# MAA  Mathematical Association of AmericaSeaway Section

## 2019 Fall Meeting – Contributed Talks

### Saturday – Nov 2

Room: Williams Hall, Room 202

1. Time:
7:15 am – 7:40 am
Title:
Iterations of the Sisyphus Function
Speaker:
Matt Coppenbarger – RIT
Abstract

The Sisyphus function is defined and we determine the smallest nonnegative integer requiring a specified number of iterations of the function that must be applied to n until the sequence generated by the iterations of this function becomes stable or cycles.

2. Time:
7:45 am – 8:10 am
Title:
Eigenvalues of Threshold Graphs
Speaker:
Cesar Aguilar – SUNY Geneseo
Abstract

Problems in algebraic graph theory provide a rich source of research projects for under-graduate students. In this talk, I will present some results obtained over the last couple of summers with SUNY Geneseo undergraduates on the study of the eigenvalues of threshold graphs. The main takeaway of the research is that there is a distinguished threshold graph that plays a prominent role in the study of the spectral properties of the entire class of threshold graphs.

3. Time:
9:30 am – 9:55 am
Title:
Solutions for some quadratic Diophantine equations
Speaker:
Anurag Agarwal – RIT
Abstract

We will discuss and investigate the positive integer solutions of some quadratic equations whose solutions have links to generalized Fibonacci and Lucas sequences.

4. Time:
10:00 am – 10:25 am
Title:
On a Time-Dependent Inverse Source Problem with an Integral Constraint
Speaker:
Sedar Ngoma – SUNY Geneseo
Abstract

We investigate an inverse time-dependent source problem for a parabolic partial differential equation with a Neumann boundary condition and subject to an integral constraint. We show the existence, uniqueness, and continuous dependence of solutions. The proof of the existence and uniqueness of solutions yields an algorithm that we used to approximate solutions of the inverse problem using a finite element discretization in space and the backward Euler scheme in time. The errors resulting from our experiments show that the proposed scheme approximates solutions of this inverse problem accurately.

5. Time:
10:30 am – 10:55 am
Title:
Direct Partitioning: Theory, Applications and Challenges
Speaker:
Abd AlRahman Almomani – Clarkson University
Abstract

In this work, we discuss the graph directed partitioning method, and its applications in complex systems science such as but not limited to coherent structures, computer vision, weather, complex networks analysis, and earth science. We introduce examples and applications from Jupiter, weather movies, network synchronization, and predicting ice shelf cracks in Antarctica's Larsen Cice shelf.

6. Time:
11:00 am – 11:25 am
Title:
Locally Anchored Swarm Optimization
Speaker:
Ahmad Almomani – SUNY Geneseo
Abstract

In the recent decade, Particle Swarm Optimization (PSO) become a favorable global optimization method the fields of science and engineering. Moreover, PSO is a meta heuristic method, and it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions, which made it an efficient method in the field of machine learning, and training of neural networks. However, two main problems face the PSO which are the possibility to trap with local minima and the slow local convergence. This work introduces an efficient method to combine the Swarm Optimization with the Local optimization solvers, which goes beyond the parallel independent implementation to use dynamic internal connections that achieve robust results.

### Saturday – Nov 2

Room: Williams Hall, Room 211

1. Time:
7:15 am – 7:40 am
Title:
Using the LibreTexts Platform to Customize OER Textbooks for Calculus II and III
Speaker:
Paul Seeburger – MCC
Abstract

The presenter will share his experiences using the LibreTexts platform to customize Open-Stax textbooks for his Calculus II and III courses. LibreTexts includes a WYSIWYG content editor to seamlessly edit the textbook content, using LaTeX only where needed to format math content.You can add your own sections, subsections, examples, and exercises using a consistent numbering system to form a textbook that looks professional and is customized for your course. Using Cal-cPlot3D, rotatable 3D figures can be added to bring the figures in the textbook to life. Anyone can use these textbooks on the LibreTexts platform or customize them for their own courses. See https://math.libretexts.org/Courses/Monroe_Community_College.

2. Time:
7:45 am – 8:10 am
Title:
Making an OER Calculus Text Our Own
Speaker:
Doug Baldwin – SUNY Geneseo
Abstract

Since academic year 2017-18, SUNY Geneseo's mathematics department has allowed instructors to use an open educational resource (OER) textbook (Openstax Calculus Volume 1) on a trial basis in its first calculus course. Many of our instructors are enthusiastic about this text, except for the large number of typographical errors it contains. During the summer of 2019, we took advantage of the book being an open resource to correct those errors. The result is a custom version of the book that is currently being used as the main text in 7 out of 9 sections of Calculus 1, and as an optional text in another section. In this talk we describe how we carried out this project, the results we have observed so far, future plans for the book, and lessons learned. We hope the project can serve as a model for others interested in using or adapting OER mathematics texts. Authors: Christopher Leary, George Reuter, Gary Towsley (SUNY Geneseo)

3. Time:
9:30 am – 9:55 am
Title:
A Report on Multiple Large-Class Active Learning Redesigns
Speaker:
Alex Rennet – University of Toronto
Abstract

In this talk, I will outline the structure of Active Learning redesigns of large (500+student) Calculus and Linear Algebra courses at the University of Toronto, Mississauga. We focused on creating a number of in-class and out-of-class components with the intention of maximizing student engagement during class, including online quizzes, polling questions, readings, and in-class activities. I will report on successes, challenges, and next steps for the redesigns. (These redesigns are still in the process of being implemented and adjusted, so this is an interim report. Each project was in collaboration with other faculty.)

4. Time:
10:00 am – 10:25 am
Title:
Data Integration in Undergraduate Mathematics Education
Speaker:
Nicole Juersivich – RIT
Abstract

We will describe our efforts in creating and evaluating the impact of teaching modules based on real-world data so that students have authentic experiences that support and motivate the investigation of concepts and techniques in calculus and linear algebra. Specifically, we looked at(1) how student disposition toward real-world data and the use of technology as a mathematical tool evolved in a course that used the modules and (2) how the completion of the data-driven and technology-integrated modules impacted student achievement in the course. We have collected data from pre and post-module student surveys, pre and post-module student focus groups, student final exam scores, instructor journals, and instructor interviews from multiple courses across our two institutions. We are now in our third year and would like to invite other institutions into the project.During this workshop, we will share our findings to date, takeaways we have learned throughout the study, and the digital modules and supporting technology files. A few computers with MATLAB will be available during the session along with hard copies of the modules so that you can explore and ask questions. To preview the module files, go toshorturl.at/csvCS.

5. Time:
10:30 am – 10:55 am
Title:
Mathematical Card Tricks
Speaker:
John Maceli – Ithaca College
Abstract

This talk will introduce some mathematical card tricks and their uses in the classroom. Many magic tricks are based on mathematics. We will discuss a few card tricks and the mathematics behind them.

6. Time:
11:00 am – 11:25 am
Title:
Orthogonality without Inner Products
Speaker:
Gabriel Prajitura – SUNY Brockport
Abstract

We will discuss and compare various concepts of orthogonality of interest in spaces without inner products and will look into their particular forms for the p norms (with p different from 2) in two dimensions.

### Saturday – Nov 2

Room: Williams Hall, Room 302

1. Time:
7:45 am – 8:10 am
Title:
An upper bound for a sum of cyclic probabilities
Speaker:
James Marengo – RIT
Abstract

Let $x_1$, $x_2$, and $x_3$ be real numbers and consider the three statements $x_1>x_2$, $x_2>x_3$, and $$x_3>x_1$$. Clearly, these statements cannot all be true. But suppose that $x_1$, $x_2$, and $x_3$ are realizations of random variables $X_1$, $X_2$, and $X_3$, and that the corresponding statements are each true with the same probability $p$. Since $p$ cannot be equal to one, the following question arises: how close to one can $p$ be? Can $p$ be greater than $1/2$? Can $p=0.7$? One can ask a similar question for $n$ random variables. After mentioning a preliminary result that answers these questions and which will be proved in a student talk at this conference, we will show that, given a univariate absolutely continuous probability distribution an $n-\epsilon>0$, there are random variables $X_1, X_2, \ldots, X_n$ having this distribution and for which each of the probabilities $\text{Pr}(X_1>X_2)$, $\text{Pr}(X_2>X_3)$, $\ldots$, $\text{Pr}(X_{(n-1)} > X_n)$, and $\text{Pr}(X_n > X_1)$ exceeds $1-\epsilon$.

2. Time:
10:00 am – 10:25 am
Title:
Designing Intellectual Need-Provoking Tasks for Introductory Calculus
Speaker:
Aaron Weinberg – Ithaca College
Abstract

Students in undergraduate mathematics classes are routinely asked to learn from text-books. In recent years, mathematics and literacy researchers have begun to investigate the ways students learn from discipline-specific texts using the perspective of disciplinary literacy, which focuses on how experts interpret, create, and critique disciplinary texts such as mathematics journal articles. However, textbooks differ from other disciplinary texts because they are specifically pre-pared for classroom use. Our work analyzes the reading practices of undergraduate calculus students and non-mathematics STEM professors as they interact with excerpts from calculus textbooks. We have proposed the idea of didactical disciplinary literacy to describe the productive reading practices we observed, and this paper zeros in on the role of readers' agency.

3. Time:
10:30 am – 10:55 am
Title:
How do College Students Read Calculus Textbooks? Using a New Theory to Understand Agency in Didactical Disciplinary Literacy
Speaker:
Ellie Fitts – Ithaca College
Abstract

Intellectual need is the need that students feel to understand how and why a particular mathematical idea came to be. We are interested in creating tasks that calculus instructors can use to provoke intellectual need. However, the current suggestions for designing such tasks lack detail and don't account for several issues specific to undergraduate introductory calculus. In this theoretical paper, we discuss the idea of intellectual need, explore three issues related to the teaching of calculus, and present a theoretical model that task-designers can use to frame important factors that affect the development and use of these tasks.

4. Time:
11:00 am – 11:25 am
Title:
Feedback on Proofs: An analysis of faculty practices
Speaker:
Sarah Hanusch – SUNY Oswego
Abstract

Mathematics faculty spend considerable time scoring and providing feedback on student-generated proofs, yet this practice is largely unresearched. In this talk, I explore the types of annotations that professors make on student proof attempts, and the manner in which the feedback is phrased. The results show that professors generously use annotations (like checkmarks) as informal grading tools or to signify things they have read when grading, most feedback focuses on a particular part of the proof that is no more than a few lines, and the majority of feedback does not convey why the feedback was given.

### Saturday – Nov 2

Room: Williams Hall, Room 309

1. Time:
7:15 am – 8:10 am
Title:
IBL Workshop: Incorporating Active Learning Strategies into Your Classroom
Speaker:
Jane Cushman – Buffalo State College
Abstract

In this discussion session, we will first have several professors briefly share their in-class activities and student-centered discovery approaches in topics of Pre-Calculus, Calculus, Linear Algebra, and Geometry. Professors will share their experiences, benefits, and challenges of using active learning in their classroom such as time management, students' participation, increasing the depth of mathematical understanding, communication skills, and more. This will be followed by a discussion which is open to anyone who is interested in incorporating active learning strategies in their classrooms.

2. Time:
9:30 am – 10:25 am
Title:
Workshop on Leadership in the Mathematical Sciences: Department Chairpersons as Leaders and Administrators
Speaker:
Mihali Barbosu – RIT
Abstract

Every semester Mihail Barbosu leads a workshop on effective leadership in the mathematical community. The latest workshop focuses on developing leadership skills and roles for chairpersons. Recent chairpersons, former chairpersons, and especially anyone who has considered the path to becoming a department chair are all welcome to participate!

3. Time:
10:30 am – 11:25 am
Title:
Listening Session with your Section Chair
Speaker:
Cheryl Miller – SUNY Potsdam
Abstract

Sit down with the Chair of the Seaway Section to discuss initiatives for the future. Do you have suggestions for future meetings? Any requests for workshops, mini-courses, or other fun events? Suggestions or thoughts about charity fundraisers? Do you want to get involved with the section? Maybe you just want to talk about mathematics? Our section chair, Dr. Cheryl Miller (SUNY Potsdam), is ready to listen!