Session Index
Click a session title to jump to the abstracts.
Faculty Session 1
9:40am--11:20am
Speakers: Kimberly Spayd, James Puckett, Qiaochu Chen, Robert Freeman, Dawn A Lott, José Contreras, Guoan Diao
Faculty Session 2
9:40am--11:20am
Speakers: William Y Velez, Cristina Bacuta, Matthew Rudy Meangru , Jonathan Keiter, Hossein Shahrtash, Michele Oswald, Maia Magrakvelidze
Faculty Session 3
9:40am--10:20am
Speakers: Daniel Cooney, Laxmi P. Paudel
Faculty Session 1
9:40, Kimberly Spayd, James Puckett, Qiaochu Chen (Gettysburg College)
Experimental Data v. a PDE Model of Two-Phase Flow in Porous Media
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The Buckley-Leverett PDE has long been used to model the flow of two fluids through a porous medium. Theoretical advances over the last couple decades have led to modifications of the PDE and new solution structures. We set out to validate some of these modifications and solutions by collecting experimental data. We were able to capture some evidence that supports new solutions, but there were significant questions raised as well. In this talk, we will discuss predictions from the PDE, the experimental results, and where we go from here.
Close Abstract10:00, Robert Freeman (Pennsylvania State University- Berks)
New Proof of the Equivalence of Weak and Viscosity Solutions to the $\texttt{p}(x)$-Laplacian in $\mathbb{R}^n$
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This talk is a discussion of a new proof for the equivalence of potential theoretic weak solutions and viscosity solutions to the $\texttt{p}(x)$-Laplacian, under certain reasonable restrictions on the function $\texttt{p}(x)$. The $\texttt{p}(x)$-Laplacian is the prototype equation for those partial differential equations exhibiting so-called nonstandard growth. The proof of the equivalence in the variable exponent case was first given by Juutinen, Lukkari, and Parviainen (2010), where their main argument is based on the maximum principle for semicontinuous functions and applied the uniqueness tools of the theory of viscosity solutions.
This proof extends the fixed exponent case approach of Julin and Juutinen (2012) to the variable exponent case, which is a direct proof that employs infimal convolutions.
Close Abstract10:20, Dawn A Lott (Delaware State University)
Optimizing Uncertainty of Information (UoI) in Decision Making via the LRM Method
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The importance of decision making cannot be overstated. Problems with decision-making exist in many fields such as mathematics, the sciences, business, agriculture, as well as in the military. Numerous challenges are present when information is provided to the decision-maker throughout the decision-making process. There are several sources of data needed and utilized in this process and decision-makers rely on the status of these sources when making a decision. In many cases, the challenges include the dependence and inter-dependence of sources/devices and the uncertainty of information (UoI) obtained from these sources. Any uncertainty of information significantly affects the decision-making process and expressing this concept to humans can highlight the underlying
reasons for uncertainty in making decisions. In this paper, a novel method called the LRM (Lott, Raglin & Metu) Method is formally introduced. The LRM method transforms the UoI concept into a linear optimization problem that is maximized using tools of operations research. The results yield the maximum value of uncertainty due to several sources of uncertainty and their relationship defined by a set of taxonomies selected as important to
humans in support of decision making.
Close Abstract10:40, José Contreras (Ball State University)
The Beauty of Posing and Solving Geometric Converse Problems: The Varignon Case
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In this presentation, I illustrate how my students use GeoGebra to discover the solutions to Varignon converse problems. Specifically, we use dynamic estimation to gain insight into the solution to the following three problems.
1) Let ABCD be a quadrilateral with medial quadrilateral EFGH. If EFGH is a rectangle, what type of quadrilateral is ABCD?
2) Let E, F, G, and H be the midpoints of the consecutive sides of a quadrilateral ABCD. If EFGH is a rhombus, characterize quadrilateral ABCD.
3) E, F, G, and H are the midpoints of the consecutive sides of a quadrilateral ABCD. Name quadrilateral ABCD when EFGH is a square.
Close Abstract11:00, Guoan Diao (Holy Family University)
Fibonacci Numbers and 2021
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In this talk, we will discuss the properties of Fibonacci numbers and find which Fibonacci numbers are multiples of 2021.
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Faculty Session 2
9:40, William Y Velez (University of Arizona)
The preparation of math major in the US and abroad
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This talk is based on an October 2020 Focus article, http://digitaleditions.walsworthprintgroup.com/publication/?m=7656&i=677122&p=28. In this talk I will compare the education of mathematics majors in the US and abroad and discuss implications for admissions to graduate programs.
Close Abstract10:00, Cristina Bacuta (University of Delaware)
Effective formative assessment in a synchronous online advanced calculus course
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In previous semesters, an advanced calculus course was designed to rely mostly on a summative type of assessment implemented at certain points of the semester. After three semesters of emergency teaching online, and after trying numerous teaching tools, strategies and formats, we concluded that formative assessment must be implemented for monitoring student learning and providing immediate feedback in order to enhance, deepen and encourage learning.
We will share a group of approaches that worked and proved to be effective such as: Poll Everywhere® combined with group work, homework online with both automatic grading and “Show work” enabled, peer student work critique and others.
Close Abstract10:20, Matthew Rudy Meangru (University of East Anglia )
Utilizing Mathematical Modelling and 3D Printing Activities to Explore and Impact Non-STEM Undergraduate Students’ Mathematical Identities
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In this presentation, I share a mathematical modelling and 3-Dimensional (3D) printing activity to help non-stem students enrolled in developmental mathematics courses develop a mathematical identity. When students engage in the activity, they portray their current and future identity – how they see themselves in the present and what they see themselves becoming in the future – as it relates to mathematics. This is known as mathematical identity work and this is the primary focus of this presentation. Across the United States, developmental mathematics courses tend to have students who aren’t interested in pursuing degrees in STEM (Science, Technology, Engineering, and Mathematics) and thus don’t see themselves as future mathematical learners. To explore potential ways students can develop their mathematical identities, I present a mathematical modelling activity that contains content from geometry and enables students to create tangible 3D objects. The activity asks students to name properties of 2D and 3D geometrical shapes and utilises a 3D modelling software called Tinkercad to produce a 3D model that will be printed using a 3D printer. I hypothesize that observing non-stem students’ engagement in the mathematical modelling activity through their group interactions, journals, and 3D printed object could offer insights into their journey in developing a mathematical identity.
Close Abstract10:40, Jonathan Keiter (East Stroudsburg University)
Laser-Cut 3D Objects to Teach Multivariate Calculus
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I will describe several projects that have the students working with 3D manipulatives to explore the concepts of partial derivatives and directional derivatives. By working with interlocking wood sheets that can be viewed as traces of a surface, the students have a deeper understanding of rates of change for functions of two variables.
Close Abstract11:00, Hossein Shahrtash, Michele Oswald, Maia Magrakvelidze (Cabrini University)
A Study Of Common Misconceptions In Mathematical Reasoning and Proofs
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In our study, we set out to gain an insight into mathematics educator's conceptions of mathematical proofs and their experience with constructing proofs. We have developed and distributed surveys whose goal is to evaluate mathematics educators’ understanding of statements, logical connectives, quantifiers, conditional connectives, and proof strategies. In this presentation, we aim to discuss some of our findings.
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Faculty Session 3
9:40, Daniel Cooney (University of Pennsylvania)
Using Game Theory and Differential Equations to Model Natural Selection Across Scales
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Natural selection often acts simultaneously upon multilevel levels of biological organization, inducing a tension between traits favoring selfish individuals and traits providing collective benefit for the group. Examples of such conflicts arise in settings including the evolution of the early cell, the evolution of virulence, and the sustainable management of common-pool resources. In this talk, we will discuss how we can the Prisoners' Dilemma game to understand conflict between what's good for the individual and what's good for the group. In this game, players can choose to cooperate or defect: defectors receive a higher payoff than cooperators, but a group of cooperators receives a higher average payoff than a group of defectors. We can model the simultaneous effects of within-group and between-group competition using a PDE describing the composition of strategies within groups. We will discuss the conditions under which this PDE model supports any cooperation in the long-time population and characterize a curious behavior we call the "shadow of lower-level selection", in which no level of between-group competition can fully erase the individual incentive to defect.
Close Abstract10:00, Laxmi P. Paudel (Albany State University)
Mathematical Modeling on the Obesity Dynamics in the Southeastern Region and the Effect of Intervention
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Overweight and obesity has been a major health problem in the United States. The severity is highest in the southeastern region. Contagious effect is a significant factor for the progression of the obesity and its identification can lead to effective planning in the intervention of the obesity epidemic. In this paper, we present a simple mathematical model for the current epidemiological dynamics of obesity in the southeastern region. We discuss the contagious nature of obesity in its transmission among friends and relatives. We also purpose some affirmative actions to the public health policy makers, the city planning authority, and the community itself that could minimize and even reverse the pattern of obesity.
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