Mathematics and Education in Mathematics

This paper presents a mathematics-focused STEAM workshop grounded in the cultural and historical context of the Varna Chalcolithic Necropolis (5th millennium BC). The proposed model organises learning around the examination of historical–archaeological hypotheses through mathematical reasoning. A set of interdisciplinary tasks has been developed to engage students with authentic data, including t…

We give a new conjecture on D_{2,k}, where D_{q,k} denotes the largest d such that a linear code of dimension k with minimum weight d meeting the Griesmer bound does not exist. We also prove that D_{2,11} = 1632, which yields that our conjecture is valid for dimensions k <= 11.

The article examines opportunities for software-based solving of economic problems by students at the upper-secondary level. A financial resource management problem and its optimal solution are presented. The problem is solved by different groups of students using traditional software methods, and the use of artificial intelligence (AI) is introduced to support the development of students’ analyt…

The paper is a short overview of the known applications of codes over a ring of integers modulo a given positive integer to error controlling in digital communications and storage. The presented successful applications demonstrate that integer codes with their simple encoding and decoding are at least commensurable with other codes with similar parameters. Moreover in many situations they are pre…

This study proposes an innovative approach to detecting structural matches in programming codes, which addresses the fundamental limitation of existing methods – their sensitivity to syntactic changes while maintaining logical equivalence. A hybrid architecture integrating semantic normalization through large language models (LLMs) with multispecies graph representation (AST, CFG, DFG) and embedd…

Professor Stefan Dodunekov made influential contributions across several domains of coding theory, number theory, and algebra. In this survey we focus on three areas in which his scientific interests were particularly substantial. The first two concern families of linear codes meeting the Griesmer bound and the Grey–Rankin bound, which have long served as central benchmarks in the study of optima…

This article marks the 80th anniversary of Prof. Dr. Avram Eskenazi and traces his exceptional scientific and teaching career. As a pioneer in computer education, creator of innovative methods for software quality assessment, with outstanding contributions to the development of software technologies, and a thinker with a bright public position, he left a lasting imprint on the science, education,…

This paper presents a bibliometric analysis of 1,862 research documents (2015–2025) focused on the application of Artificial Intelligence (AI) for Critical Infrastructure (CI) cybersecurity. Data from Scopus and Web of Science were processed using the Bibliometrix R-package. The study quantifies publication dynamics and maps thematic and sector-specific patterns in AI methods applied to OT/ICS/SC…

This study introduces an innovative, game-based approach to teaching specific abstract concepts in Number Theory (prime numbers, the Fundamental Theorem of Arithmetic, and divisibility rule) to middle school students by immersing them in a simplified cryptographic world. The author developed two original educational board games: "The White Hat and the Ancient Key" and "Hacker Duel," which use cus…

It is shown that the ternary extended perfect Golay [12, 6, 6]_3-code can be constructed by the modified GC-construction. For the binary Golay [24, 12, 8]-code this has been shown by us earlier. In particular, the Golay [12, 6, 6]_3-code can be constructed using the GC-construction with the inner codes of length 3 and the outer codes of length 4.

This study proposes a set of techniques for optimizing the performance of hybrid pipelines combining large language models (LLMs) and graph neural networks (GNN) for comparison of program code fragments. On the basis on previous work [1] on semantic normalization and graph embeddings, the main computational bottlenecks are identified and solutions are proposed including parallel processing, dynam…

Current evaluation benchmarks for large language models often conflate genuine reasoning ability with memorization and statistical pattern matching. As a result, high benchmark scores do not necessarily indicate the capacity to induce abstract rules or to reason systematically from limited data. In this paper, we propose a methodological framework for evaluating linguistic reasoning in large lang…

We revisit pivotal aspects of computing the weight distribution of the binary Reed– Muller code R(4, 9) and introduce a verification technique based on the Heninger– Rains–Sloane integrality congruences for Reed–Muller codes. The consistency checks fully confirm the correctness of the distribution obtained in our previous work: “The weight distribution of the fourth-order Reed–Muller code of leng…

This paper summarizes the known results about near-MDS codes proved in the past thirty years. The main focus is put on the problem of determining the value of the function m'(k, q) defined as the maximal length of a near-MDS code of dimension k over the field with q elements. For dimensions k > q +2 we improve the upper bound m'(k, q) <= 2q+k−2 which follows from the nonexistence of maximal…

The paper examines problems illustrating the three main cases of sections of a rotational cone with a plane, solved by the methods of descriptive geometry. The examples are presented in cabinet projection and can be useful in illustrating results achieved by the means of analytical geometry and in teaching descriptive geometry to university students of engineering majors.

We investigate when a maximum distance separable (MDS) code over Fq is also completely regular (CR). For lengths n = q + 1 and n = q + 2 we provide a complete classification of the MDS codes that are CR or at least uniformly packed in the wide sense (UPWS). For the more restricted case n <= q with q <= 5 we obtain a full classification (up to equivalence) of all nontrivial MDS codes: there …

As of early 2026, Artificial Intelligence (AI) has transitioned from an experimental auxiliary tool to a foundational pillar of modern mathematical pedagogy. This paper evaluates the rapid evolution of AI-driven mathematics tools over the academic year 2025–2026, emphasizing the shift toward adaptive, Socratic tutoring systems. We analyze key platforms and tools such as Khanmigo, Mathos AI, and T…

In this article, we show that the minimal vectors of the extremal even unimodular lattices in R^{32} define T-avoiding universally optimal spherical codes for suitable sets T. Moreover, these codes are minimal T-avoiding spherical designs and maximal Tavoiding codes for appropriate choices of T.

Decades of active digitisation of cultural heritage in galleries, libraries, archives and museums (GLAM institutions) have led to the accumulation of vast amounts of openly accessible digital content. Research and education are the two fields in which this content is most frequently used. The strongest connections have been developed with the teaching of history, literature, art, and music, where…