable in $M$ if, and only if, in $N$ there exists some Riemann integrable function $g \colon [a, b] \to \mathbb{R}$ extending $f$. In this case, the values of the integrals computed in each model are the same. Furthermore, the function $g$ is unique except for a measure zero set.

This research focuses on exploring the mathematical reasoning abilities of Madrasah Aliyah students in solving problems that integrate mathematical concepts with the Islamic science of faraidh (inheritance law), specifically within the topic of fractions. The study employs a qualitative approach with a case study design and was conducted among 11th-grade students enrolled in the Religious Program at MA Raudlatul Ulum Putri. Data collection techniques included written tests, semi-structured interviews, and classroom observations, focusing on three selected students who represented high, moderate, and low levels of mathematical ability. The analysis centers on several key indicators of mathematical reasoning: identifying problems, formulating hypotheses, presenting logical arguments, and drawing conclusions. The results show that most students fall into the moderate reasoning category, while a smaller number are categorized as high or low. Students in the high category demonstrate a strong capacity to approach problems systematically and accurately, combining mathematical logic with a proper understanding of Sharia-based inheritance rules. In contrast, students in the low category struggle with interpreting problem contexts and executing fraction calculations correctly, which indicates gaps in both conceptual understanding and application skills. These findings underscore the importance of contextual and integrative learning, particularly the combination of mathematics with Islamic values, to enhance deeper comprehension. By embedding religious relevance into mathematical instruction—especially through real-life contexts such as inheritance laws—educators can support the development of more meaningful reasoning abilities. The study suggests that integrating mathematics and Islamic teachings can significantly benefit student learning outcomes and foster stronger conceptual foundations.

Relevance. The efficiency and reliability of the relay protection system is influenced by many factors, such as: failure of the power switch, malfunction of the relay protection device components, errors in the operation of the current measurement, etc. These failures can lead to a complete failure of the protection system or incorrect protective action and, in the case of a short circuit, often result in damage to the protected object. Therefore, the development of more advanced methods for detecting failures in the protection system elements is crucial. THEPurpose. The purpose of the article is to briefly analyze the problem of reliability in relay protection system in the event of a failure of protection elements, develop a new algorithm for the operation of longitudinal differential relay devices that detects current transformer failure (CT) on any side protected element, and recognizes network mode. The proposed algorithm allows relay protection devices to adapt when a CT failure is detected in each cycle, thus increasing the reliability of the protection system.Methods. The algorithm is developed using mathematical logic methods. Protection devices utilize inter-station communication channels to exchange information with adjacent devices. Additionally , these devices automatically adapt their operating algorithm to the type failure that occurs, and reconfigure protection zones accordingly.Results. The article examines the problem, and develops an algorithm for the automatic detection of failures in current transformer and relay protection circuits. This algorithm is based on Kirchhoff's first law and utilize an intersubstation information network. The proposed algorithm not only enables the unambiguous detection of such failures, but also allows for the instant adaption of differential relay protection zones when necessary, ensuring the speed relay protection is maintained . The algorithm has been validated through testing in the PSCAD/EMTDC program using a case study of busbar differential protection.Conclusion. As a result of the research, significant findings have been obtaine that can be enhance the reliability of the digital relay protection system in the event of failures in protection elements.

The article presents a new alternative approach for determining the sensitivity of mathematical models. Mathematical models (MM) operate on the basis of input and output, which are transmitted to and extracted from embedded mathematical algorithms. These algorithms, which have parameters, change when these sensitivity parameters of mathematical models change. This change in sensitivity can lead for the better, or maybe for the worse. The construction of a mathematical model is usually accompanied by problems in calculating the influence of inputs (other names: argument or factor). These problems are solved in the field of mathematics, which is called sensitivity analysis of mathematical models. To solve the problem of finding the sensitivity of mathematical models, the author proposes to find a criterion that allows not directly, but indirectly to determine the sensitivity. This criterion is derived on the basis of mathematical logic, and its experimental confirmation is also carried out. Further in the article, using a new criterion, one example is the best sensitivity of computer systems. In the article there is a proof of the criterion using the Monte Carlo method.

Label the ten vertices of a hexagonal half-cube with digits 0, 1, 2, …, 9 (using each digit exactly once) such that the induced labels of the six faces (other than the hexagon), given by the sums of the labels of the vertices around those faces, are all Fibonacci numbers. We want a complete list of all solutions to the puzzle using mathematical logic, without a complete search of all permutations of the digits. The purpose of this paper is to inspire logical reasoning.

This research aims to determine the feasibility of the monopoly media "MAK (FUN MATHEMATICS) ROUND" made from loose parts for children aged 5-6 years. This research is research using research and development methods or what is called Research and Development (R&D) using the ADDIE development model. The ADDIE instructional model is an instructional process that consists of five phases, namely analysis, design, development, implementation and evaluation. The subjects of this research were group A at Darul Hikmah Kindergarten, totaling 10 children consisting of 5 boys and 5 girls. In this research, media validation and observation validation of learning results were carried out first by material experts and media experts, after that the validator produced an evaluation of the media and observation sheets used. The aim is to test the suitability of the media used. The research instrument used in this research is an observation sheet that has been validated by experts. The observation sheet contains an assessment based on indicators of achievement in the development of mathematical logic in children in group A2. The indicators of the development of mathematical logic studied are knowing simple classifications, knowing numbers, knowing arithmetic operations, knowing geometric shapes. Learning media with the monopoly game MAK ROUND using loosepart media which was developed for group A2 children at DARUL HIKMAH Kindergarten has been validated by experts and received a percentage score of 92.72%. This shows that the MAK ROUND monopoly is declared worthy of being tested. Before being given treatment, the average acquisition of mathematical logic skills was below average, namely 66.8% and was declared incomplete. This means that children's mathematical logic is still low. After being given treatment, the average gain in mathematical logic skills in group A2 children increased to 84.7%. This shows that learning media using the MAK ROUND monopoly game is effective in improving mathematical logic skills in group A children aged 5-6 years.

The paper considers the problem of applying GAN-technology in intelligent domain environments (IDEs) for the need to structure large amounts of data and generate initial knowledge. Obtaining new knowledge, which is not explicitly formed by experts, based on available data is an important aspect. The purpose of the study is to determine the features of GAN-technology in IDEs, their close integration with the system of concepts of the subject area expressed in the form of an ontology, the development, use and development of which can be considered as support for the intelligence and development of IDEs as a system. The correlation of cognitive and semantic processes of IDEs is studied to determine the ontological basis of the possibilities of ensuring the evolutionary properties and adaptability of creating the structure and training of neural networks (NN) as NP-complex tasks. The main difference of the study is the cognitive-semantic analysis based on the theory of categories, mathematical logic and universal algebra, relational algebra, namely, the transformation of the ontological dictionary, ontological constructions in open languages of knowledge representation, which makes it possible to apply promising methods based on metaheuristics, the mechanism of which can be represented by a problem-independent high-level algorithmic structure in the form of a set of guiding principles or strategies. GAN-technologies in IDEs are defined as an ontological basis, taking into account the fact that evolutionary properties are taken into account in optimization and adaptability methods. Metaheuristics, based on the metaphor of a natural or artificial process, as the basis for a learning scheme for different groups of features, is an effective basis for solving specific problems of evolutionary origin.

The Universality, Parameter, and Recursion Theorems are three foundational results of classical computability theory. We show how these theorems can be programmatically illustrated and partially validated in Lisp. Our programs can be used as supplementary materials to texts on theoretical computer science, mathematical logic, or metamathematics.

Assessing conceptual understanding in mathematics remains a persistent challenge for educators, as traditional assessment methods often prioritize procedural fluency over the complexity of connections between mathematical ideas. Consequently, these methods frequently fail to capture the depth of students’ conceptual understanding. This paper addresses this gap by developing and applying a novel rubric based on the Structure of Observed Learning Outcomes (SOLO) Taxonomy, designed to classify student responses according to demonstrated knowledge capacity and cognitive complexity. The rubric introduces transitional levels between the main SOLO categories and includes provisions for evaluating unconventional solutions, enabling a more nuanced assessment of student work based on knowledge depth and integration. The rubric was constructed through an analysis of the conceptual knowledge components required to solve each problem, validated by expert review, and guided by criteria aligned with SOLO level classifications. It also incorporates qualitative feedback to justify each SOLO level assignment. Using this rubric, the study analyzed responses from 57 first-year undergraduate students—primarily chemistry and computer science majors at a private university in the Philippines—to test items on linear approximations and the Extreme Value Theorem. Interrater reliability was established through weighted Cohen’s kappa coefficients (0.659 and 0.667 for the two items). The results demonstrate the rubric’s capacity to differentiate levels of conceptual understanding and reveal key patterns in student thinking, including reasoning gaps, reliance on symbolic manipulation, and misconceptions in mathematical logic. These findings underscore the value of the SOLO Taxonomy in evaluating complex and relational thinking and offer insights for enhancing calculus instruction. By emphasizing the interconnectedness of mathematical ideas, the study highlights the potential of conceptually oriented assessments to foster deeper learning and improve educational outcomes. Furthermore, the rubric’s adaptability suggests its applicability beyond calculus, supporting a broader shift toward concept-focused assessment practices in higher education.

The research purpose is for developing effective mathematical logic learning model to early childhood through play activities using natural material media. This model is designed to stimulate children's logical thinking and mathematical abilities by utilizing natural materials such as shells, seeds, banana fronds, leaves, and stones as concrete and engaging learning media. Function of those materials is hope for enhancing children's interest and motivation in learning mathematics while considering their cognitive development stages comprehensively. The research method employed is a development research approach with stages of design, validation, and trial of the developed learning model. Validation is conducted by experts in education and early childhood learning to assess the feasibility of the model, while trials involve teachers and students at TK Negeri 1 Dharma Wanita Desa Eti, SBB Regency. The results indicate that this learning model is valid and practical for use, and it positively influences the improvement of children's mathematical logic abilities. These findings provide significant contributions for make developing of enjoyable also effective mathematics learning in early childhood education with a play-based approach using natural media. Teachers and educators can adopt this model to create an interactive learning environment that aligns with children's developmental characteristics. Additionally, the use of natural material media also supports children's awareness of their surrounding environment. Therefore, this model is a viable alternative to be developed and implemented in early childhood education.

Background: Using Boolean algebra to assist in the diagnosis of hematologic disorders involves applying logical operations (AND, OR, NOT, etc.) to symptoms, lab values, and clinical findings to arrive at probable diagnoses. Aim: This study used Boolean algebra (mathematical logic) to calculate the diagnosis of hematologic disorders. Results: Each lab value and clinical finding was encoded as a Boolean variable. The solution of the Boolean equations was risking the of hematologic disorders. Conclusion: Boolean algebra can be used to precisely calculate the diagnosis of hematologic disorders.

Mobile scaffolding is essential in construction but presents significant safety risks, particularly falls from height (FFH) due to improper use and insufficient monitoring. While prior research has identified hazards, it often lacks robust, actionable solutions, especially regarding the comprehensive analysis of worker behaviors and the spatial context. This study proposed a computer vision-based safety monitoring system that leverages depth cameras for accurate spatial assessments and incorporates temporal conditions to reduce false alarms. The proposed system extends object detection algorithms with mathematical logic derived from safety rules to classify four key unsafe conditions related to safety helmet use, guardrail and outrigger presence, and worker overcrowding on mobile scaffolds. A diverse dataset from multiple sources enhances the model’s applicability to real-world scenarios, while a status trigger module verifies worker behavior over a 3 s window, minimizing detection errors. The experimental results demonstrate high precision (0.95), recall (0.97), F1-score (0.96), and accuracy (0.95) for safe behaviors, with similarly strong metrics for unsafe behaviors. The qualitative analysis further confirms substantial improvements in worker position detection and safety compliance using 3D data over 2D approaches. These findings highlight the effectiveness of the proposed system in improving mobile scaffolding safety, addressing critical research gaps, and advancing construction industry safety standards.