We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

After the COVID-19 pandemic was over, the teaching and learning process in the world of education underwent several changes. The COVID-19 pandemic forced the global learning community to transition within a very short period of time from the traditional in-class method of learning to a mode of online learning. After the pandemic started to…

In this paper, a problem set activity focused on understanding and applying unsupervised and supervised chemometric methods for the analysis of biodiesel-diesel blended fuels is described. This problem set was utilized in two upper-level analytical elective courses aimed for junior and senior level students. The data set consists of peak areas…

Flipped classrooms have been shown to be useful in both introductory and advanced computational Earth Science courses. However, to date they have not been implemented in advanced level non-computational courses. Here we assess a three-year study into the use of flipped classroom techniques in a fourth year undergraduate Mineral Deposits class. One…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by…

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

Testing is a highly important tool, used ubiquitously in academia, to assess student comprehension and understanding of material. Unfortunately, the emphasis placed on test grades has resulted in a modern epidemic of test-related anxiety, which can have adverse health effects on students. Over time, novel testing strategies have been developed to…

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

The study quantitatively explores the differential impact of a Flipped Classroom approach (FC) on specified learning outcomes in an Advanced Auditing and Assurance class for a one-year master's in accounting Programme. It uses a dataset from a Ghanaian university to compare a flipped-classroom approach to a traditional teaching approach. The…

Purpose: Interest in using popular movies in higher education has flourished, but determining their actual impact remains tricky. Some studies suggest these movies can positively affect student satisfaction, yet many criticize this method as ineffective or lazy. Our study compared two ways of using popular movies -- watching them in class versus a…

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…