Friday, May 31, 2019: 4:45 – 5:40

Antonucci Science Center, Room 133

Moderator: Heiko Todt

4:45-5:00 Engaging Middle School Students in Mathematics: Lessons Learned

Laura McSweeney*, Fairfield University

Janet Striuli, Fairfield University

Michelle Formato, Fairfield Woods Middle School

This presentation discusses the creation of the Fairfield Woods Middle School (FWMS) team of Mathletes and the FWMS Math Circle open to all middle school students. The activities of these programs, which were designed to expose the middle schoolers to more advanced mathematical ideas while improving their ability to collaborate and communicate with their peers, will be highlighted. We also describe the intentional vertical integration of mentoring and collaboration between the middle schoolers at FWMS, the Mathletes, their teacher, and Fairfield University undergraduates and faculty. The successes and challenges of this outreach program, as well as planned changes based on this year’s experiences, will also be discussed.

5:05-5:20 A Different Approach to Teaching Mathematics

Nina Sater Fernandes, Fitchburg State University

To successfully compete globally and to maintain its economic growth, the U.S. needs to build its national citizenry of professionals, which starts with producing more post-secondary graduates. American high school graduates are enrolling in higher educational institutions, but many students are not persisting in their majors or graduating. One reason for such shortage of persistence can be attributed to the lack of students’ engagement and involvement in their own education.

Experiential learning is a promising framework to engage students, aid them in learning, and prepare them for professions post-graduation (Kolb, 2005), particularly in mathematics courses. However, there is a dearth of scholarly articles evaluating the effects of experiential learning in higher education mathematics courses. Experiential learning- influence pedagogy was introduced in a first-year mathematics class, and students’ academic achievement and retention were examined. The study employed a convergent mixed methods research design, in which the quantitative phase was quasi-experimental, and the qualitative strand was in the format of open-ended questionnaires and focus groups. The collection and analyses of the quantitative and the qualitative data were separate, yet concurrent (Creswell, 2015), and connections were made between the results of the quantitative data and the qualitative data. The study shows a positive correlation between experiential learning-influenced pedagogy, and students’ academic achievement and retention in a mathematics course. The students’ perceptions on the experiential learning-influenced class show a need to expand on using experiential learning as an approach to teaching mathematics at higher educational institutions.

5:25-5:40 Creating and Sustaining a SoTL Network in Mathematics

Fei Xue, University of Hartford

In this session we will discuss how to create and sustain a network of mathematics educators who are engaged in the scholarship of teaching and learning with an eye towards implementing research-based teaching practices to improve undergraduate mathematics teaching. In particular, we will describe the summer workshops, technologies used in creating a virtual community, and different research projects developed in the network. This project “Supporting and Sustaining Scholarly Mathematical Teaching” is supported by an NSF grant (IUSE 1725952).

Antonucci Science Center, Room 217

Moderator: Vincent Ferlini

CANCELED

4:45-5:00 On the Diophantine Equation 1/a + 1/b = (q + 1) / pq.

Jeremiah W. Johnson, University of New Hampshire

It is well-known that no general method exists for solving Diophantine equations. Thus, those Diophantine equations that admit a complete, finite set of solutions are often noteworthy. In this paper, using only elementary methods, we find all integer solutions to the Diophantine equation $1/a + 1/b = (q+1)/pq$, where $p$ and $q$ are distinct primes such that $q+1 | p - 1$. A restricted special case of this equation recently appeared in the 2018 William Lowell Putnam Mathematical Competition. A preprint of this article can be found at https://arxiv.org/abs/1905.03056.

5:05-5:20 Parabolic Equation with Initial Value and Moving Boundaries from DCIS

Heng Li, Hartwick College

Ductal carcinoma in situ(DCIS) -- a special cancer that is confined within the breast ductal only. In this talk we discuss problem of a class of non-classical parabolic equations in which the boundaries are time-dependent function. Then we consider the inverse problem of determining the potential function of model from moving boundary information, which related to the mammography screening of DCIS. The existence and uniqueness of both problems are proved. Finally, algorithm and numerical simulation are presented.

5:25-5:40 Change Point Analysis of Global Temperature Records

Eric Ruggieri*, College of the Holy Cross

Michelle Yu, University of California Berkeley

Climate change is the result of complex interactions between a wide array of climatic variables. Over a long period of time, climatic patterns can shift, possibly multiple times. Abrupt shifts that occur over a relatively short period of time are known as change points. During these intervals, different climatic variables may undergo dramatic shifts posing serious consequences for many biological and physical systems. In this paper, we discuss a Bayesian algorithm for detecting the location of change points in time series data. In particular, we utilize our method to analyze five different global surface temperature anomaly datasets, as well as temperature records associated with land, ocean, and different zonal bands in an attempt to identify common features of these datasets. Change points in the five global records were detected between 1902-1917, 1936-1945, and 1963-1976, but do these change points also manifest themselves across other parts of the globe? Our analysis indicates that the timing of change points is consistent from one record to the next, but not all change points appear in all records. In particular, there were more change points in the ocean than on land, and also more change points in southern latitudes than in northern latitudes.

Antonucci Science Center, Room 218

Moderator: Jenna Reis

4:45-5:00 Higher Connectivities for Realization Graphs

Michael Barrus, University of Rhode Island

The realization graph of a degree sequence d is the graph whose vertices are the labeled realizations of d (i.e., the graphs having degree sequence d), with two of these "realization-vertices" adjacent exactly when the realizations can be transformed into each other by a simple edge-switching operation. It is well known that the realization graph is connected for any d. We describe a proof that all but a few realization graphs are 3-connected and discuss some prospects for even higher connectivity.

5:05-5:20 Analyzing the Game of Sprouts

Courtney Kamansky, University of Hartford

Faculty Advisor: Michelle Rabideau, University of Hartford

In this talk, we will introduce the game of Sprouts invented by John Horton Conway and Michael S. Paterson. This project began through an independent study that continued into a discrete mathematics course where we analyzed different aspects of the game. As we describe the game, we will also give some basic definitions from graph theory. In particular, this talk will focus on analyzing the relationship formed between the number of beginning spots and the number of moves as well as its correlation to winning.

5:25-5:40 Generalization Theory of Linear Algebra I

Christina Pospisil, University of Massachusetts, Boston

Faculty Advisor: Professor R. Brown, University of California Los Angeles

An algorithm for multiplying and adding matrices regardless of dimensions via an embedding is presented. An equivalent embedding for a general determinant theory is also investigated. In future work there will be applications to physics and other natural sciences be explored.

Antonucci Science Center, Room 243

Moderator: Jason Molitierno

4:45-5:00 Assessing the Impact of Exclusive Extreme Response Style on Estimation of the Treatment Effect in Randomized Control Group Designs

Emily Mo, Boston University

Faculty Advisor: Allen Gregg Harbaugh, Boston University

Survey respondents may interpret Likert-type response scale levels differently depending on personal backgrounds. Under the Exclusive Extreme response style, respondents only select the most extreme options. Data was simulated to mimic a setting in which participants are randomly assigned to a treatment or control condition and participate in pre- and post-intervention surveys. As skewness increases in ordinal distributions of manifest item responses, an increasing presence of Exclusive Extreme response style has an increasingly depressive effect on the estimated treatment effect.

5:05-5:20 LSA Cryptosystem, Part I (theoretical)

Francesco Lucente Stabile*, Salem State University

Carey Patrick Atkins, Salem State University

Faculty Advisor: Brian Travers, Salem State University

The LSA cryptosystem is an asymmetric encryption algorithm which is based on both group and number theory that follows Kirchhoff’s principal, and relies on a specific case of Gauss’s Generalization of Wilson’s Theorem. Unlike prime factorization based algorithms, the eavesdropping cryptanalyst has not indication that he has successfully decrypted the cypher text. For this reason, we aim to show that LSA is not only more secure than existing asymmetric algorithms, but is also computationally faster.

5:25-5:40 LSA Cryptosystem, Part II (practical)

Carey Patrick Atkins*, Salem State University

Francesco Lucente Stabile, Salem State University

Faculty Advisor: Brian Travers, Salem State University

The LSA cryptosystem is an asymmetric encryption algorithm which is based on both group and number theory that follows Kirchhoff’s principal, and relies on a specific case of Gauss’s Generalization of Wilson’s Theorem. Unlike prime factorization based algorithms, the eavesdropping cryptanalyst has not indication that he has successfully decrypted the cypher text. For this reason, we aim to show that LSA is not only more secure than existing asymmetric algorithms, but is also computationally faster.

Saturday, June 1, 2019: 1:15 – 2:10

Antonucci Science Center, Room 133

Moderator: Brett Collins

1:15-1:30 The effect of response styles on the distribution of modification indices for congeneric factor models

Lin Zou*, Boston University

Haoyan Tong - Boston University

Faculty Advisor: Allen Gregg Harbaugh, Boston University

The objective of this study is to examine the effects of three response styles (Extreme Avoiding, Exclusive Extreme and Exclusive Extreme with central point inflation.) We simulated data sets to represent response on a 5-item survey and contaminated it with different response styles. Analyzing the modification indices using generalized linear models, we showed that the effects of response styles were not negligible, especially when the percentage of contaminated responses increased in the simulation.

1:35-1:50 A Surprising Link Between Integer Partitions and Euler's Number $e$

Tim Antonelli, Worcester State University

At first glance, the multisets of positive integers that add to $n$, known as integer partitions, and Euler’s number $e$ do not have much in common. However, if you take the reciprocal product of the partition parts and the factorials of their multiplicities, then the sum over all partitions of $n$ that do not include 1 gives the $n$th Taylor series approximation of $e^{-1}$. This surprising identity arises from the probabilities in a matching problem, and we show how it is a special case of a theorem by Nathan Fine. The general result describes sums over partitions that converge to any $e^{a-1}$.

1:55-2:10 Using Overleaf in an Abstract Algebra Course

Jason Hardin, Worcester State University

This past semester I required students in my Abstract Algebra course to complete assignments through Overleaf, a free, online LaTeX editor designed for collaborative projects. Overleaf provided a convenient way of grading weekly homework sets and allowing for inadequate proofs to be resubmitted for regrading. I was also able to assign "partner project problems" in which students worked in pairs to collaboratively solve more difficult problems. In this talk, I will discuss how I incorporated Overleaf into my course and how I went about using it for the aforementioned assignments. I will also provide some student feedback I received regarding Overleaf usage.

Antonucci Science Center, Room 217

Moderator: Joe Fields

1:15-1:30 A Course on Ancient Greek Mathematics, Archaeology and Religion

Heiko Todt, Stonehill College

A learning community is a general education requirement at Stonehill College that consists of one or more courses that are co-taught by two or more faculty members from different disciplines. I recently had the opportunity to teach a learning community together with a professor of Religious Studies. We decided to add a mathematical component to his course on Greek Archaeology and Greek Religion, and introduced the students to Ancient Greek mathematics and thinking. In this talk, I will give an overview of the topics we discussed and some of the connections between Greek mathematics and religion. I will also share some of my experiences from teaching this course.

1:35-1:50 From the Courtroom to the Classroom: Gerrymandering and Mathematics Education

Kyle Evans*, Trinity College

Adam Giambrone, Elmira College

In recent years, the mathematics community has entered the political arena offering research-based solutions to the process of redistricting. Not only is this issue current, it also offers a unique intersection between mathematics, politics, and maps. Redistricting and the associated practice of gerrymandering served as an inspiration to create an authentic learning experience for students. In this talk, I will discuss my evolution of this educational experience, from its origin to the full semester course I will be offering in the Fall.

1:55-2:10 How a Math Club Project Inspired an Open Graph-theoretic Question

Joe Fields, Southern Connecticut State University

Our Math Club members were building a model icosahedron (using a skeleton involving three mutually perpendicular golden rectangles). We wanted to reinforce the model by running cords between the vertices of the model -- along the edges of the icosahedron. This led to an interesting question: does there exist a decomposition of the edge graph of an icosahedron into paths that are equivalent under the action of the group of the solid?

We quickly established the affirmative answer, which naturally led to the question ""how many?"" That question remains open, but a lower bound is 7. The generalization to path decompositions of other graphs that have a group acting on them is also interesting.

Antonucci Science Center, Room 218

Moderator: Nermin Bayazit

1:15-1:30 Integration by the Wrong Parts

Vincent J. Ferlini, Keene State College

When applying integration by parts, one needs to choose the functions u and v so that the new integral is simpler to evaluate. With some simpler integrals, one can make the “wrong” choice and through an “infinite” sequence of integrations by parts, still come up with the correct antiderivative of the original integral. This presentation will demonstrate the idea through examples.

1:35-1:50 Multiple Representations in the Calculus Curriculum, Student Understanding and Gender

Ileana Vasu, Holyoke Community College

Multiple representations of mathematical ideas are deemed essential to creating mathematical habits of mind, but not all classroom instruction includes them. The study examines the relationship between college students' experience with multiple representations of the Fundamental Theorem of Calculus (FTC) in the enacted curriculum and their use of multiple representations. The effect of gender on the relationship between the use of multiple representations in the FTC curriculum and student understanding is also examined. Results suggest that meaningful use of multiple representations in an active learning environment support a fuller understanding of the FTC, and that the relationship is stronger for female students. A mixed methods design was used, which includes lesson observations, classroom assessments, and semi-structured think-aloud interviews. The study contributes to the existing literature on Calculus education by providing a more complete picture of the ways in which an enacted college curriculum that includes multiple representations of the FTC supports deeper learning and understanding of Calculus for all students. In particular the study augments selected findings from the Mathematical Association of America’s (MAA’s) study of College Calculus by adding a fine-grain exploratory texture to this important work.

1:55-2:10 Outcomes and Issues from an NSF SSTEM Grant: Recruiting, Research, and Curriculum Evolution

James Quinlan, University of New England

The SUCCESS program at the University of New England was funded through the National Science Foundation Scholarships in Science, Technology, Engineering, and Mathematics Program (Award #1259896). The grant has provided Maine students majoring in Science, Technology, Engineering and Mathematics (STEM) disciplines that are underrepresented or first-generation college students up to $10,000 per year for all four years at UNE. This presentation will discuss and highlight the successes, challenges, research culture, and general outcomes of the SUCCESS scholar program at our University that would be of interest to others seeking similar funding.

Antonucci Science Center, Room 243

Moderator: Erin Denette

1:15-1:30 Reliability of ACCUPLACER Score in Predicting Success in Quantitative Reasoning Course

Upasana Kashyap*, Regis College

Santhosh Mathew, Regis College

The purpose of this study was to determine the correlation between the ACCUPLACER placement test score (elementary algebra) and the student success in the quantitative reasoning course at Regis College. Our study points to a weak correlation between the ACCUPLACER placement score and the student success in the quantitative reasoning course. We propose that an in-house placement system based on the unique requirements of the institution will be a much more pragmatic approach to place the students at appropriate levels of instruction.

1:35-1:50 Risk Factors that Influence Bicyclist Injury Level in Bicycle-Motor Vehicle Crashes at North Carolina

Mohammed H. Talukder*, Elizabeth City State University

Shatoya Estime, Elizabeth City State Universtiy

North Carolina implemented a strategic highway safety plan to reduce fatalities and serious injuries. The plan defined 9 areas of focus to address safety issues. In the present study, two main areas were investigated; unsignalized intersections and bicyclist safety with the intent of evaluating (1) Potential factors associated with bicyclist injury severity in bicycle-motor vehicle crashes at unsignalized intersections and (2) The impact of these factors on bicyclist safety, by initially using ordinal logistic regression. A partial proportional odds model was used as an alternative. Out of 8,418 bicycle motor vehicle crash records from the UNC Highway Safety Research Center, 1,273 cases were evaluated to determine potential factors that are associated with bicyclist injury severity in bicycle-motor vehicle crashes at unsignalized intersections. Multiple factors were statistically significantly associated with bicyclist injury severity: bicyclists 55 and older, the driver’s speed, roadway features, day of week, light condition, and season.

1:55-2:10 Estimating and Quantifying Uncertainty in Time-Varying Parameters

Andrea Arnold, Worcester Polytechnic Institute

Estimating and quantifying uncertainty in unknown system parameters remains a big challenge in computational and applied mathematics. A particular challenge lies in estimating parameters that vary with time but have unknown dynamics. This talk will address the time-varying parameter estimation inverse problem from a Bayesian statistical perspective and explore how uncertainty in sequential Monte Carlo estimates of such parameters affects the corresponding model output predictions. Results will be demonstrated on several applications from the life sciences.