Bloomsburg University
Mathematics, Computer Science, and Statistics Department
High School Speakers Program
Brief Description
If you would like to have one of these talks given in your classroom completely free of charge, then please contact Dr. Kevin Ferland either by phone 389-4502 or by email kferland@bloomu.edu. Requests should be made at least two weeks (and preferably longer) before the desired presentation date.
Talks Offered
Logical Paradoxes and Infinite Loops
Dr. William Calhoun
In the 6th century B.C., Epimenides of Crete is reported to have said "Cretans are always liars." If he meant that no Cretan ever tells the truth, he must have been lying! Variations on this ancient paradox crop up many places in mathematics and computer science.
Two of the most interesting implications of the "Liar Paradox" were discovered in the 1930's. The Austrian mathematician Kurt Gödel showed that there are mathematical truths that cannot be proved. A few years later, English mathematician Alan Turing adapted Gödel's ideas to computer science, showing that some problems cannot be solved by any computer!
Turing's work has practical implications for computer programming. A common "bug" in computer programs is an "infinite loop" - a loop that never terminates. It would be nice if computer software could check a program to make sure no infinite loops are present. Unfortunately, no such software can exist. Turing showed that the problem of determining whether a program contains an infinite loop.
An Introduction to the Fun of Graph Theory
Dr. Kevin Ferland
Graph theory is a beautiful area of mathematics of which most high school students are probably unaware. Nonetheless, its fundamentals are quite accessible to teenagers who might be turned on by mathematics that is not intensive in formulas and algebra. We will introduce the basics of graph theory and present fun problems and applications. Contrary to what its name may suggest, graph theory does not deal with graphs of functions. However, it does lead to the drawing of lots of pictures when solving problems.
Simpson's Paradox: Statistics that make you think.
Dr. Kevin Ferland
There is more to statistics than simply looking at standard summary statistics like averages and percentages. We will discuss some examples in which different choices of summary statistics lead to different conclusions. These examples will challenge our intuition and force us to look more carefully at the data. We will consider examples like baseball batting averages and survival rates of smokers versus nonsmokers.
A Computer Science Talk Catered to What You Want
Dr. Curt Jones
Dr. Jones is open to suggestions from you. What computer science topic would you like him to discuss with your class? How about topics such as programming, networks, hardware, software, or the internet. However, don't restrict yourself to any list. He's a lively speaker and will surely be a joy for your class.
Sequenced That Do Interesting Things
Dr. Paul A. Loomis
Everyone has seen sequences of some type, from "2, 4, 6, 8, who do we appreciate?" to 1,1,2,3,5,8,13,... . I will talk about integer sequences that are less predictable and thus more interesting. Along the way we will run into perfect numbers, numbers found in the Bible, and some sequences that the experts still haven't figured out. If you can add, multiply, and factor integers, you have all you need to understand these sequences. Predicting what they will do is another matter.
A "Magical Way" for Solving Some Word Problems
Dr. Youmin Lu
In a cage, there are chickens and rabbits with 36 heads and 100 legs in total. How many chickens and how many rabbits are in the cage. A traditional way for solving this problem is to formulate a linear equation or a system of linear equations, and then solve it with methods learned in algebra. Actually, many word problems like this one can be solved without using paper and pen. We will apply the "magical way" on this problem and practice it with some other problems.
Mathematical Modeling of Tennis
Dr. Reza Noubary
Most tennis fans are so interested in Andre Agassi's forehand (or outfit) and Pete Samprass' serve that they never give any thought to the role of mathematics, and statistics in the game. In fact, these subjects have a more important place in tennis than any of the crowd favorites.
The nature of the score keeping in a tennis match allows for the important role of arithmetic. The player who wins a point is given a score that ascends as follows: 0 (love), 15, 30, 40, and 60 (won game). A set is then made up of six won games with a margin of two. A men's match is won by the player who is ahead in the best of five and a women's match is won in the best of three sets. Because a game of tennis is a system, these situations can be predicted using ideas from basic probability. This presentation will discuss this and other applications of mathematics in the game of Tennis.
Baseball and Mathematics
Dr. John Polhill
Fans of baseball love to compare players of today with players of the past. Using some basic statistics we can try to answer questions like, "Who had the greatest season of home run slugging in Major League history?" There are plenty of other applications of math in baseball, such as game theory. It will be clear why so many baseball fans love math and mathematicians love baseball.
Error-Correcting Codes
Dr. John Polhill
Was all mathematics finished 300 years ago? No way! We will talk about one very current field, the theory of error-correcting codes. It has only been around for about 50 years, and your computers and compact disks wouldn't work without such codes. Have you ever wondered how we get pictures from outer space? We will answer that question, too.
Games and Mathematics
Dr. Yixun Shi
Through a study of a few interesting games we will demonstrate how mathematics, at a level accessible to secondary students, can be applied to analyze these games. We will also show how mathematics can be used to help making decisions when playing these games. Students will be encouraged to participate in discussions and, if interested, to develop similar projects. Since many students enjoy playing games, these works may in general promote their interest in mathematics and may also help improving their problem solving skills.