Imagine for a moment that you are sitting through a boring lecture and you start playing with your calculator. You input a number into the calculator and then hit the cosine key. Then you keep hitting the cosine key and look at what happens to the numbers. Do they converge to a ?finite number or do they tend to in?finity? Do the numbers start to repeat in a pattern, or do they continue to change without any pattern? This is an example of a discrete dynamical system. Discrete dynamical systems have important applications in biology and other sciences as well as being interesting on their own. In this talk, we will discuss the properties of discrete dynamical systems and some tools that can be used to determine the behavior of discrete dynamical systems. No previous knowledge of dynamical systems is required to understand the talk, and there will be only one theorem.