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This study addresses the challenges of tracking and analyzing students' learning trajectories, particularly the issue of inadequate knowledge coverage in course assessments. Traditional assessment tools often fail to fully cover course…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
Knowledge Graphs (KGs) are composed of structured information about a particular domain in the form of entities and relations. In addition to the structured information KGs help in facilitating interconnectivity and interoperability between…
E-learning environments are increasingly harnessing large language models (LLMs) like GPT-3.5 and GPT-4 for tailored educational support. This study introduces an approach that integrates dynamic knowledge graphs with LLMs to offer nuanced…
Knowledge Graphs (KGs) are structured knowledge repositories containing entities and relations between them. In this paper, we study the problem of automatically updating KGs over time in response to evolving knowledge in unstructured…
Knowledge graphs can represent information about the real-world using entities and their relations in a structured and semantically rich manner and they enable a variety of downstream applications such as question-answering, recommendation…
Navigating, visualizing, and discovery in graph data is frequently a difficult prospect. This is especially true for knowledge graphs (KGs), due to high number of possible labeled connections to other data. However, KGs are frequently…
Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal…
The e-book market is currently in a strong upswing. This research study deals with the question which practical uses the e-book format EPUB3 offers for (higher) education. By means of a didactic content analysis, a range of interactive…
Knowledge Graphs (KGs) store information in the form of (head, predicate, tail)-triples. To augment KGs with new knowledge, researchers proposed models for KG Completion (KGC) tasks such as link prediction; i.e., answering (h; p; ?) or (?;…
Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
The current learning systems typically lack the level of metacognitive awareness, self-directed learning, and time management skills. Most of the ontologically based learning management systems are in the proposed phase and those which are…
Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets…
Knowledge Graph Embedding (KGE) aims to represent entities and relations of knowledge graph in a low-dimensional continuous vector space. Recent works focus on incorporating structural knowledge with additional information, such as entity…
Entity alignment (EA) for knowledge graphs (KGs) plays a critical role in knowledge engineering. Existing EA methods mostly focus on utilizing the graph structures and entity attributes (including literals), but ignore images that are…