## Session Index

Click a session title to jump to the abstracts.

Faculty/Graduate Session 1

1:00pm--1:55pm, Gambet 206

Speakers: Guoan Diao, Derek Smith, Erin R. Moss

Faculty/Graduate Session 2

1:00pm--1:55pm, Gambet 214

Speakers: Christopher Vaughen, Michael Yatauro, Ethan Berkove

Faculty/Graduate Session 3

1:00pm--1:35pm, Gambet 224

Speakers: Myung Song, Baoling Ma

Faculty/Graduate Session 4

1:00pm--1:55pm, Gambet 232

Speakers: Wing Hong Tony Wong, Kevin Byrnes, Benjamin Nassau

## Faculty/Graduate Session 1, Gambet 206

1:00pm, **Guoan Diao** (Holy Family University)

*Are students ready for Lagrange Multipliers?*

View Abstract

When solving optimization problems with constraints in a multi-variable calculus class, students may choose to use the Method of Lagrange Multipliers. Although the method itself is not hard for students to understand, students often have difficulty fully implementing it. In this talk, I will provide some examples in which many students have trouble using this method. This talk will also include some suggestions and solutions for students to overcome their difficulties and prepare them for using this method.

Close Abstract1:20pm, **Derek Smith** (Lafayette College)

*The Batfox Assignment, and Other 3D Printing Adventures in Third-Semester Calculus*

View Abstract

Is it a bat? Or a fox? Reasonable people will disagree! Despite this, the Batfox is definitely a nice hands-on activity for finding the extrema of a two-variable function subject to a constraint. In this hands-on discussion, we will see how the Batfox and other 3D printing projects help students learn core material in multivariable calculus.

Close Abstract1:40pm, **Erin R. Moss** (Millersville University)

*Liberal Arts Mathematics: Online Resources and Flexible Framing*

View Abstract

Mathematics for Liberal Arts is a class that can benefit tremendously from an instructor’s flexibility, and teaching it can be an immensely rewarding and creatively fulfilling experience. To provide students with a more customized experience and the benefits of Open Educational Resources (OERs), I used materials created for The Art of Mathematics, an NSF-funded project at Westfield State University. With these texts and information gathered about my students, I constructed a unique learning trajectory that incorporated students’ interests—our class’s “story”—in a way that established continuity and introduced new ideas while repeatedly connecting back to earlier mathematical concepts. In this presentation, I discuss free online resources that can be used for this course and ways to frame the class in order to be responsive to students’ interests.

Close AbstractBack to index

## Faculty/Graduate Session 2, Gambet 214

1:00pm, **Christopher Vaughen** (Montgomery County Community College)

*The Kerbal Math & Physics Lab*

View Abstract

I will present a lab workbook for math and physics, useful as a supplement for classes or with math and physics clubs. The workbook covers topics of rocket science and orbital mechanics and is inspired by the computer game Kerbal Space Program. The workbook contains questions from algebra level through differential equations.

Close Abstract1:20pm, **Michael Yatauro** (Penn State - Brandywine)

*Mathematics in The Simpsons and Futurama*

View Abstract

In today’s pop culture environment, knowledge and intellect seem to be celebrated more so than in the past. One prominent example is in the recent success of the show The Big Bang Theory. However, to quote an episode of South Park, “The Simpsons already did it”. Although not the first television show to reference science and mathematics, the writers of The Simpsons (many of which have advanced degrees in STEM fields) used such references to take their jokes to a higher level. While these references were subtle in The Simpsons, they were front-and-center in its sister show Futurama (so much so that a mathematical paper was published based on results from an episode). We will look at some of my favorite moments from both shows that showcase the ability of the writers to use mathematics for entertainment purposes.

Close Abstract1:40pm, **Ethan Berkove** (Lafayette College)

*Polynomial division, generating functions, and sum formulas*

View Abstract

In this talk we'll describe how the right polynomial long division problem allows us to derive sum formulas like this one involving Fibonacci numbers:
$$
f_0 + f_1 + \ldots + f_n = f_{n+2} -1
$$
We will outline how this lucky coincidence can be explained using generating functions. The resulting technique can also be applied to other number sequences that arise from linear recurrence relations.

Close AbstractBack to index

## Faculty/Graduate Session 3, Gambet 224

1:00pm, **Myung Song** (Kutztown University)

*A Numerical Likelihood-Based Approach to Combining Information*

View Abstract

Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analysis are studied. A multivariate numerical integration method for developing a better approximation of the likelihood for correlation matrices is studied. Analyses for inter-correlations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Evaluation and Visualization of the likelihood and the MLE is conducted. Comparison with two conventional methods (joint asymptotic weighted average method & marginal asymptotic weighted average method) is shown.

Close Abstract1:20pm, **Baoling Ma** (Millersville University of Pennsylvania)

*Mathematical models to investigate the interactions between malaria parasites and host immune response*

View Abstract

Malaria infection has posed a major health threat for hundreds of years in human history. In this talk, new mathematical models are developed to study the complex interactions between a host immune response and the Plasmodium falciparum parasite. Model simulations are applied to investigate the interplay between the host immune response and the parasite dynamics, the disease dynamics in acute infection, and treatment effectiveness with different drugs.

Close AbstractBack to index

## Faculty/Graduate Session 4, Gambet 232

1:00pm, **Wing Hong Tony Wong** (Kutztown University of Pennsylvania)

*A bijective proof for the probability in a random walk game*

View Abstract

Consider a random walk that starts from $0$ on the integer number line and moves $+1$ or $-1$ at each step with equal probability. Let $q(k)$ denote the probability that the random walk does not land on any positive integers in the first $k$ steps. In 2019, Leung and Thanatipanonda showed using Maple that for every positive integer $m$, $q(2m)=q(2m-1)=\frac{\binom{2m}{m}}{2^m}$. In this talk, we provide a bijective proof of this result.

Close Abstract1:20pm, **Kevin Byrnes** (Wilmington, DE)

*The Asymptotic Order of Circuit Codes*

View Abstract

A circuit code of spread $k$ is a simple cycle $C$ in the graph of the $d$-dimensional hypercube $I(d)$ with the property that for any vertices $x,y\in C$, $d_{I(d)}(x,y)\ge \min \{d_C(x,y),k\}$. One application of circuit codes is as error-correcting codes, so it is of interest to find the maximum length of a circuit code in dimension $d$ with spread $k$, $K(d,k)$. For $k\le 2$ it is known that the asymptotic order of $K(d,k)$, $\nu(k):=\lim_{d\to \infty} \frac{\log_2 (K(d,k))}{d}$, is maximum (i.e. equal to $1$). However for $k\ge 3$ the asymptotic orders of the best known general lower and upper bounds on $K(d,k)$ quickly diverge.
In this talk, suitable for a general audience, we give an introduction to circuit codes and establish the asymptotic formula $K(d,k) = 2^{d+O_k(\log^2d)}$ by using analytic methods to interpolate lower bounds on $K(d,k)$ that exist for a sparse subset of dimensions. In particular, this proves that $\nu(k)$ exists and equals $1$ $\forall k\ge 3$.

Close Abstract1:40pm, **Benjamin Nassau** (University of Delaware)

*On the Biaffine Part of \(PG(2,q)\) and its Myriad Properties*

View Abstract

Let \(P_3=L_3=\mathbb{F}_q^3\) with \(q\) an odd prime power. We define \(\Gamma(q;p_1l_1,p_1l_1^2)\) to be the bipartite graph with partition sets $P_3$ and $L_3$ such that \(p=(p_1,p_2,p_3)\in P_3\) and \(l=[l_1,l_2,l_3]\in L_3\) are adjacent if and only if
\begin{align*}
p_2+l_2&=p_1l_1,\\
p_3+l_3&=p_1l_1^2.
\end{align*}
Then \(\Gamma(q;p_1l_1,p_1l_1^2)\) is the biaffine part of the generalized quadrangle \(PG(2,q)\) \(-\) an induced subgraph at distance 3 from a fixed edge in the quadrangle. It has girth 8 and diameter 6.
Over finite fields of odd characteristic we know of only one generalized quadrangle in a graph theoretic sense. Given that the biaffine part is an inherent part of \(PG(2,q)\), an interesting question arises: can we construct a previously unknown generalized quadrangle by way of the biaffine part? More precisely, do there exist functions \(f_2\) and \(f_3\) different from \(p_1l_1\) and \(p_1l_1^2\) such that the bipartite graph \(\Gamma_3(q;f_2,f_3)\) can be "reattached" to a tree in a way that would result in a generalized quadrangle non-isomorphic to \(PG(2,q)\)?
In this talk we will discuss a natural extension of available methods and what it may mean for the question as a whole. This is joint work with Felix Lazebnik and Andrew Woldar.

Close AbstractBack to index