Title: Chaos and the Game of Life
Presenter: Julia Barnes, jbarnes@email.wcu.edu, 828-227-3943
Abstract: Chaos means a lot of different things to different people. In mathematics we have our own definition of chaos. In this presentation, we look at what chaos means to a mathematician. Then we look at one example based on Conway’s Game of life which is a mathematical model of population growth. We will do a hands-on activity to introduce the game, and then we will explore a computer applet that generates more complicated patterns.
Room requirements / constraints: For the computer applet, I would need to use a computer projector and connect my laptop to it. I would also need an Internet connection. For the hands-on activity, it would be best to have movable tables or flat desks at least the size of a placemat. However, I can usually make this work in any room… even if it means going to the floor. I would need to know how many students are going to be there.
Level: This could be done in any middle school or high school classroom.
Length: One class period… I can adjust to 50 min or 75 min classes, etc.
Title: Fractals and the Chaos Game
Presenter: Julia Barnes, jbarnes@email.wcu.edu, 828-227-3943
Abstract: Fractals have been a buzz word for several years now, and this talk will hit on some of the most common ideas. We will look at what it means to be a fractal and talk about some examples of fractals. We will generate some fractals by hand, some by paper folding and some by using an activity on Bob DeVaney’s web page that creates a Sierpinski triangle. Then we will use a computer program to generate more accurate fractals. As time permits, we would also explore target practice, which is an applet on DeVaney’s web site that is related to the Sierpinski triangle.
Room requirements / constraints: For the computer demonstrations, I would need to use a computer projector and connect my laptop to it. I would also need an Internet connection. For the hands-on activity, it would be best to have movable tables or flat desks at least the size of a piece of paper, however, any writing surface could work. I would also need either an overhead projector or a document presenter. I would need to know how many students are going to be there.
Level: This could be done in any middle school or high school classroom.
Length: One class period… I can adjust to 50 min or 75 min classes, etc.
Title: What exactly is the Mandelbrot set, and how does it relate to Julia sets?
Presenter: Julia Barnes, jbarnes@email.wcu.edu, 828-227-3943
Abstract: The Mandelbrot set and Julia sets have images that many students could have seen without looking – like on a poster or a book cover. But, what many people don’t know is that these images come from very interesting, yet very basic techniques. In this talk, we define the Mandelbrot Set and the Julia Set, we look at pictures of these sets, and we explore a variety of properties of these sets.
Room requirements / constraints: I would need to use a computer projector and connect my laptop to it. I would also need an Internet connection. In addition, it would be nice to have either a white board or a chalk board available.
Level: To understand this talk, a student would have to be comfortable with what a function is, and be able to follow a little bit of complex multiplication. I define everything I use with complex numbers, but a student would need enough mathematical maturity to be comfortable with i.
Length: One class period… I can adjust to 50 min or 75 min classes, etc.
Title: Pythagoras, his Followers, and his Theorem
Presenter: Sloan Despeaux *, despeaux@email.wcu.edu, 828-227-3825
Abstract: A 50- minute talk on Pythagoras, the Pythagoreans, the Pythagorean theorem, proofs of the theorem, and the theorem BEFORE Pythagoras.
Level: Middle school.
Length: 50 minutes
*Note: Good times for Dr. Despeaux are Tuesdays, Thursdays 9-11 am or 2-3:30 pm, or Fridays after 11 am. Dr Despeaux will only be available until November this semester.
Title: The First Attacks on a ‘Man-Eating Problem’: the Four Color Problem in Nineteenth-Century Britain
Presenter: Sloan Despeaux *, despeaux@email.wcu.edu, 828-227-3825
Abstract: A 50-minute talk on the history of the Four Color Problem. This problem took over a century to prove, and engaged some of the best mathematical minds of the 19th and 20th centuries.
Level: High school
Length: 50 minutes.
*Note: Good times for Dr. Despeaux are Tuesdays, Thursdays 9-11 am or 2-3:30 pm, or Fridays after 11 am. Dr Despeaux will only be available until November this semester.
Titles: How many ways are there for N horses to finish a race if ties are allowed?
Presenter: Joe Klerlein, klerlein@email.wcu.edu, 828-227-3827
Abstract: The problem for 4 horses was asked several years ago as an NPR puzzle.
We generalize the problem and give a “Pascal triangle” like solution.
Level: High school – Math Club or Honors
Title: One to one functions that really count
Presenter: Joe Klerlein, klerlein@email.wcu.edu, 828-227-3827
Abstract: This talk involves counting the number of objects in a collection. The idea is to establish a one to one correspondence between the given set and a second set. Then count the number of objects in the second set.
Level: High school – Math Club or Honors
Title: Combinatorial identities from N dice.
Presenter: Joe Klerlein, klerlein@email.wcu.edu, 828-227-3827
Abstract: We begin by asking the probability that the sum of the faces values of two dice is even. We generalize to N dice and different divisors of the face value.
Level: High school – Math Club or Honors
Title: How proportional are we?
Presenter: Axelle Faughn, afaughn@email.wcu.edu, 828-227-3829
Abstract: How do paleonthologists reconstruct an entire skeleton from only a few bones found in the ground? How can a forensic scientist determine the height, weight, and age of a body with as little evidence as a skull? We will use measurements and proportionality to show how mathematics combines with science in these real-world situations.
Level: Middle school
Length: 50-90 minutes
Title: What is it like to major in Mathematics at WCU? What will I do afterwards?
Presenter: A group of students accompanied by Axelle Faughn, afaughn@email.wcu.edu, 828-227-3829
Abstract: Thinking about College? Why not choose the Mathematics and Computer Science Department at WCU? Currently enrolled students will answer questions regarding our programs, life on campus, and what makes WCU unique.
Level: High school
Title: Connect the Dots from Geometry to Botany
Presenter: Kathy Jaqua, kivey@email.wcu.edu, 828-227-3826
Abstract: How can logic and geometric ideas help us determine what tree a particular leaf came from? In this activity, students learn to read a dichotomous key and identify common leaves from the area.
Level: Middle school or High School
Length: 50-90 minutes
Title: Art and Mathematics
Presenter: Kathy Jaqua, kivey@email.wcu.edu, 828-227-3826
Abstract: Using a variety of grids, students create different cartoon-like pictures that show the effects of nonstandard grids.
Level: Middle school or High School
Length: 50-90 minutes
Title: 2-D, 3-D, and Mystery Buildings
Presenter: Kathy Jaqua, kivey@email.wcu.edu, 828-227-3826
Abstract: Using building blocks, students learn how to read three-dimensional tables and translate them into shapes. These ideas form the basis for multi-dimensional analysis of data at a beginner’s level. This activity can be tailored to more or less complexity to include the topics of reading data tables, creating buildings from tables, exploring 3-D shapes through contour plots, even double integrals from a discrete viewpoint.
Level: Middle school or High School
Length: 50-90 minutes