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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 to allow for this type of closing activity and give suggestions for how to create an epic finale.

This article discusses a pedagogical technique for utilizing breakout rooms for small group discussions and synchronous drawing features in Zoom to create crowdsourced solutions to mathematical problems that involve graphing or visualization. Students begin with specific examples and then move quickly to the development of a more general understanding of the concepts. The process was primarily used in synchronous settings, although certain aspects could be utilized in asynchronous settings. The method discussed in this paper incorporates active learning techniques into the online classroom, helps students build community by working in groups, and increases student engagement in the online class meetings.

Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study into environmental and sustainability issues in the history of Easter Island. Using results that appeared in recent journal articles, students investigate the date of arrival of early settlers, the impact they had on natural resources through population growth as well as through the introduction of non-native species, and the effect of European diseases on the population. (Contains 1 figure.)

We describe a set of manipulatives developed to help students learn three-dimensional Cartesian, cylindrical, and spherical coordinate systems. (Contains 6 figures.)

We study the dynamics of a family of polynomial functions and the relationship to the dynamics of a related entire transcendental family of functions. As the degree of the polynomial approaches infinity, the polynomial functions converge uniformly on compact sets to a function that is a product of a power map and the exponential function. The advantage to the approach in the paper is that we can use the relatively simple, although high degree, polynomial functions to aid our understanding of the dynamics of the related transcendental entire function. We study properties both in the dynamical plane as well as in the parameter plane. [ABSTRACT FROM AUTHOR]

In this paper, we investigate parametrized families of elliptic functions on real rectangular lattices. Although these functions have at most four critical values, we prove that they have at most one attracting or parabolic cycle of Fatou components. We find some families for which the Julia set is always the entire sphere. [ABSTRACT FROM AUTHOR]