The Mathematical Association of America Maryland-District of Columbia-Virginia Section

The Spring 2022 Meeting of the MD-DC-VA section of the MAA was held at the Germantown campus of Montgomery College, on April 22-23, 2022.

On Friday, Rebecca Segal of VCU ran a workshop on Building Interdisciplinary Partnerships to Create Application-Focused Mathematics Content, A SUMMIT-P Project, and Sam Ferguson of Metron, Inc. gave the banquet address, Back in the Saddle: Cutting through Clutter with Analytic Combinatorics.

The Saturday morning address, Applying Formal Methods to Safety-Critical Systems, was given by J. Tanner Slagel of NASA, and the Saturday afternoon address, Cosh, Cosh, B-Cosh, was given by Alex Meadows of St. Mary's College.

Rebecca Segal (on behalf of MD-DC-VA COMMIT)

Friday workshop: Building Interdisciplinary Partnerships to Create Application-Focused Mathematics Content, A SUMMIT-P Project

Abstract: This workshop will showcase the collaborative process of creating class activities at Virginia Commonwealth University (VCU) with partner discipline input, allowing Differential Equation students to interact with mathematical content in an application focused format. VCU is part of SUMMIT-P: A National Consortium for Synergistic Undergraduate Mathematics via Multi-institutional Interdisciplinary Teaching Partnerships that is an extension of work begun in the Curriculum Renewal Across the First Two Years (CRAFTY) project. Along with sample activities, we will discuss how faculty conversations between departments can enrich the mathematics curriculum and lead to stronger student engagement.

Biographical Sketch: : Dr. Rebecca Segal is a Professor and Interim Chair in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. Her mathematics research is in differential equation models of disease processes and biological systems and she works collaboratively with faculty across the campus and around the United States. She earned her PhD at North Carolina State University, completed a postdoctoral fellowship at CIIT Centers for Health Research, and was a teaching fellow at University of Bristol, England. She is PI on two NSF grants focused on undergraduate and graduate mathematics education and training

About MD-DC-VA COMMIT: The MD-DC-VA COMMIT was formed in early 2016 (the group was originally called the MD-DC-VA IBL Consortium) as a network of college math instructors with a common interest in teaching and learning using inquiry. We recognize that teaching with inquiry can look very different in different contexts, and view our role as supporting instructors in utilizing the version that works for them and their students. Names that have been used for teaching with inquiry include: ambitious teaching, project-based learning, complex instruction, inquiry-oriented learning, discovery learning, inquiry-based learning, and student-centered teaching. We welcome members who are new to teaching with inquiry as well as those who are more experienced. Please join us! See the MD-DC-VA COMMIT webpage and the COMMIT Network webpage for more.

Sam Ferguson

Banquet Address:Back in the Saddle: Cutting through Clutter with Analytic Combinatorics

Abstract: When sailors fall overboard in a storm, their lives depend on searchers' abilities to find them before it is too late. Their positions must be tracked until they can be picked up by other vessels. But the tracking instruments are so sensitive that they yield many "false alarms" or, as we call them, "clutter" measurements. The task of finding the targets' most likely positions gets bogged down by the clutter due to a combinatorial explosion in the number of assignments of measurements to targets. Rather than rely on too-slow enumerative methods, we introduce two ideas from analytic combinatorics in the context of amusing examples involving Stirling's approximation of n! and the Fibonacci numbers. Combining these ideas, we get a new "saddle point" approximation of the positions' likelihoods that delivers sufficiently accurate estimates without the slowdown of traditional probabilistic methods.

Biographical Sketch: Sam Ferguson is a Research Scientist at Metron Inc. in Reston, Virginia. Metron researchers are known for finding the sunken treasure ship SS Central America, finding the lost Air France Flight 447, their ongoing project to find the lost cities of gold in South America, and developing software the Coast Guard uses to find sailors lost at sea—all with the math of probability theory. Ferguson is also an Adjunct Professor at George Mason University in Fairfax, Virginia, and a Professorial Lecturer at George Washington University in DC. A popular speaker at seminars and math department colloquia, his articles have been published in Notices of the AMS, Communications in Pure and Applied Mathematics, and The American Mathematical Monthly, among others. In 2019, he received his PhD from NYU's Courant Institute and the inaugural NExT teaching grant from the MAA's Metro New York section. His use of mathematical analysis to resolve divergence issues in IRS guidance was recognized with a film clip and article in Money in 2018. The son of an archaeologist, he looks forward to active participation in our MAA section when he's not out hunting for lost treasures amidst the ruins of ancient civilizations.

J. Tanner Slagel

Saturday Morning Address:Applying Formal Methods to Safety-Critical Systems

Abstract: How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard.

'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs.

This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Biographical Sketch: J. Tanner Slagel has been a Research Computer Scientist at NASA Langley Research Center since 2019. He applies and develops formal methods tools to safety- and mission-critical avionics systems. Before working at NASA, Tanner completed his Ph.D. in massive inverse problems at Virginia Tech. In Tanner's free time, he enjoys Matrix perturbation theory and walking his dog, Rupert.

Alex Meadows

Saturday Afternoon Address:Cosh, Cosh, B-Cosh

Abstract: The hyperbolic cosine function (cosh) is well known for many reasons, both analytic and geometric. In this talk, we start with a not often celebrated property, that the area under any portion of the graph of cosh is equal to the graph's length. We will explore playful generalizations of this property, by changing our perspective. What if we measure length on the graph differently, say using the length inspired by taxicabs? Beginning from basic ideas of calculus, our investigation of generalized cosh functions and related curves will lead us to some advanced ideas in analysis and geometry, with a few surprises along the way. This talk is based on joint work with Casey Douglas from the University of Houston and Beth Thomas, current grad student at VCU.

Biographical Sketch: Alex Meadows has been teaching at St. Mary's College of Maryland since 2005 and is currently chair of the department of Mathematics and Computer Science. He now teaches courses in both Math and CS. Originally trained as an analyst, he also works in geometry and combinatorial game theory, involving many undergraduate students in the joy of thinking about mathematics.