Related papers: Assumption Digging in Euclidean Geometry
The Lecture-Tutorials for Introductory Astronomy have been designed to help introductory astronomy instructors actively engage their students in developing their conceptual understandings and reasoning abilities across a wide range of…
The invention of non-Euclidean geometries is often seen through the optics of Hilbertian formal axiomatic method developed later in the 19th century. However such an anachronistic approach fails to provide a sound reading of Lobachevsky's…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…
We introduce Voevodsky's univalent foundations and univalent mathematics, and explain how to develop them with the computer system Agda, which is based on Martin-L\"of type theory. Agda allows us to write mathematical definitions,…
Theory of Computing (ToC) is an important course in CS curricula because of its connections to other CS courses as a foundation for them. Traditional ToC course grading schemes are mostly exam-based, and sometimes a small weight for…
In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…
Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from…
Basic programming and algorithm learning is one of the compulsory subjects required for students majoring in computers. As this lesson is knowledge base, it is very important and essential that before learn programmings languages students…
Traditional tests are not effective tools for diagnosing the content and structure of students' knowledge of physics. As a possible alternative, a set of term-association tasks (the "ConMap" tasks) was developed to probe the…
Current investigations into pedagogical goals of introductory algebra-based physics students at the University of Central Arkansas, by learning orientation towards an in-class metacognitive group problem solving task, seek to determine…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the…
Presents a differentiated teaching proposal that allows the student to be the agent in the construction of knowledge, overcoming the difficulties that Mathematics presents. Aiming to understand how the use of statistical tools can…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
Conceptual modeling is a strongly interdisciplinary field of research. Although numerous proposals for axiomatic foundations of the main ideas of the field exist, there is still a lack of understanding main concepts such as system, process,…
This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the…