Contributed presentations

Contributed presentations, Saturday 11/23, 2:00-3:00 PM

WINN AUDITORIUM Moderator: Karen Stanish, Keene State

2:30-2:45 Derivations and Applications of Helical Harmonics

Ryan Pellico*, Trinity College

Brian Pollack, University of Pittsburgh

Henry Glass, Fermi National Accelerator Laboratory

Cole Kampa, Northwestern University

Michael Schmitt, Northwestern University

In this talk we will recall a 3-dimensional helical coordinate system introduced by R.A. Waldron in 1958, and use a modified separation of variables technique to determine the separable helical harmonic functions. Then we will note some connections with the more familiar cylindrical harmonics, and present a modern application to the efficient modeling of certain magnetic fields.

2:50-3:05 3D Flows in Porous Media

James Quinlan, University of New England

Understanding fluid flow through porous media is an important and challenging problem with a broad range of applications in science and engineering, including medical biology, environmental science, and petroleum engineering. In subsurface formations, properties such as permeability and porosity are difficult to collect, observe, and measure, resulting in a high degree of uncertainty. Moreover, this data displays large variability on all scales. Models developed to describe flow, require millions of simulations to reduce uncertainty in parameter estimation for tasks related to the applications of interest, including production predictions, risk assessment, and management activities. The computation required to perform the simulations on the global measurement scale is prohibitive. Thus, model coarsening is necessary. In this work, we develop and test a three-

dimensional iterative multi-point procedure to homogenize parameters to obtain accurate and robust flow results.

3:10-3:25 Teaching the Algebra of Deep Learning

Gilbert Strang, MIT

Deep learning gives us a fantastic opportunity in teaching. The construction of the learning function depends on the tools of linear algebra. The weights go into matrices. Fitting the training data is overparametrized interpolation on an amazing scale -- with unexpected stability. We will report on four years of teaching (and learning) data science.

OLIN 101 – Moderator: Peter Staab, Fitchburg State College

2:30-2:45 A Regional Kronecker Product and Multiple-Pair Latin Squres

Braxton Carrigan*, Southern Connecticut State University

James Hammer, Cedar Crest College

John Lorch, Ball State University

We develop and apply an analog of the Kronecker product, called a regional Kronecker product, that allows new, larger multiple-pair latin squares to be created from existing multiple-pair latin squares, and likewise for mutually orthogonal families of multiple-pair latin squares. We are particularly interested in applications of this product to sudoku-pair latin squares, which are a special class of multiple-pair latin squares. We show that the regional Kronecker product, when combined with new results about orthogonal sudoku-pair latin squares, has important implications for the existence and orthogonality of sudoku-pair latin squares.

2:50-3:05 Graphs with Few Trivial Characteristic Ideals

Michael D. Barrus*, University of Rhode Island

C. Alfaro, Banco de Mexico

J. Sinkovic, Brigham Young University-Idaho

R. Villagran, Center for Research and Advanced Studies of the National Polytechnic Institute

Many interesting properties of a graph $G$ can be deduced from properties of its adjacency matrix or other variants. Turning things around, notable properties of the matrices sometimes correspond to graphs having other nice characterizations. We will begin with a short, gentle introduction to the characteristic ideals of a graph, defined in terms of determinantal ideals related to the characteristic polynomial. Graphs having few ``trivial'' characteristic ideals are closed under taking induced subgraphs, and we present forbidden subgraph characterizations for the first few of these families.

3:10-3:25 Same Score Streaks in Major League Baseball

Peter Staab, Fitchburg State University

Rick Cleary, Babson College

The same score over consecutive games occurs in many sports despite this being a rare event. We define a same-score streak as a sequence of games in which one team has the same score in each game and its opponents score is the same in each game. Due to the ease and availability of Major

League Baseball data, we examine the probability of same-score streaks of length 2 and higher, for instance wins by the score of 3 to 2. The distribution and basic statistical analysis of such games using historical data is studied. In addition, a model for this is developed and a simulation of the model is created to compare to the historical data.

OLIN 220 – Moderator Shannon Lockard, Bridgewater State University

2:30-2:45 Visualizing the Transformative Role of Mathematics in the Fin de Siècle Culture with Social Network Analysis

Donna Beers, Simmons University

Recently we collaborated with a Chemistry faculty member to develop and co-teach a sophomore, interdisciplinary learning community, Visualizing Cultural Change Using Social Network Analysis: The Birth of the Modern Era. The central question of the learning community is: How can social network analysis be used to visualize the drivers for the cultural changes that took place between the fin de siècle and the birth of the modern era? In this talk we will describe how social network analysis has led us to discover how the new, higher dimensional spatial thinking of mathematics became a transformative idea, impacting writers, philosophers, and artists in the period 1880-1920. In addition, for Albert Einstein and Pablo Picasso, the icons of the twentieth century, we will describe the networks of individuals who influenced them, particularly singling out the mathematicians in their networks and the nature and extent of their interactions and contributions.

2:50-3:05 Mindsets and Beliefs of Incoming College Freshmen on Math

Yevgeniya Rivers*, University of New Haven

Danielle Cooper, University of New Haven

Michaela Takac, University of New Haven

Dr. Cooper and Professor Rivers have been conducting research with college students for the past several years, wherein they provide them with their mindset profiles, interview students about their beliefs about math, and blend developmental math curriculum with learning at the intersection mindset and metacognition . The goal with this mentored summer research study was to get a look into students' mindsets and beliefs before they step into one of their classrooms. Carol Dweck, a professor of psychology at Stanford University, created the concept of growth and fixed mindsets. Dweck conducted a study with a group of 10-year olds and discovered that those with a growth mindset "understood that their abilities could be developed,” (Dweck, 2014). Someone with a growth mindset understands that intelligence is flexible and can improve over time (Degol, 2017). On the other hand, Dweck noticed that those with a fixed mindset "run from difficulty," (Dweck, 2014). Those with a fixed mindset learn to have the highest level of intelligence and see success in their victories rather than in their improvement (Degol, 2017).

3:10-3:25 Mersenne Matters

Karl-Dieter Crisman, Gordon College

If you have taught a number theory course or even watched the mathematical news, you know that occasionally a new (and enormous) ""Mersenne prime"" is discovered. Those who have introduced

students to the prehistory of calculus may know of a certain Marin Mersenne as the interlocutor who drew Fermat and Descartes (and others) out to discuss their methods of tangents (and more).

But who was Mersenne, and what did he actually do? This presentation will give an overview of his times, his role in the history of science, and his own writings. We'll especially look into why a monk from an order devoted to being the least of all delved so deeply into (among other things) exploratory mathematics, practical acoustics, and defeating freethinkers.