When this author first began to take classes in theater and comedy improvisation, his motives were largely creative and social, though there was some supposition that his mathematics teaching (at a community college) could benefit as well. Students are known to tout their favorite teachers as "funny." Taking improv classes would presumably loosen…

The usual definition of the Riemann integral as a limit of Riemann sums can be strengthened to demand more of the function to be integrated. This super-Riemann integrability has interesting properties and provides an easy proof of a simple change of variables formula and a novel characterization of derivatives. This theory offers teachers and…

The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form y = u[subscript 1]y[subscript 1] + u[subscript 2]y[subscript 2], a sum of function products using solutions to the homogeneous equation y[subscript 1] and…

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own…

In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities.…

Students often complain that the rules of mathematics are being changed. A short conversation between a professor and a class of college algebra students dramatizes this in the realm of complex numbers and the legal realm of speed limits.

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)

In this article, the author describes the development and implementation of a measurement-based group activity designed to support students in understanding the connection between angle magnitude and the shape of the sine function. She explains that the benefit of this activity is that it allows students to build their trigonometric knowledge…

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

The term "flipped" or "inverted" classroom includes a broad range of pedagogical innovations, and has recently received a significant amount of press. Although flipping an entire course might be a more extreme step than most are able to take, we discuss modular ideas for change that can be more easily implemented. This paper…

This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

Distributions are the basis for an enormous amount of theoretical and applied work in statistics. While there are formal definitions of distributions and many formulas to characterize them, it is important that students at first get a clear introduction to this basic concept. For many of them, neither words nor formulas can match the power of a…

In an effort to enhance the quality of education, universities and colleges are developing programs that help faculty and staff internationalize curriculum. These programs will purposefully develop the intercultural perspectives of students. "Curriculum Internationalization and the Future of Education" is a critical scholarly resource…

In this article, I summarize how I present the Rayleigh-Ritz procedure, in a second-semester differential equations course that I teach, and describe some benefits that I believe my students have derived from exposure to this topic. (Contains 3 figures.)