In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or…

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…

This article examines the use of the computer algebra system SAGE for undergraduate student research projects. After reading this article, the reader should understand the benefits of using SAGE as a source of research projects and how to commence working with SAGE. The author proposes a tiered working group model to allow maximum benefit to the…

The Applied and Industrial Mathematics program partners applied mathematics students with businesses, governments, laboratories, and agencies to solve real problems. We will discuss the logistics of the program and give advice on starting and running similar programs. We also give a detailed example of a specific project, namely our work with the…

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

This article describes how the author used a wiki-based website in a real analysis course, and assesses its effectiveness. The wiki was used to post course materials, maintain a forum, enable students to write collaborative projects, and enable students to develop a glossary of important terms. The wiki proved to be very successful; it facilitated…

Presented are classroom-tested examples of instructional materials (courseware) for ordinary differential equations using the software package PHASER. All of the examples include in-class demonstration techniques and commentaries for instructor use, student homework and laboratory exercises, and suggestions for in-class examination questions. (JJK)