Related papers: An open day in the metric space
Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is…
The pose of a rigid object is usually regarded as a rigid transformation, described by a translation and a rotation. However, equating the pose space with the space of rigid transformations is in general abusive, as it does not account for…
Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length…
The Explorations in Statistics Research workshop is a one-week NSF-funded summer program that introduces undergraduate students to current research problems in applied statistics. The goal of the workshop is to expose students to exciting,…
We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the…
One of key goals of contemporary physics (and, realistically, STEM) education is to develop students' science literacy and critical thinking skills. In this paper, we present the construction and use of several versions of a simple…
The physics that underpins modern technology is based on Einstein's theories of relativity and quantum mechanics. Most school students complete their compulsory science education without being taught any of these Einsteinian concepts. Only…
Measurement uncertainty and experimental error are important concepts taught in undergraduate physics laboratories. Although student ideas about error and uncertainty in introductory classical mechanics lab experiments have been studied…
Physics outreach programs provide a critical context for informal experiences that promote the transition from new student to contributing physicist. Prior studies have suggested a positive link between participation in informal physics…
As is well known, classical systems approximate quantum ones -- but how well? We introduce a definition of a "distance" on classical and quantum phase spaces that offers a measure of their separation. Such a distance scale provides a means…
This paper will present a model for pedestrian motion by defining a spacetime metric. This model considers the factors that are effective in the movement of pedestrians (such as obstacles, walls and other pedestrians) by defining a proper…
Measurement uncertainty plays a critical role in the process of experimental physics. It is useful to be able to assess student proficiency around the topic to iteratively improve instruction and student learning. For the topic of…
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…
We investigate the utility of two qualitative measures of equity. Our data are videos of groups of first-generation and Deaf or hard-of-hearing students in a pre-matriculation university program designed to help them persist in STEM fields…
Temporary school closures caused by the Covid-19 pandemic have posed new challenges for many teachers and students worldwide. Especially the abrupt shift to online distance learning posed many obstacles to be overcome and it particularly…
Our main purpose here is to study some qualitative aspects of space and time. These include the notion of space and time regarded as the containers of respectively bodies and events, the divisibility of space, and the unrepeatability of…
Technology has changed both our way of life and the way in which we learn. Students now attend lectures with laptops and mobile phones, and this situation is accentuated in the case of students on Computer Science degrees, since they…
What is the "right way" to define dimension? Mathematicians working in the early and middle $20$th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these…
The concept of Type-2 soft sets had been proposed as a generalization of Molodstov's soft sets. In this paper some shortcomings of some existing distance measures for Type-1 soft sets have been shown and accordingly some new distance…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…