Related papers: Integral Calculus of One-Dimensional Functions: Pe…
This article describes a curricular innovation designed to help students experience authentic physics inquiry with an emphasis on computational modeling and scientific communication. The educational design centers on a new type of…
The Iltis project provides an interactive, web-based system for teaching the foundations of formal methods. It is designed with the objective to allow for simple inclusion of new educational tasks; to pipeline such tasks into more complex…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the…
In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
Students' answers to tasks provide a valuable source of information in teaching as they result from applying cognitive processes to a learning content addressed in the task. Due to steadily increasing course sizes, analyzing student answers…
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine…
The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
Charts provide visual representations of data and are widely used for analyzing information, addressing queries, and conveying insights to others. Various chart-related downstream tasks have emerged recently, such as question-answering and…
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research…
Large-enrollment university courses face persistent challenges in providing timely and scalable instructional support. While generative AI holds promise, its effective use depends on reliability and pedagogical alignment. We present a…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.