Adam Starr | Searcharxiv

arXiv2017

Towards a Social Virtual Reality Learning Environment in High Fidelity

Virtual Learning Environments (VLEs) are spaces designed to educate students remotely via online platforms. Although traditional VLEs such as iSocial have shown promise in educating students, they offer limited immersion that diminishes learning effectiveness. This paper outlines a virtual reality learning environment (VRLE) over a high-speed network, which promotes educational effectiveness and efficiency via our creation of flexible content and infrastructure which meet established VLE standards with improved immersion. This paper further describes our implementation of multiple learning modules developed in High Fidelity, a "social VR" platform. Our experiment results show that the VR mode of content delivery better stimulates the generalization of lessons to the real world than non-VR lessons and provides improved immersion when compared to an equivalent desktop version.

cs.HC↗

arXiv2016

$p$-adic quotient sets

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.

math.NT↗