SUMS 2019: Math and Teaching

Faculty Talks

Calculus Reordered: A History of the Big Ideas

David Bressoud, Macalester College

This talk will use the calculus curriculum to illustrate how history and research in mathematics education can inform our teaching of mathematics. The standard order of the four big ideas of calculus—limits then derivatives then integrals then series—is historically and pedagogically problematic. Drawing on history and recent research in undergraduate mathematics education, I will make the case for calculus introduced first as problems of accumulation (integration), then ratios of change (differentiation), then sequences of partial sums (series), and finally the algebra of inequalities (limits).

The Intersection of Research and Public Engagement

Kelsey Houston-Edwards, Olin College

Math for public engagement is presented in blogs, books, videos, museum exhibits, etc. and designed to reach the broadest possible audience. By contrast, research math is often presented in specialized journals and written for experts with shared motivations and background knowledge. But this division isn’t always so sharp. I will give some examples of work (by myself and others) that integrate math research and public engagement, and suggest ways to encourage further work in this direction.

How to correct your errors without knowing what they are

Henry Cohn, Microsoft

In this talk we'll look at why error terms aren't random and how to take advantage of this lack of randomness to carry out calculations with far more accuracy than we seemingly deserve. Along the way, we'll see a surprising connection between discrete and continuous mathematics.

Mathematical Knowledge: Where does it come from? How certain is it? What do I do with it?

Christina Smith, Brown University

In this interactive workshop/lecture we will identify the authorities, sources, and validity of knowledge that are used in mathematics learning environments. From this discussion we will make connections between how our students show up in the classroom in regards to their assumptions about mathematical knowledge and how mathematics is taught, focusing on how to create more inclusive, equitable learning spaces. Participants will leave having identified their own epistemological assumptions and how they can use that knowledge to create more equitable classrooms.

Student Talks

Energy-Aware Optimization of Scalable Load Balancing Strategies

Rajita Chandak, Brown University

As we move towards an increasingly digitized world, concerns of energy consumption have become more prominent. Modern day data centers and cloud networks are just one such technological evolution that present financial and environmental challenges. The TABS scheme was first proposed by Mukherjee et. al.(2015) as a scheme that aims to increase efficiency and reduce energy consumption on average for large scale distributed systems with parallel queues. Our research aims to understand the dependence of the TABS scheme on various parameters of data centers. Specifically, we are interested in understanding how server set up time and idle-on server standby time impacts the convergence limit of the system through a diffusion-scaling limit theorem proof. We also look at simulations of data centers under the TABS scheme to see how different service time distributions affect its performance.

What Percentage of Triangles are Acute?

Patrick Dragon, University of Massachusetts Amherst (Lecturer)

As we move towards an increasingly digitized world, concerns of energy consumption have become more prominent. Modern day data centers and cloud networks are just one such technological evolution that present financial and environmental challenges. The TABS scheme was first proposed by Mukherjee et. al.(2015) as a scheme that aims to increase efficiency and reduce energy consumption on average for large scale distributed systems with parallel queues. Our research aims to understand the dependence of the TABS scheme on various parameters of data centers. Specifically, we are interested in understanding how server set up time and idle-on server standby time impacts the convergence limit of the system through a diffusion-scaling limit theorem proof. We also look at simulations of data centers under the TABS scheme to see how different service time distributions affect its performance.

Posters

Application of Topological Data Analysis to Quantify Invasive Tissue Architectures Observed In Confocal Microscopy

Zachary Neronha, Brown University

Topological data analysis (TDA) offers a promising new approach for inferring the intrinsic structure of high dimensional data, with many exciting applications in quantitative biology. In particular, persistent homology of point cloud data can be used to identify number of connected components (clusters), loops and voids (holes) at multiple spatial scales. My research focuses on the development of topological methods to analyze confocal microscopy data using cell nuclei positions as the input. A key advantage of using this approach is that computationally expensive image segmentation can be replaced with extraction of Betti intervals from simplicial complexes and the resulting topological signature can be used as a feature vector to classify distinct tissue architectures is an unsupervised manner. I will present an application of TDA to elucidate transitions in tissue morphology observed during epithelial to mesenchymal transition, an important progenitor of cancer metastasis.