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The article is devoted to a problem of elaboration of the real-time interactive videosystems for accelerated nonverbal cognitive computer and telecommunications. The proposed approach is based on the using of droems (dynamically…
Educational technology has attained significant importance as a mechanism for supporting experiential learning of science concepts. However, the growth of this mechanism is limited by the significant time and technical expertise needed to…
Interleaved practice enhances the memory and problem-solving ability of students in undergraduate courses. We introduce a personalized learning tool built on a Large Language Model (LLM) that can provide immediate and personalized attention…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
An elementary introduction to functional methods and the Schwinger-Dyson equations is presented. Emphasis is placed on practical topics not normally covered in textbooks, such as a diagrammatic method for generating equations at high order,…
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces…
Syllabus is essentially a concise outline of a course of study, and conventionally a text document. In the past few decades, however, two novel variations of syllabus have emerged, namely "the Graphic Syllabus" and "the Interactive…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
A pedagogical approach of problem-based learning with embedded librarianship in several undergraduate mathematics courses is implemented in this educational research. The students are assigned to work on several projects on various…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
In-context learning (ICL) allows transformer-based language models that are pre-trained on general text to quickly learn a specific task with a few "task demonstrations" without updating their parameters, significantly boosting their…
Functional programming represents a modern tool for applying and implementing software. The state of the art in functional programming reports an increasing number of methodologies in this paradigm. However, extensive interdisciplinary…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
The Imaging Computational Microscope (ICM) is a suite of computational tools for automated analysis of functional imaging data that runs under the cross-platform MATLAB environment (The Mathworks, Inc.). ICM uses a semi-supervised…
The PICUP Collection of Exercise Sets (https://www.compadre.org/PICUP/exercises/) contains over 60 peer-reviewed computation-infused activities for use in various physics courses from high school through graduate study. Each Exercise Set…