AlexDOPEAF

Great Plains Alliance

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.


Current       Past       Members

Previous Talks

Date

Presenter
Support
Institution
9/22/17

Erica Miller
Paula Egging
Creighton University


Mathematical Knowledge for Teaching Examples in Pre-Calculus: A Collective Case Study



The purpose of this collective case study is to examine mathematical knowledge for teaching examples in pre-calculus. 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 pre-calculus? 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 pre-calculus 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 Nebraska-Kearney


The card game SET and tic-tac-toe 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 tic-tac-toe 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 square-root-of-2-order derivative or a pi-th order derivative.)

We will focus on derivatives on a discrete domain, i.e. differences. We will start by investigating whole-order 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, two-dimensional 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.