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Chapter 1 Foundations

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.