ABSTRACT
As we begin to study the properties of fields, it is reasonable to start by looking at finite fields. Finite fields are much easier to visualize, since we can display the addition and multiplication tables to find patterns. Also, finite fields are completely understood. We can classify all finite fields in terms of their size. Finally, finite fields have many applications, playing a key role in the classification of finite simple groups, and also in error corrections codes such as the ones used for compact disks.
