When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Physics, even though it is guided by simple principles, tends for many topics to be obscured in the mathematics redundancy. MATLAB®, as interactive software for computer algebra, has already had an important impact on the way physics is taught by educators. It has also had a substantial impact on the way research is performed by students to…

Currently, there is a rapid development of artificial intelligence systems that can solve and explain the solution of mathematical problems in the same way as students do. The problem of organizing interaction of artificial and human intelligence which does not lead to the degradation of the student's thinking skills arises. The article proposes…

We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are equations where the unknown variable appears under at least one square root and where two steps are needed to…

In this document, we search for and define an infinite limit of sequences that is correct and accepted by the mathematical experts, the final purpose of which is to analyze its phenomenology, in Freudenthal's sense. To make the choice, experts were consulted on two issues. The first one was not decisive because of the effect that the divergence…

The mathematical method of linear equations involving the coefficients of the equation of a chemical reaction can be used to balance the equation of nearly every chemical reaction. For its application, only the rules of simple algebra need be known. Hence, the method could even be used by students of an elementary chemistry course.

In the paper, the authors propose a variant of the mathematical model for justifying the optimal ratio of researchers of different categories to conduct scientific research of the highest possible quality in conditions of limited resources. The discrepancy is formulated between the quality of scientific research and the restriction on financial…

The ideal gas law, "PV = nRT," is one of the simplest physical laws in nature that is introduced to students as early as in high school and first year in college. In this equation, "P" stands for pressure, "V" is the volume, "n" is the amount expressed in mole, "T" is the temperature in Kelvin…

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary…

In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in…

Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and…

In both general chemistry and analytical chemistry courses, students are introduced to the concept of predominant species in solution when discussing acid/base chemistry. Speciation diagrams are often used to illustrate the concept and predict the relative abundance of species in solution. Herein, we describe a laboratory experiment for an…

Commonly used methods to simulate the oxidation-reduction (redox) titration curves include the three-step method and the rigorous method. The simple three-step method simulates the redox titration curve with the assumption that the reaction is complete, which is widely used in undergraduate quantitative analysis courses. For the rigorous…

Composite scores are an exceptionally important psychometric tool for behavioral science research applications. A prototypical example occurs with self-report data, where researchers routinely use questionnaires with multiple items that tap into different features of a target construct. Item-level missing data are endemic to composite score…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.