MAA  Mathematical Association of America

Seaway Section

Location: Valentine Hall 104

Note: Special Session on the History of Mathematics, organized by Toke Knudsen (SUNY Oneonta), Duncan Melville (St. Lawrence University), and Naveen Somasunderam (SUNY Plattsburgh).

1. Time:

   1:15 pm – 1:35 pm

   Title:

   Using History to Tell a Story in a Mathematics Class

   Speaker:

   Robert Rogers (SUNY Fredonia)

   Abstract

   Typically, mathematics courses and textbooks present definitions, theorems, and problems with little regard to the story underlying the mathematics presented. This talk will demonstrate how to use the heritage of mathematics to tell the story behind the mathematical results in a mathematics class. This not only adds a human element but also provides a context for the mathematical results. Examples from precalculus, differential and integral calculus, and vector calculus will be presented along with references for such materials.

2. Time:

   1:45 pm – 2:05 pm

   Title:

   Dr. Vera Sanford and her textbook "A Short History of Mathematics"

   Speaker:

   Leah Bridgers (SUNY Oneonta)

   Abstract

   Dr. Vera Sanford was a prominent faculty member at SUNY Oneonta for more than a quarter of a century, including an extensive period as department chair. This was a time where it was unusual for women to hold such a position at an institution of higher education and reach such heights in both scholarship and teaching. Her textbook on the history of mathematics, "A Short History of Mathematics" was published in 1930. We will discuss Dr. Sanford’s life and the textbook through which we came to know more about her.

3. Time:

   2:15 pm – 2:35 pm

   Title:

   Questioning Mesopotamian Cut-and-Paste Geometry

   Speaker:

   Zoë Misiewicz (SUNY Oswego)

   Abstract

   Thousands of years ago, ancient Mesopotamian scholars writing on cuneiform tablets solved problems that we would today describe as quadratic equations. But how did they think about their work? Modern scholarship has moved away from interpreting Mesopotamian procedure texts as “equations”, since that sort of symbolic representation was a much later development. Instead, there has been broad acceptance of a “cut-and-paste geometry”, where completing the square was a very literal process that involved moving a rectangle from place to place. Yet close reading reveals that certain key instructions are missing from the texts, specifically any instructions describing movement that cannot simply be interpreted as arithmetical operations. Years of teaching this material to undergraduates have also highlighted the gaps that need to be filled in. This raises questions about the “cut-and-paste geometry” interpretation, and suggests that while that approach may have led to the creation of the procedure, it does not necessarily reflect the perspective of the scholars who wrote the surviving texts and carried out the calculations that they described.

4. Time:

   2:45 pm – 3:05 pm

   Title:

   Euclid's Neglected Postulate

   Speaker:

   Jeff Johannes (SUNY Geneseo)

   Abstract

   The first three postulates are for compass and straightedge, the fifth is rightly famous. The fourth is ... peculiar and usually dismissed. Euclid might as well say "All 7s are equal" as "All right angles are equal". In this talk we will explore what was meant, how it was used, and its dependence on the fifth. Come to investigate a neglected corner of the Elements.

Location: Valentine Hall 106

1. Time:

   1:15 pm – 1:35 pm

   Title:

   Defining an isosceles trapezoid-mathematical and pedagogical considerations

   Speaker:

   Sarah Hanusch (SUNY Oswego)

   Abstract

   While preparing notes for my geometry for future elementary school teachers, I realized that the definition of isosceles trapezoid that I had previously used required a concept that I had not adequately defined, namely the base angles of a trapezoid. From both a pedagogical and mathematical perspective, it seemed less than ideal to define a concept whose sole purpose was to define another concept. This led me to look for alternative definitions for isosceles trapezoid. In my talk, I will demonstrate the equivalence of three definitions for an isosceles trapezoid, and then discuss the pedagogical considerations I made before choosing a definition for my lecture notes.

2. Time:

   1:45 pm – 2:05 pm

   Title:

   Fibonaccci, His Place in the History of Mathematics, and a Recent Controversy

   Speaker:

   Gary Towsley (SUNY Geneseo)

   Abstract

   The first time I taught History of Mathematics (1982 or so) all the major textbooks simply assumed that when Leonardo of Pisa (Fibonacci) returned to Europe after following his merchant father around the Mediterranean and wrote his book Liber Abbaci (1202 and 1228) he really did bring new mathematics to Italy and started both a commercial and a mathematical revolution. Over the past twenty five years this simple picture has been both strongly questioned and strongly reaffirmed (but not by the same people). I want to present my view on where we stand today on the importance of Fibonacci in both the history of finance and of mathematics.

3. Time:

   2:15 pm – 2:35 pm

   Title:

   Is it Algebra yet?

   Speaker:

   Olympia Nicodemi (SUNY Geneseo)

   Abstract

   In this talk, we will take a close look at an excerpt from a pre-modern algebra manuscript from around 1360 c.e. in which the author presents a rule for solving a quadratic equation and then gives us examples as to how to use it. Nice pedagogy. What could be different from what we now do in Algebra I? A lot, it turns out. Enough to prompt the questions “Is it algebra yet?” and “If not, why not?”

Location: Valentine 124

1. Time:

   1:15 pm – 1:35 pm

   Title:

   SCORE Resources for Teaching with Sports Applications

   Speaker:

   Robin Lock (St. Lawrence University)

   Abstract

   The NSF-funded SCORE (Sports Content for Outreach, Research, and Education) project is building a network of educators and sports analytics professionals to create, review, and disseminate datasets and teaching modules for bringing sports applications into statistics and data science courses. We discuss the sorts of resources available now at the SCORE website (https://scorenetwork.org/) and illustrate how faculty can use these materials in class and students can find interesting data for projects. We are also working to grow the network and encourage new contributions from faculty and students.

2. Time:

   1:45 pm – 2:05 pm

   Title:

   Developing A Sports-Centered Approach To Strengthen Data Science Education

   Speaker:

   Faith Rhinehart (St. Lawrence University)

   Abstract

   The SCORE Network provides hands-on learning in sports analytics to build skills and spark career interest in quantitative stem fields. Through my fellowship, I created modules and data repositories in a variety of sports for numerous statistical topics for SCORE.

3. Time:

   2:15 pm – 2:35 pm

   Title:

   GAISE Recommendations for Introductory Statistics and Data Science

   Speaker:

   Patti Lock (St. Lawrence University)

   Abstract

   The GAISE report (Guidelines for Assessment and Instruction in Statistics Education) provides recommendations and learning outcomes for introductory statistics and data science. The report was originally written in 2005, was revised in 2016, and is currently being revised again. The reports and revision are endorsed by the American Statistical Association. The speaker is co-chair of the national revision Steering Committee and will discuss the new recommendations and learning outcomes.

Location: Valentine Hall 117

1. Time:

   1:15 pm – 1:35 pm

   Title:

   Peridynamic Heat Conduction Problems

   Speaker:

   Yozo Mikata (Aquarius)

   Abstract

   In this talk, formulation of peridynamic heat conduction problems and their solutions will be discussed. Peridynamic theory is a nonlocal theory of continuum mechanics, and it was originally developed by Silling (2000) for elasticity. It has since been applied to many different engineering problems including heat conduction (Bobaru, et al., 2010; Mikata, 2020). The primary result of this paper is a systematic development of peridynamic governing equations in heat conduction for general anisotropic peridynamic materials. Unlike several existing studies on peridynamic heat conduction, where the development of the theory relies more on heuristics and numerical results, the development of the theory in this paper is more systematic and completely analytical. 3D peridynamic heat equation with heat source is analytically solved with two different configurations. Numerical results and comparison with the classical solutions for the same physical configurations will be discussed.

2. Time:

   1:45 pm – 2:05 pm

   Title:

   A mathematical model of the immune system to understand response to regulatory T cell therapy in type 1 diabetes

   Speakers:

   James Greene (Clarkson University), Mackenzie Dalton (Sanofi), Emmanuel Asante-Asamani (Clarkson University)

   Abstract

   Type 1 diabetes (T1D) is an autoimmune disease in which the immune system attacks pancreatic beta cells, leading to high blood glucose levels and requiring lifelong insulin therapy. There is no cure, and individuals with T1D may face a reduced lifespan of up to 12 years. Defects in regulatory T cells (Tregs) are a key contributor to disease onset and are being explored as a therapeutic avenue. However, the effectiveness of Treg therapy remains uncertain. Research is further limited by the inability to directly observe pancreatic and lymph node activity during the long presymptomatic stage of T1D. In this study, we develop a mathematical model for beta and T cell dynamics. We find both Treg quality and quantity affect disease progression, and that antigen-presenting cell (APC) dynamics play a central role. Notably, Treg therapy combined with APC depletion improves outcomes, especially with strong peptide-induced APC activation.

3. Time:

   2:15 pm – 2:35 pm

   Title:

   Efficient Sustainability Solutions Using Particle Swarm Optimization

   Speaker:

   Ahmad Almomani (SUNY Geneseo)

   Abstract

   Optimization plays a crucial role in advancing sustainability by improving the efficiency of resource management and system design. In this talk, Particle Swarm Optimization (PSO) to sustainability problems such as water harvesting and energy efficiency, and compares its performance with commonly used algorithms, including Genetic Algorithms and Simulated Annealing. Results indicate that PSO achieves faster convergence and higher-quality solutions in nonlinear, multi-objective settings, while traditional methods remain competitive in certain problem structures. The findings highlight the significance of algorithm selection in sustainable system design, providing practical guidance for developing cost-effective, resilient, and environmentally responsible solutions.

4. Time:

   2:45 pm – 3:05 pm

   Title:

   Comparing Methods for Ranking through Pairwise Preferences

   Speaker:

   Shandeepa Wickramasinghe (Utica University)

   Abstract

   Ranking a set of items is a fundamental problem with a wide range of applications in fields such as information retrieval, machine learning, data science, and cybersecurity. In this talk, I will focus on comparison-based ranking, where items are judged in pairs and the outcomes are aggregated to produce an overall ordering. Pairwise comparisons are both mathematically manageable and user-friendly: instead of giving absolute scores, we just decide which of two items is better. For example, when grading student projects, comparing two at a time is easier and more consistent than assigning exact scores. I will provide an overview of three major families of methods for pairwise ranking: count-based, Markov chain-based, and regression-based, and discuss their mathematical foundations, strengths, and limitations. Using both simulated and real data, I will present how these methods perform and identify when one approach may be better. By the end of this talk, you will have a clear picture of the landscape of ranking methods and why finding the “best” ranking is still a fascinating open question.

Location: Bewkes Hall 109

1. Time:

   1:15 pm – 1:35 pm

   Title:

   A Geometric Derivation of the Irwin-Hall Distribution

   Speaker:

   James Marengo (RIT)

   Abstract

   The probability distribution of the sum of n independent uniformly distributed random variables on the interval (0,1) is known as the Irwin-Hall distribution. With the help of the of the inclusion-exclusion principle, its cumulative distribution function will be derived geometrically. The central limit theorem tells us that when n is “large” , the Irwin- Hall distribution can be approximated by a normal distribution, and this fact will be illustrated in this talk. The talk should be accessible to any student who has had a calculus-based probability and statistics course.

2. Time:

   1:45 pm – 2:05 pm

   Title:

   Moreau Inequality

   Speaker:

   Gabriel Prajitura (SUNY Brockport)

   Abstract

   As part of marking 100 years since the first edition of Polya \& Zsego's Problem Book in Analysis (the original German edition) I will discuss one of the problems included in the book. I will present few simpler proofs than the one included in the book.

3. Time:

   2:15 pm – 2:35 pm

   Title:

   Pushing the Envelope Theorem: What Do Lagrange Multipliers Actually Measure?

   Speaker:

   Gordon Craig (Université Laval)

   Abstract

   The method of Lagrange multipliers is the most basic technique for solving nonlinear constrained optimisation problems, and is a standard topic in most multivariate calculus courses. But in these courses,  the actual Lagrange multipliers are treated as auxiliary variables which we want to get rid of as quickly as possible. In fact, the Envelope Theorem, which is well-known in optimisation and economics, allows us to interpret the Lagrange multipliers as so-called "shadow prices", which measure the effects of relaxing the constraint on the optimal value. In this talk, I'll explain what the Envelope Theorem says, why it's true, and discuss some consequences.

4. Time:

   2:45 pm – 3:05 pm

   Title:

   Diophantine equations related to integer eigenvalues of a graph

   Speaker:

   Anurag Agarwal (RIT)

   Abstract

   Integral graphs are those graphs whose spectrum of eigenvalues consists entirely of integers. The identification of all integral graphs is quite challenging. However, for some special graphs the prospects are much better. We will discuss a particular family of graphs for which the question of it being an integral graph relates to solving a Diophantine equation. We will present a complete (and rather surprising) solution to this Diophantine equation.