In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

Gateway courses are foundational, college-level courses that apply to a student's program of study or to a college's general education requirements. These courses are typically considered first-year or lower-division courses and serve as a basis for more advanced studies. Research has demonstrated that completing gateway courses in two key…

For teachers to provide students with meaningful instruction in area measurement, teachers need robust understandings of area. Here, I describe two cycles of a "lesson experiment" used to investigate prospective teachers' understandings of area units in an undergraduate mathematics class. For each cycle, I collected and analyzed the…

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…

While assessment, curricular, and pedagogical reforms have improved overall success rates in college math courses, they have been less effective in closing racial equity gaps and fostering equitable classroom experiences for racially minoritized students. Following the insights of critical race math scholars, we argue that racial inequity persists…

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…

The activity described in this paper is based on the idea that reading an introductory undergraduate mathematics text is similar to reading instructions. I want my students to think about how to read when the goal is to learn to complete a task. I give them written instructions for doing a card trick and ask them to complete the trick. The…

We describe a lecture-free problem-solving Mathematical Communication and Reasoning (MCR) course that helps students succeed in the Introduction to Advanced Mathematics course. The MCR course integrates elements from Uri Treisman's Emerging Scholars workshop model and Math Circles. In it students solve challenging problems and form a supportive…

Nationwide, many students fail to complete the key mathematics courses that are required for most STEM majors, including Precalculus. This paper describes the rationale, implementation, and impact of the redesign of Precalculus at one regional west coast institution. Prior to the redesign, pass rates in Precalculus were modest (75.8% of all…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

We introduce a ruler and compass activity designed around Islamic Geometry and provide a detailed description of the various components of the activity along with ideas for students exhibitions in both digital and print form. In our experience, this activity helps students to "buy into" actively doing mathematics, making it an ideal…

In this paper we provide a description of the project DrIVE-MATH, highlighting the main goals, intellectual outputs, outcomes, the involved partners, and activities and reports from the three-years' project. At the end we discuss the impact of the new proposed Education models at various levels, from students, to HEIs, to stakeholders.

We describe an organizing principle for online learning materials; we term coherently organized digital exercises and expositions. Larger in scale than individual lessons but smaller than a programme of study, this innovation in instructional practice is increasingly guiding our thinking in the development of university mathematics courses.…

We show that the total distance traveled by an under-damped oscillating spring mass system with sinusoidal displacement results in a nice, closed-form expression.