The Great Plains Alliance (GPA) was initiated in 2017 in
order to connect UNL mathematics graduate students with
speaking opportunities at nearby institutions.
Please email Alex Zupan at zupan@unl.edu to volunteer as a
speaker or a support role or to request a student talk at
your college or university.
Date 
Presenter 
Support 
Institution 

9/22/17 
Erica Miller 
Paula Egging 
Creighton University 

Mathematical Knowledge for Teaching Examples in PreCalculus: A Collective Case Study  
The purpose of this
collective case study is to examine mathematical
knowledge for teaching examples in precalculus. The
instructors involved in the study were experienced
graduate teaching assistants who were teaching their
course for the third time who had been identified by
their department as good teachers. Utilizing a
cognitive theory approach, I analyzed video
recordings of enacted examples. The central question
that guided this analysis was: What is the
mathematical knowledge for teaching examples in
precalculus? The goal of this study is to examine
postsecondary mathematical knowledge for teaching
from the perspective of practice, instead of relying
on existing frameworks. As a result of this study,
the author developed a model of mathematical
knowledge for teaching examples in precalculus that
includes knowledge of connections, representations,
students, instruction, and content when enacting
high cognitive demand examples. 

9/29/17 
Derek deSantis  Jesse Moeller  Dordt College  
Turning Hard Problems Into (Infinitely) Many Easy Problems  
In mathematics, we tend to
study only a few classes of functions. Examples
include polynomials, rational functions, trigonometric
functions, exponentials, and step functions. Why is
this? Certainly other, more complex functions appear
in nature. Could it be that any other type of function
is too hard to study in generality? A pragmatic answer
to this question is the following: the “complicated
functions” are lots of simple functions in disguise. This talk is primarily about the approximation of complicated functions using simpler functions. We will begin by reviewing the types of approximations learned in calculus – tangent line and Taylor series approximations. We will discuss what we mean by approximation, and the flaws that these techniques have. We will then move on to talk a bit about a different type of approximation, and how linear algebra can solve many of these problems. For better or for worse, this will take us to a world of infinite dimensional spaces. Applications of this approach are vast, including machine learning, signal processing, and a formulation of quantum mechanics to name a few. 

10/12/17 
Matt Mills  Andrew Hayes  University of NebraskaKearney  
The card game SET and
tictactoe on a torus 

SET is a card game played with a special deck of 81 cards. Each card contains four features: color (red, purple or green), shape (oval, squiggle or diamond), number (one, two or three) and shading (solid, striped or outlined). The game begins by setting out 12 of these cards and the goal of the game is to quickly find a set of 3 cards such that each individual feature is completely uniform or completely different. If no such set exists with the initial 12 cards then 3 additional cards are added until a set can be made. This leads to a natural question. What is the minimum number of cards that must be played in order for us to be certain a SET exists? We will answer this question by relating a set of cards to a configuration on a tictactoe whose edges are glued together and counting something in this new setting. The talk will be accessible to a general audience.  
10/24/17 

Neil Steinburg 
Austin Eide 
Wayne State College 

Removing excess surface
area with a little soap, water, and the Divergence
Theorem 

Suppose you want to find a surface that will enclose a certain amount of volume while having as little surface area as possible. You might be quick to suggest a sphere. But how do you know a sphere is the best shape? And what if you have to meet other conditions for the surface as well? Maybe you need that surface to contain two separate volumes or maybe you want it to have a specific boundary. As it turns out soap bubbles and soap films solve these problems naturally. In this talk we will discuss how we mere mortals can learn from the bubbles and use a little Calculus 3 magic to actually prove which surfaces are best.  
11/16/17 
Areeba Ikram 
Jessie Jamieson 
Augustana University 

Fractional Derivatives on a Discrete Domain  
In your calculus course, you
learned a lot about derivatives. But how do we make
sense of taking a half derivative of a
function? L'Hopital asked this very question in his
1695 letter to Leibniz, to which Leibniz responded "It
will lead to an apparent paradox, from which one day
useful consequences will be drawn." Since then,
fractional calculus has developed to extend
derivatives to be of any fractional order in many
different ways. (In fact, we call them fractional
derivatives only for historical reasons; we can make
sense of a squarerootof2order derivative or a
pith order derivative.) We will focus on derivatives on a discrete domain, i.e. differences. We will start by investigating wholeorder differences and observing various results which have analog counterparts in calculus. Then we will develop the Caputo fractional difference and consider its properties. Finally, we will describe problems involving the Caputo fractional difference that are analogous to problems in ordinary differential equations. 

11/17/17 
Paula Egging 
Stephen Becklin 
Creighton University 

Triphos: An Alternative Coordinate System  
In this talk, we investigate characteristics and properties of the Triphos coordinate system, an alternative, twodimensional coordinate plane consisting of three axes evenly spaced 120 degrees apart. We will examine similarities and differences between the Triphos system and the Cartesian coordinate system, explore its algebraic and geometric properties, and discuss some advantages and applications of this nonconventional coordinate system. 