13th Emmy Noether High School Mathematics Day Texas Tech University, Department of Mathematics and Statistics May 13th, 2015

 Workshops for Students  Cards, magic and the hidden secrets of Math. Dr. Giorgio Bornia A magician has a very noble task: to be a generator of Wonder. It's been said that "a magician never tells his secrets". Sometimes the secret is just a fast hand, or the sleeve of a shirt. Other times, it's all about mathematics. We will talk about some card tricks and (possibly) discover the undiscoverable. After that, for the sake of Wonder, you are encouraged to keep the undiscoverable to yourself... Project Lazarus. John Calhoun, Graduate Student In the summer of 2013 a group of professors and students at Texas Tech University began the LAZARUS project. The goal of this project was to transform a small-scale zombie walk model into a massive simulation, and do so in the most efficient manner. This was accomplished in two ways. The first way was to adapt the simulation code to run on graphical processing units since these provide high processing performance at a low cost. The second way was to build a supercomputer to run this new simulation code. This computer would be built with standard off-the-shelve computer parts in order to keep costs down. While this sounds straight forward, this project faced many unforeseen problems and opportunities. This talk will tell the story of how the project progressed and will stress the multidisciplinary nature of the project, involving ideas from engineering, geometry, math, biology, computer science, video gaming, and teaching. Parallel lines never meet, or do they? Dr. Lars Christensen We learn in geometry class that parallel lines never meet, but every time we let our eyes follow a straight stretch of highway all the way to the horizon, we doubt it. Of course mathematics has a way to make sense of what we see. In projective geometry, two parallel lines do meet in a point infinitely far away! And, actually, a line and a parabola always have two intersection points, provided that one looks carefully and counts properly. Beat the Professor in these math games! Dr. Jerry Dwyer We will play some interactive games that challenge students' strategies and logical thinking skills. The games involve numbers, geometry, and graphs. We will show how these games help in the type of mathematical reasoning essential to success in high school and college mathematics. Time scales fly when you're having fun. Dr. Raegan Higgins This will be a hands-on down-to-earth introduction to difference equations and time scales. We will introduce a variety of basic sequences and see how to establish recursive relationships. In some instances, we will see how to use these recursive relationships to establish explicit formulas. Mathematics in Population Biology. Dr. Sophia Jang In this workshop we will learn how mathematics can be used to study biological populations. Specifically, we will go over some well known single population models and then introduce several predator-prey systems. We will also use computer simulations to explore the complex behavior of the mathematical models. An Invitation to Projective Geometry. Dr. David Weinberg By introducing a new system of coordinates, a new world of geometry is revealed. The projective line, the projective plane, and points at infinity will be explained. We will see why there are no parallel lines in projective geometry (they intersect at infinity). Time permitting, we will see the great unifying power of projective geometry by studying conic sections in the projective world.

 Workshops for Teachers  The most complicated derivation of the area formula for a rectangle that you have ever seen. Dr. Gary Harris We will explore the most complicated derivation of the area formula for a triangle possible by using characterization results for multi-linear functions on n-dimensional Euclidean space. 'Why?' You might ask. "Good question." I might respond. For one thing, it is the exact same reasoning that gets us the formulas for the volumes of pyramids in higher dimension that we can imagine. After all, isn't a triangle just a 2-dimensional pyramid? Using Zombies and High Performance Computing to Motivate Students. Dr. Brock Williams This session will be a hands-on introduction to LAZARUS, the Lab for the Analysis of Zombie Activity and Research into Undead Simulations. We'll discuss the math we use to model disease outbreaks - from the "zombie virus" to ebola. We'll visit the lab's new GPU cluster so you can see how a supercomputer is constructed. Finally, we'll describe the outreach mission of the lab and the web resources (at lazarus.ttu.edu) you can use to get your own students excited about math and computing.

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