Dr. Molly Dickens (Texas Tech University)

A Picture Contains Thousands of Numbers

“A picture is worth a thousand words.”  - Napoleon Bonaparte

This famous quote is a reminder of the incredible impact a picture can have on our perception.  Pictures have always had the ability to quickly tell us about a person, place, situation, or event but did you know that most pictures today are made from numbers?  Thousands of them?  These types of pictures are called digital images and they are everywhere!  Every image on a computer, transmitted via the Internet, reproduced on a printer, and even taken by most modern cameras is a digital image defined by a large array, or grid, of numbers.  Each number in a digital image represents the color or grayscale value of the image at the location of that number within the grid.  And because digital images are made up of numbers, mathematics can be used to improve, analyze, and compress them.  In this workshop, we will see examples of digital images and learn how they are described by numbers.  We will look at how mathematics can be applied to the numbers of an image for purposes such as improving a blurry or noisy image, analyzing the content of an image, and reducing the amount of numbers necessary to describe an image.

  Dr. Kathleen Gilliam (Texas Tech University)

Mathematical Modeling and Signal Processing in Wind Related Research 

Our society is increasingly exposed to atmospheric hazards such as hurricanes, tornadoes, and severe thunderstorms. Every year, these hazards cause many fatalities and injuries, major disruption in community lifelines such as power, communications, transportation, and significant property damage. Recent advances in mathematical modeling and signal processing techniques offer the promise of better understanding of these wind events. This workshop will focus on how signal processing techniques based on data analysis can be used to solve some wind related problems. Illustrations presented in the workshop will include the following applications: using three-dimensional Doppler radar data for tornado detection; modeling a hurricane storm track; studying the formations of the wind-induced vortices on a building; detecting localized structures during thunderstorm outflows.

  Assistant Professor Dr. Petros Hajicostas (Texas Tech University)

Diophantine Equations 

In this talk we will discuss Diophantine equations, which are equations with two or more unknowns for which we search for integer solutions. We will examine first and (possibly) second degree Diophantine equations, and we will solve some applied problems where these equations appear.

  Assistant Professor Dr. Lourdes Juan (Texas Tech University)

                                The Curves of Love

Since ancient times people have drawn hearts to convey a message of love. Few of them would ever imagine that such a picture would arise in a mathematical exercise: First draw a circle in the plane. Then imagine that another similar circle is moving along it. Let A denote the point on both circles where they meet at the beginning and trace its trajectory as the second circle moves. The trajectory will be a heart-shaped curve called a cardioid. Cardioids are interesting examples of curves whose mathematical expression is tedious if one uses the rectangular coordinate system but becomes fairly simple if instead one resorts to polar

coordinates. In this workshop we will take a look at cardioids, polar coordinates and a seductive mathematical transformation that makes something tedious become neat.

 Horn Professor Dr. Clyde Martin (Texas Tech University)

Mathematics has no Answers

Have you ever wondered where the word problems in your algebra book come from? In this workshop we will expose their source and try to decide if a selection of these problems are dumb, dumber or dumbest! We will take a close look at one problem in particular. We look at the problem “If Jane can mow the yard in 1 hour and her brother John can mow the yard in two hours how long will it take them to mow the lawn if they work together?” in some detail. We will find the origins of this problem in cave art from the Pleistocene. We will ask the eternal question “Does this problem make sense?” and find the answer that is surely NO. However, we will try to find a version of the problem that does make sense and in doing so we discover that mathematics doesn’t have answers but is only a tool for helping to make real life decisions.

  Assistant Professor Dr. Magdalena Toda (Texas Tech University)

   THE ENTIRE WORLD COMPRESSED IN A DISK OR HYPERBOLIC GEOMETRY

The hyperbolic plane is embedded inside of a disk; the edge of the disk represents infinity.

In hyperbolic geometry, the sum of the angles of a triangle is always less than 180 degrees. An amazing fact here is that there is an upper limit to the possible area a triangle can have, even though there is no upper limit for the lengths of the sides of the triangle.

We will interactively draw polygons in the hyperbolic plane, and prizes will be given for creating the most beautiful hyperbolic snowflakes!

   Workshops for Teachers

  Assistant Professor Dr. Lih-Ing Roeger (Texas Tech University)

    What Does Mathematics Have to Do with Infectious Diseases?
Epidemics have seriously affected human populations throughout history. One of the most notorious epidemics in history is the "Black Death" (bubonic plague), which spread throughout Asia and Europe. Between 1346 and 1350, it is estimated that one third of the European population died from plague. Mathematics has played an important role in the study of infectious diseases. One of the first scientists to use mathematics in connection with the spread of diseases was Daniel Bernoulli. In 1760, Bernoulli used a mathematical model to
investigate whether inoculation of people with a weak virus affected the
spread of smallpox. Since then, mathematical models have become
increasingly important tools in studies on the impact of vaccination
programs. We will discuss some of the ways mathematics is used to model
the spread of infectious diseases.
 

 Assistant Professor Dr. Jerry Dwyer (Texas Tech University)

                  Mathematical games in k-12 classrooms

A series of mathematical games will be presented. These games will
illustrate problem solving strategies that are applicable to all grade
levels. Different pedagogical approaches will be explored. Connections
with state and national standards will be described. The use of games as
enrichment in the K-12 classroom will be discussed.