A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…

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.

Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems.…

We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of…

We present a concrete situation where there is a difference between the theoretical security of a cipher and its limitations when implemented in practice. Specifically, when entering a PIN, smudges on the keypad substantially reduce its security. We show how the number of possible keys in the presence of the "smudge attack" can be…

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…

The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11%…

The Department of Mathematics & Statistics at Pomona College has long worked to create an inclusive and welcoming space for all individuals to study mathematics. Many years ago, our approach to the lack of diversity we saw in our majors was remediation through programming, which sought to ameliorate student deficits. More recently, however, we…

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…

The article describes how to derive the equation of curves that are obtained from string art. Conversely, if the equation of a curve is given, one can find the relation between the intercepts either on a rectangular axes, skewed axis, or a circle to trace out these curves. Some of these curves can be easily traced out using the string art if they…

This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model…

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into…

This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…