Chapter 1 Foundations
Recognize whether simple statements about the integers are true or false.
Give examples that illustrate true statements about the integers.
Give counterexamples for false statements.
Compute powers of integers.
Apply the properties of exponentiation.
This chapter has two purposes. It is a reminder of some of the more basic mathematics that you have learned growing up at the same time we give an introduction to the language of mathematics. In particular we discuss statements about integers and definitions of properties of integers. We introduce variables as placeholders for integers and explain how they are employed in mathematics. We end the section with an introduction to exponentiation and properties of exponentiation.
Although in this section we work with integers, the same mathematical language is used when considering other mathematical objects. Sets, functions, and groups are other mathematical objects that we will consider in coming chapters.