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.

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…

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 Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

A deficit perspective is a propensity to locate the source of academic problems in deficiencies within students, their families, their communities, or their membership in social categories (such as race and gender). While the deficit perspective is a common topic of discussion in K-12 mathematics education, it is a much rarer topic of discussion…

Mentoring undergraduate students in research is both rewarding and challenging. In this paper we present how we established a summer Research Experience for Undergraduates (REU) program in the mathematical sciences at Michigan State University. A goal of our REU is to include students who are at an early stage of their study of mathematics. We…

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as…

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Over the past decade there has been a dramatic increase in undergraduate research activities at colleges and universities nationwide. However, this comes at a time when budgets are being tightened and some institutions do not have the resources to pursue new initiatives. In this article we present some ideas for obtaining funding and support for…

This article provides an overview of the scholarship of teaching and learning (SoTL) in mathematics. It describes the origins of SoTL in higher education and distinguishes SoTL from good teaching, scholarly teaching, and mathematics education research. It includes a widely adopted taxonomy of SoTL questions and presents several examples of SoTL…

The decreasing number of U.S. citizens with advanced degrees in the mathematical sciences is a growing concern. Also of concern is the small number of advanced degrees in the sciences going to African Americans, Latinos, and women. Several Research Experience for Undergraduates (REU) programs have been developed to address these issues. In this…

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)