Sonia Kovalevsky High School Mathematics Day

Mississippi State University
April 22, 2005

Sponsored by

The Association for Women in Mathematics
Mississippi State University


About Sonia Kovalevsky

Hosted by
Mississippi State University

Department of Mathematics and Statistics
Mississippi University for Women

Division of Science and Mathematics
Schedule
Workshop Abstracts
Event
All participants
Learning Biology Through Numbers
Dr. Naisyin Wang, Professor
Department of Statistics
Texas A & M University
Abstract: With the rapid growing of modern technologies, the amount and types of data biologists collect also grow. Consequently, statisticians or mathematicians who handle the data are often among the first to learn the information embedded in the large among of numbers. In this talk, several examples varying from circadian rhythms data from Cyanobacterial, relationship between Bcl2 protein levels and DNA adduct damage in colon carcinogenesis to partially degraded mRNA microarray data will be given as illustrations of learning Biology through numbers.
Prerequisites: Suitable for all attendees.
Morning Workshop Session
Students
Choose one workshop. In making your selection, please pay attention to prerequisites.
Workshop #1
Playing with Patterns
Dr. Bruce Ebanks
Department of Mathematics and Statistics
Mississippi State University
Abstract: We will ponder puzzles and problems pertaining to primes, polyhedrons, perpendiculars and perhaps parties.
Prerequisites: Suitable for all attendees.
Workshop #2
Equations or Experiments: Using Math to do Chemistry
Dr. Steve Gwaltney
Department of Chemistry
Mississippi State University
Abstract: Not only is mathematics the language of science, in many cases we use mathematics to do science. In this presentation we will see several examples of using mathematical models to help explain experiments. In addition, we will see how mathematical modeling lets us answer questions we cannot study experimentally.
Prerequisites: Algebra I.
Workshop #3
Fractals / The Koch Snowflake
Ms. Annalisa Ebanks
East Mississippi Community College
Abstract: Fractals are all around us, in the shape of a mountain range or in the windings of a coastline. The mathematical concept of a fractal characterizes objects with structures on various scales, large as well as small. Fractal objects are self-similar in that they do not change their appearance significantly when viewed under a microscope. Who says Mathematics cannot be fun? In this presentation we are going to look at the perimeter and area of a fractal called the ''Koch Snowflake.'' This will be a hands-on workshop where participants will construct their own ''Koch Snowflake.''
Prerequisites:Suitable for all attendees.
Workshop #4
Lotto Luck: A Computer Demonstratio of the Lottery
Dr. Dongfeng Wu
Department of Mathematics and Statistics
Mississippi State University
Abstract: People of all ages seem fascinated by the lottery, making it a ready tool for illustrating basic probabilistic concepts. This workshop will demonstrate how the lottery really works through the use of a computer program called "Lotto Luck", developed by Ronald L. Wasserstein. The program demonstrates what happens to the "earnings" of the frequent lottery player over a period of time. The ideas of probability as a long-run frequency illustrated by this program will be extended to statistics and the testing of hypotheses.
Prerequisites: Suitable for all attendees.
Teachers
Easy to Use Free Statistical Software
Ms. Lorraine Hughes
Department of Mathematics and Statistics
Mississippi State University
Abstract: We will learn how to use statistical software called StatCrunch, freely available over the Web. Specifically we will use the software to make histograms and boxplots.
Afternoon Workshop Session A
Students
Choose one workshop. In making your selection, please pay attention to prerequisites.
Workshop #1
Inverse Problems
Dr. Tuncay Aktosun
Department of Mathematics and Statistics
Mississippi State University
Abstract: The aim in solving an inverse problem is to determine a cause from one or more of its effects. In this talk intended for a general audience, inverse problems are described and their significance in various fields is indicated through examples.
Prerequisites: Suitable for all attendees.
Workshop #2
Using Chi-square Tests to Determine the Genetics of Corn and of Corn Snakes
Dr. Marty Harvill
Division of Science and Mathematics
Mississippi University for Women
Abstract: Statisticians use a metthod called the chi-square (X<sup>2) test to check whether the numbers observed from an experiment provide evidence of an effect. The test compares the experimental observations to the values expected under ''no effect''. The Chi Square Test answers just one question: ''Are the results obtain from an experiment (observed results) close enough to the predicted results (expected results) to indicate no effect exists?'' In the first part of the presentation, we will use Corn (Zea mays) as a model for understanding basic genetics. Each cob on a corn plant contains several hundred kernels, and each kernel is the result of a separate fertilization event. That is to say, each kernel grows out of a separate fertilized egg. The eggs all come from the same maternal plant. If a geneticist takes care to ensure all the eggs on a single corn plant are fertilized by pollen (sperm) from a single paternal plant then a single cob of corn will contain several hundred ''sibling'' kernels, all derived from the same two parents. The second part of the presentation, we will look at some corn snake parents and their offspring and determine their genetic make up using the same principles we used on the corn cobs.
Prerequisites: Algebra I.
Workshop #3
Time Travel
Dr. Patrick Lestrade
Department of Physics and Astronomy
Mississippi State University
Abstract: : In your dreams -- and I am speaking here of the daydreams you don't always share with others -- don't you relish the idea of traveling back in time? Or perhaps forward, faster than the normal flow takes us? Historically, we have perceived two types of barriers to doing such fun things: technology and the laws of physics. Patience, money, and brainpower often overcome the former; the latter can seem insurmountable.

But there's good news. Come hear how Einstein's laws of relativity, instead of being barriers, actually provide the key to how your dreams may one day be realized. My goal is to show you that the mathematics needed to understand relativity and the space-time continuum are within your grasp. This isn't your father's universe. It's yours. Explore it and be inspired.
Prerequisites: Algebra I.

Workshop #4
Cubics and Quartics
Dr. Kevin Knudson
Department of Mathematics and Statistics
Mississippi State University
Abstract:: Everyone knows how to find the roots of a quadratic equation, but what about cubic equations? Or even harder: how about quartic (4th degree) equations? In this talk, I will show you the formulas for finding the roots of such equations and talk about what happens for equations of higher degree.
Prerequisites: Algebra II.
Teachers
Making the Connections
Ms. Kim Walters
Department of Mathematics and Statistics
Mississippi State University
Abstract: Too often students believe that they can do algebra but not geometry or vice versa. In this workshop we will explore some connections between algebra and geometry that might help students have a more positive point of view of both topics.
Afternoon Workshop Session B
Students
Choose one workshop. In making your selection, please pay attention to prerequisites.
Workshop #1
The Seven Bridges of Konigsburg
Dr. Ted Dobson
Department of Mathematics and Statistics
Mississippi State University
Abstract: Suppose that you drive a garbage truck (or read a gas meter, or any other job where you have to visit every home in a neighborhood). Our problem here is to determine a good route for your garbage truck. What would a good route look like? Well, your job is to start your day at work, pick up all the garbage cans on your route, and then return to where you started. A good route would be one where you had to do as little work as possible. That is, you would want to drive by every house on your route once, but if possible, not twice. We will discuss the solution to this problem, as well as discuss the historical background of the solution-which has nothing whatsoever to do with garbage trucks.
Prerequisites: Suitable for all attendees.
Workshop #2
Mathematics Meets Biology: Some Elementary Mathematical Models
Dr. Seth Oppenheimer
Department of Mathematics and Statistics
Mississippi State University
Abstract: We will present some mathematical models of biological and medical phenomena that require only high school (algebra II) mathematics. We will illustrate these models using computer simulations.
Prerequisites: Algebra II.
Workshop #3
The Great Apple Market Game
Dr. Keith Coble
Department of Agricultural Economics
Mississippi State University
Abstract: Central to understanding market economies is an understanding of the Laws of Supply and Demand. Increasingly, economists use games in a laboratory setting to test hypothesis of how people will behave when confronted with economic problems. In this session, students will participate in a classroom experiment that illustrates supply and demand, how the mathematical equilibrium is reached, and how intervention in the market creates disequilibrium.
Prerequisites: Suitable for all attendees.
Teachers
Connections Between Secondary Mathematics and Popular Films
Dr. Bonnie Oppenheimer
Division of Science and Mathematics
Mississippi University for Women
Abstract: A guided tour through the special features about a current popular file (Lord of the Rings: the Fellowship of the Ring) will show the amount of mathematics required to create a believable world.
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