Mathematics is described using a very precise language. Its basic ingredients are sets and logic. Proofs consist of a number of steps based on formal rules of logic. This is not an introduction to these technical topics, but a description of some basic ideas and notational conventions that we will use in this course - in fact, these are, with slight modifications, part of the basic language common to all mathematicians. Since one of the purposes of the course is to introduce students to proofs, it is imperative that the ideas discussed here be thoroughly understood.