For many of the students, this is a first course in university-level, modern mathematics. The purpose of the course is to learn how to form correct, rational arguments called "proofs". This is done in the context of a rigorous development of the calculus of functions of one variable. Particular emphasis is place on constructing correct, logically sound derivations and arguments. We will cover the material of chapters 1 through 5 of the textbook (and also chapter 6 if time permits).