In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and…

This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where…

This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors.…

The University of Tennessee has a Master of Mathematics (M.M.) program for secondary educators interested in college-level teaching. The program includes a capstone course on topics related to college-level teaching and can be thought of as a kind of professional development which allows secondary educators to explore options for their careers.…

This article describes a major capstone course centered on public writing, whose underlying pedagogical principles are transferable to courses across the curriculum. The course aims to strengthen students' mathematical agency and their ability to effectively communicate mathematical ideas. In its unique format, students repeatedly take turns…