Mathematics Colloquium

Dr. Kate Melhuish, Texas State University

Abstract

In recent years, professional organizations in the United States have suggested undergraduate mathematics shift away from pure lecture format. However, in the proof-based setting, transitioning to a student-centered class is a complex undertaking that involves managing a number of tensions related to staying authentic to student contributions while promoting the mathematical norms of the discipline. In this presentation, I'll discuss how high leverage teaching practices (HL TPs) (established in the K-12 literature) can be adapted to the proof context in order to help manage these tensions. In particular, I'll focus on a set of abstract algebra tasks that we have been developing as part of an NSF grant, Orchestrating Discussions Around Proof. We will spend some time engaging with the tasks and examining the ways that students approach them. I'll conclude with discussion and illustrations of various HL TPs and how they can support student engagement in the classroom.

Bio Sketch

Dr. Melhuish is an Associate Professor of Mathematics at Texas State University. Their research focuses on the promotion of student-centered classrooms with attention to measures and instructional practices. Dr. Melhuish leads the design and development of the Group Theory Concept Assessment, the Math Habits Instructional Observation Tool (NSF #1814114), and is part of project teams developing proof comprehension tests in real analysis (NSF #1821553) and modelling self-efficacy assessments (NSF #1750813). Additionally, they have served as PI (NSF #1836559) and co-PI (NSF #122307 4) on grants studying interventions to promote more student-centered classrooms ranging from advanced mathematics to elementary level.

Dr. Henry Scharf, Department of Mathematics & Statistics, San Diego State University

Abstract

The social structure of a population can often influence movement and inform researchers on a species' behavioral tendencies. Social networks can be studied through movement data; however, modern sources of data can have complex patterns of missingness that are not straightforward to address using existing methods. For example, drone-gathered observations of trajectories, while highly precise, can introduce labeling issues when individuals in a study population move in and out of the camera's active field of view. When individuals cannot be uniquely identified visually, multiple labels may be assigned to a single individual. Since all available social movement models rely on unique identification of all individuals in the population, we extend an existing Bayesian hierarchical movement model that makes use of a latent social network to accommodate "multiply-labeled" movement data. We apply our model to drone-gathered observations of dolphins to study the effect of sonar exposure on the dolphins’ social structure. Our proposed framework can be applied to all unlabeled movement data for various social movement applications and has potential implications for the study of privacy-protected movement data.

Dr. Estrella Johnson, Department of Mathematics, Virginia Tech (Estrella Johnson website)

Abstract

Inquiry-oriented instruction has shown promise in regards to many features of student success, including conceptual understanding, affective gains, and persistence in STEM degrees. However, instructional change is difficult (especially at scale) and the research literature has documented a number of challenges instructors face when shifting their instructional practice. During this talk I will provide a characterization of inquiry-oriented instruction; discuss an instructional support model that was developed to support inquiry-oriented instruction in undergraduate mathematics courses; and present preliminary evaluation findings, drawing on a national sample of content assessment data, collected from 513 students at 46 different institutions. Analysis of this assessment data revealed no difference in the performance of men and women in the comparison sample; however, under the inquiry-oriented treatment, a gender performance difference was present - with men outperforming women. In an effort to understand this finding, I present related research literature on gendered experiences in collaborative settings and some of our ongoing analysis into the experiences of our students in these inquiry-oriented courses.

Bio Sketch

Dr. Johnson is the Director for Inclusion and Diversity for the College of Science, and a Associate Professor of mathematics, at Virginia Tech. Her research focuses on the pedagogical practices of mathematicians, with the goal of better understanding and supporting high quality, ambitious teaching in undergraduate mathematics classrooms. She has worked extensively on investigating and supporting mathematicians as they work to implement inquiry-oriented instructional materials (NSF #143195). Additionally, Dr. Johnson has worked on large-scale national survey projects investigating instructional practice, and influences on practice, in undergraduate STEM education (e.g., NSF #1430540, NSF #0910240, NSF #1726281).

Dr. Xiaochuan Tian, Department of Mathematics, UC San Diego

Abstract

Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations. While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved. In this talk, we will give a review of the asymptotically compatible schemes for nonlocal models with a parameter dependence. Such numerical schemes are robust under the change of the nonlocal length parameter and are suitable for multiscale simulations where nonlocal and local models are coupled. We will discuss finite difference, finite element and collocation methods for nonlocal models as well as the related open questions for each type of the numerical methods.

Dr. Katherine Kinnaird, Smith College. (Katherine Kinnaird website)

Abstract

Data science seems to be everywhere these days. This talk will discuss examples of data science being applied to music and TED talks, as well as introducing publicly available resources for exploring culturally motivated data. This talk will delve deeply into the multidisciplinary field of Music Information Retrieval (MIR) motivated by the comparisons that we, as humans, make about music and the various contexts of these comparisons. By defining tasks such as building better song recommendation systems or finding structural information in a given recording, MIR seeks to algorithmically make these musical comparisons in the same manner that a human being would, but on a much larger scale. In this talk, we will introduce the field of MIR, including popular tasks and cutting edge techniques, including aligned hierarchies, a structure-based representation that can be used for comparing songs, and new extensions of aligned hierarchies that leverage ideas from topological data analysis.

Dr. Michael Barany, History of Science, University of Edinburgh (Michael Barany website)

Abstract

If mathematics is in principle universal, mathematicians certainly are not. The striking demographic differences between the world of mathematicians and the world at large are a product of the history of where and how mathematicians have been trained, supported, and celebrated. In the twentieth century, a particular image of mathematics as a "young man's game" came to dominate both popular images of mathematicians and many mathematicians' own ideas of who can do mathematics and how. I will identify specific historical circumstances and developments that made mathematics appear to be a "young man's game" in the context of the politics and institutions of an internationalizing discipline. These circumstances converge in the quadrennial International Congresses of Mathematics and the history of the Fields Medal, which has become an accidental symbol of the preeminence of young men in modern mathematics. Recognizing the history, contingency, and politics of this dominant mathematical identity and image can offer a means of understanding and confronting present and future challenges around identity and diversity that continue to matter for mathematics and mathematicians.