 10th Emmy Noether High School Mathematics Day Texas Tech University, Department of Mathematics and Statistics May 17th, 2012

 Workshops for Students  What is infinity? How far is it to infinity?, Room MATH 112. Dr. Roger W. Barnard Abstract: We will discuss Zeno's Paradox and the stereographic projection to determine if infinity isunattainable or can one get there. Fun with Difference Equations, Room MATH 114. Dr. Raegan Higgins Abstract: This will be 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. How math can help you survive a zombie apocalypse and win the lottery, Room MATH 110. Mr. Levi Johnson, Mr. John Calhoun Abstract: The talk will be an interactive examination of how simple probability can help us understand the world around us. We will specifically examine games of chance and zombie outbreaks. We will also discuss college and career opportunities for students who are interested in learning more. Greeks, Graphs, Bridges, and Brains, Room Math 109. Dr. Brock Williams Abstract: Dice games usually use 3-dimensional, 6-sided cubes as dice. Cubes are completely regular - all the sides and angles are the same - so they make great dice. But it is also possible to make dice with 4, 8, 12, or 20 sides using the other Platonic solids. The ancient Greeks discovered, however, that those are the only regular dice you can make! We'll discuss why that's true and how it applies to current research on visualization of very irregular surfaces such as brains. Mathematics, Quilting, and Design, Room MATH 108. Mrs. Carol Williams Abstract: There is a tremendous amount of mathematics in the creation and design of quilts, clothes, and other textiles. We will design our own quilt blocks and discuss along the way the connections to fractions, scaling, symmetry, and economics. What can a mathematician do?, Room MATH 111. Dr. Clyde Martin Abstract: In this talk I will discuss some of the many things that you can do with mathematics from teaching to research. Most people think that about all you can do with mathematics is teaching but that is not the whole truth. Some of the questions that mathematicians ask are things like: Why are diabetes and obesity related? How do stress fractures develop in the leg bones? Can stress fractures be eliminated? What will happen if many children don't receive their vaccinations? These are questions that I have and am studying and we will talk about some other questions time permitting. Dynamics of Predator-Prey and Competition Interactions,Room MATH 113, COMPUTER LAB. Dr. Sophia Jang Abstract: Mathematical models are important tools to study biological phenomena. We shall introduce several classical models from ecology and use computer simulations to study population interactions. We will explore the cyclic behavior of the predator-prey interactions and of the competition outcomes for two competing populations. We will see when the predator and prey populations can coexist and when the predator will drive the prey population to extinction in a predator-prey system. We will also examine which population can out-compete the other population, when two populations utilize the same limited resources.

 Workshops for Teachers  10:00-10:50 AM: Geometry in Pictures and in Proofs, Room MATH 115. Dr. Jerry Dwyer Abstract: We will examine some interesting geometric results and how they can be visualized. Connections to algebraic reasoning will be presented. Elementary proof techniques will be discussed and examples for student exploration will be given. 11:00-11:50 AM: A deep look at some elementary math, Room MATH 115. Dr. Gary Harris Abstract: In this presentation we will explore some interesting mathematical questions that arise in elementary and middle school mathematics. For example there are two ways to determine whether are not two fractions are equal. One is to cross multiply and see if you get the same integer, the other is to see if they have the same reduced form. Why are these equivalent? Also there are two ways to define the rational numbers. One is to define the rational numbers to be the set of all integer fractions and the other is to define the rations numbers to be the set of all finite, or infinitely repeating, decimals. Why are these equivalent? For that matter, what does it mean for an infinitely repeating decimal to be anything? Also, we all have seen the proof that there is no fraction whose square is 2. Why should, or must, there be any number whose square is 2? Finally, can we characterize the set of all fractions which are themselves some power of a fraction? In other words, which fractions have the property that their p-th root is rational.

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