MAA  Mathematical Association of America

Seaway Section

Location: Valentine/Bewkes Hall 1

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:

   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/Bewkes Hall 2

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:

   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.

Location: Valentine/Bewkes Hall 3

1. Time:

   1:15 pm – 1:35 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.

2. Time:

   1:45 pm – 2:05 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.

Location: Valentine/Bewkes Hall 4

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:

   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.