7th Emmy Noether High School Mathematics Day
Texas Tech University, Department of Mathematics and Statistics

May 6th 2009

Workshops for Students


Fun with Difference Equations
Dr. Raegan Higgins
Abstract: This will a brief and down-to-earth introduction to difference equations. We will introduce a variety of basic sequences. We will see how to establish recursive relationships and in some instances, see how to use these recursive relationships to establish explicit formulas.

Optimization: the art of making things better through math
Dr. Victoria Howle and Dr. Kevin Long
Abstract: What do protein structure, investment planning, engineering design, delivery truck routing, and soap bubbles all have in common? All are problems in optimization, the branch of mathematics studying how quantities take on their minimum or maximum values. For example, a trucking company will want to deliver as many items as possible while using as little fuel and driver time as possible, and a building engineer will want to minimize construction costs subject to safety code constraints. Remarkably, many problems in the natural world are also fundamentally based on optimization: for example, proteins will spontaneously fold into a configuration that minimizes a quantity called free energy, and soap bubbles will naturally take on a state of minimum energy.
We'll show some examples of optimization in the real world, and then talk about how one goes about computing the optimal value of a mathematical function.

Mathematics and Biology
Dr. Sophia Jang, Texas Tech University
Abstract: This workshop will introduce students to how mathematics can be applied to study biology. We will look at how the long time trend of a single population and of population interaction can be described by some simple maps. We will explore the cyclic behavior of the predator-prey interaction and of competition exclusion for two competing populations.

Mathematics of 3-D Animation
Dr. Chris Monico
Abstract: More and more movies and television shows make use of Computer Generated Imagery (CGI). Some movies, like Wall-E, were created entirely by computer. It might be surprising to learn just how much mathematics goes into this process. In this talk, we'll give a brief overview of the process of 3-D animation and some of the mathematics behind it.

Is the Universe Curved?
Dr. Magdalena Toda
Abstract: This is a brief introduction to some theories which mean to confirm or infirm the belief that the universe is curved. We will discuss the mathematical ideas behind the notion of curvature, and we will look at some elementary examples which make this notion more approachable.

So You Want to be a Statistician?
Dr. Alex Trindade
Abstract: This will be an overview of what statistics is, how statistics is present behind the scenes in every field of scientific endeavor, what statisticians do, some projects I've worked on, and how to become a statistician.

Workshops for Teachers


A conceptual approach to calculus
Dr. Jerry Dwyer
Abstract: We will explore some of the fundamental analysis underlying the familiar concepts of calculus. Group work and inquiry based instruction will be modeled. Teacher feedback will be solicited in order to develop approaches for diverse student populations.

Just where are the two roots of a quadratic polynomial, I mean really?
Dr. Gary Harris
Abstract: In this workshop we will see how to exploit the graphing capabilities of MAPLE to locate, in real space, the roots of any quadratic polynomial with real coefficients. The locations of the roots of the polynomial $x^2 - x - 3 $ in real space may not be particularly surprising; however, the locations of the roots of the polynomial $ x^2 + x +1$ in real space may be quite surprising.

Real uses of imaginary numbers
Dr. Brock Williams
Abstract : We typically introduce imaginary numbers to students as a way to deal with that pesky minus sign which sometimes shows up under the square root in the quadratic formula. But what good are these imaginary numbers anyway? Are they just figments of some mathematician's demented imagination? Or are they really useful for something we and our students care about? In this workshop we'll discover real world uses of imaginary numbers ranging from biology to image recognition.

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