Anaerobic digestion is a complex biochemical process that is represented by the stoichiometric Buswell's equation. Buswell's equation is the study of the interface among biochemistry, mathematics, and chemistry. Students often have difficulty in understanding the nature of biochemical stoichiometry. Buswell's equation is significant for the…

Bayesian methods to infer model dimensionality in factor analysis generally assume a lower triangular structure for the factor loadings matrix. Consequently, the ordering of the outcomes influences the results. Therefore, we propose a method to infer model dimensionality without imposing any prior restriction on the loadings matrix. Our approach…

Mathematical self-efficacy refers to an individual's belief in their ability to successfully perform tasks and solve problems in mathematics. This Snapshot examines gender differences in mathematical self-efficacy and the levels of confidence that students feel in doing a range of formal and applied mathematics tasks. It also examines the extent…

Most textbooks and lecturers present Michaelis-Menten kinetics using the equation v = V[subscript max][S]/(K[subscript m] + [S]). There are advantages to presenting this relationship in a slightly different form, namely v = V[subscript max]/{1 + (K[subscript m]/[S])}. We articulate advantages for single-substrate reactions and extend the formalism…

This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

Transfer of structural math knowledge to physics is difficult for students. While research suggests various improvement techniques, enhancing parallelism of algebraic structures used in physics to those studied in mathematics courses seems underrepresented. This paper proposes an alternative way of introducing wave functions as a set of parametric…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

The question of the sources of electric and magnetic fields and their causes has been discussed extensively in the literature over the last decades. In this article, we approach this problem from the unified treatment of electromagnetic fields emphasizing the role of their sources in accordance with the cause-effect relationships. First, we…

Oblique angle collisions of two penny coins on a smooth, horizontal surface were filmed with a video camera to investigate the physics of the collision process. If one of the coins is initially at rest, then the two coins emerge approximately at right angles, as commonly observed in billiard ball collisions and in puck collisions on an air table.…

The Young-Laplace (Y-L) equation relates the pressure difference across the interface of two fluids (such as air and water) to the curvature of the interface. The pressure rises on crossing a convex interface such as a rain drop and falls on crossing a concave interface such as the meniscus of water in a glass capillary. The relation between…

This article investigates the potential mathematical learning opportunities arising from a digital activity designed to enhance students' comprehension of equations. Employing a commognitive-oriented lens, the analysis explores the potential mathematical discourses that could emerge from students' interactions with a digital scale inspired by the…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

Optimal design of multisite randomized trials leverages sampling costs to optimize sampling ratios and ultimately identify more efficient and powerful designs. Past implementations of the optimal design framework have assumed that costs of sampling units are equal across treatment conditions. In this study, we developed a more flexible optimal…

This article introduces an innovative teaching and learning tool called "Edelman Gamblegrams" that aims to help medical learners better understand disorders related to water/plasma tonicity homeostasis, i.e., hyponatremia and hypernatremia. Gamblegrams, named after physician James L. Gamble, are bar diagrams displaying the relative…

Slamecka and McElree (1983) and Rivera-Lares et al. (2022), like others before them, factorially manipulated the number of learning trials and the retention interval. The results revealed two unsurprising main effects: (a) the more study trials, the higher the initial degree of learning, and (b) the longer the retention interval, the more items…