Interdisciplinarity and Inclusivity: Natural Partners in Supporting Students

Mathematics Across the Sciences is an applications-based course designed to strengthen students’ mathematical skills in preparation for calculus or for a major in the sciences. Its development relied heavily on input from faculty members in several science departments. This article describes the course; many of the scientific applications taught; pedagogical strategies; and scholarship on inclusion, equity, and diversity in education. These descriptions make clear that the goals of inclusion and academic excellence are intertwined, and an interdisciplinary approach can help each to improve

Senior Seminar: Across a Department and Across the Years

The Department of Mathematics at Bates College has offered a senior seminar capstone course for over a dozen years. In this article, we discuss the coexistence of seminar and thesis, our other capstone experience. We discuss in detail the goals of our seminar, various ways we structure the seminar to accomplish those goals, and methods of assessment. We provide a detailed look into a recent seminar, and we offer a variety of strategies for implementing such a capstone course successfully

Blogs Hit Classroom: Students Start Reading

A professor and student have a conversation about using blogs as part of a mathematics class. The goals of using a blog include giving students a motivation to read ahead in their textbooks, providing another means of communication between students and the professor, and creating a space for students to write about mathematics. The article also poses behind-the-scenes technical questions to be considered in selecting and implementing blogging software

Determining If Two Ellipsoids Share the Same Volume

An analytical method is presented for determining if two ellipsoids share the same volume. The formulation involves adding an extra dimension to the solution space and examining eigenvalues that are associated with degenerate quadric surfaces. The eigenvalue behavior is characterized and then demonstrated with an example. The same method is also used to determine if two ellipsoids appear to share the same projected area based on an oberver\u27s viewing angle. The following approach yields direct results without approximation, iteration, or any form of numerical search. It is computationally efficient in the sense that no dimensional distortions, coordinate rotations, transformations, or eigenvector computations are needed

Determining If Two Solid Ellipsoids Intersect

An analytical method is presented for determining if two ellipsoids share the same volume. The formulation involves adding an extra dimension to the solutions space and examining eignevalues that are associated with degenerate quadric surfaces. The eigenvalue behavior is characterized and then demonstrated with an example. The same method is also used to determine if two ellipsoids appear to share the same projected area based on an observer\u27s viewing angle. The following approach yields direct results without approximation, iteration, or any form of numerical search. It is computationally efficient in the sense that no dimensional distortions, coordinate rotations, transformations, or eigenvector computations are needed

Mathematical Epidemiology Goes to College

Every year waves of illnesses sweep through college campuses. This seems a natural result of sleep-deprived college students living, working, and playing together. Such outbreaks suggest questions: How many people will become infected? How can illnesses be contained? And crucially: How is mathematics involved? Mathematical epidemiology is the study of modeling diseases, often using compartmental models. We can use such models to learn from past outbreaks and investigate theoretical future outbreaks. In this article we present models that were inspired by two real-life outbreaks at a small residential college campus: H1N1 influenza in 2009 and, surprisingly, mumps in 2016

Engaging Crisis: Immersive, Interdisciplinary Learning in Mathematics and Rhetoric

This paper describes an interdisciplinary activity that crosses over between Mathematics and Rhetoric. The professors who created this activity both sought active-learning opportunities for their students, a sense of realism--even urgency--in what can otherwise be perceived as abstract material, and a meaningful liberal arts experience. Evidence of the power of this experience is seen in the media coverage, both from our college and from the Portland Press Herald newspaper. Both courses described in this paper are at the elective level, taken by majors or minors in their respective disciplines. Students have moderate to extensive backgrounds in their subject areas. However, adapted versions of our activity could involve students at more introductory levels

Modeling Pitch Trajectories in Fastpitch Softball

The fourth-order Runge–Kutta method is used to numerically integrate the equations of motion for a fastpitch softball pitch and to create a model from which the trajectories of drop balls, rise balls and curve balls can be computed and displayed. By requiring these pitches to pass through the strike zone, and by assuming specific values for the initial speed, launch angle and height of each pitch, an upper limit on the lift coefficient can be predicted which agrees with experimental data. This approach also predicts the launch angles necessary to put rise balls, drop balls and curve balls in the strike zone, as well as a value of the drag coefficient that agrees with experimental data. Finally, Adair’s analysis of a batter’s swing is used to compare pitches that look similar to a batter starting her swing, yet which diverge before reaching the home plate, to predict when she is likely to miss or foul the ball

A Mathematical Analysis of the Dynamics of Prion Proliferation

How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data