I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

As an often recommended but under-utilized pedagogical strategy, writing in mathematics has many benefits for students. However, creating and grading worthwhile writing projects can be more time-consuming than utilizing more traditional forms of assessment. This paper provides a concrete example of a writing project prompt, questions, directions,…

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

The Mathematical and Theoretical Biology Institute (MTBI) is a successful summer research experience for undergraduates, with a strong record of mentoring Ph.D. graduates, particularly, underrepresented minority students. However, the MTBI program was designed for education in research, not for research in education, and the mechanisms of the…

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

In this paper we discuss why a senior capstone course is the perfect setting to reward graduating seniors with some of the more fun and interesting aspects of advanced mathematics. We provide a beginner's list of topics to consider as well as a method of implementing these tidbits outside of the classroom if time is an issue.

Math in the City is an interdisciplinary mathematics course offered at University of Nebraska-Lincoln in which students engage in a real-world experience to understand current major societal issues of local and national interest. The course is run in collaboration with local businesses, research centers, and government organizations, that provide…

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Freely rising air bubbles in water sometimes assume the shape of a spherical cap, a shape also known as the "big bubble". Is it possible to find some objective function involving a combination of a bubble's attributes for which the big bubble is the optimal shape? Following the basic idea of the definite integral, we define a bubble's surface as…

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs.…

This project served as a capstone event for the United States Military Academy sophomore Calculus II course. This multi-disciplinary problem-solving exercise motivated the link between math and biology and many other fields of study. The seven-lesson block of instruction was developed to show students how mathematics play a role in every…