The purpose of this application is to use Maple as a mathematical foundation for the development of an Artificial Neural Network (ANN). I recommend that you follow each of the sections even though they are repetitious because they will show you the process of how ANN is built. I have chosen the Preceptron to be used in this application because it was the first ANN to be developed (Caudill & Butler, 1992; Caudill & Butler, 1993; Lau, 1991). The first part of the application focuses on using basic mathematics. The second part focuses on linear algebra. Thus no matter what your level of mathematical expertise, you will be able to follow this application.