We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Teaching mathematics by project-based learning (PBL) method on the use of educational technology offers an innovative teaching pedagogy at college. The "World Culture Art Created with Calculus Graphs of Equations" poster project was designed by the first author and was completed in the pilot Calculus course during the spring 2016…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

The number "e" is one of those fascinating numbers whose properties are of special interest to mathematicians. In this article, the author aims to provide a method of introducing a visual concept of the number "e". These ideas are suitable for secondary school and undergraduate tertiary students. The main concept involves areas…

We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of "National LambdaRail". We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the "National LambdaRail" network. Finally, we give…

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Three examples of the use of intuitive geometrical ideas in clarifying analytical results. (MM)