ABSTRACT
In this chapter we present a collection of topics which serve as a background for the ideas you will see in this text. In Section 1.1, we present equivalence relations which foreshadow many important structures in abstract algebra such as cosets of a group, the orbits of a group action, and much more. In Section 1.2, we present basic ideas about functions, since all the structures presented in this text will have special functions associated with them. Section 1.3 will highlight some fundamental properties of the integers as a prelude to the more general topic of rings. In Section 1.4, we describe in more detail congruence modulo n which is an equivalence relation with additional properties. The equivalence classes of this relation produce one of the basic examples of a group and of a ring. Although, not explicitly presented, ideas in basic set theory are prevalent in this text and are an important background topic.
