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Chapter 2 Fields and Rings
You have been exploring numbers and the patterns they hide within them since your earliest school days. In Chapter 1 we reminded ourselves about some of those patterns (with the goal of understanding factorization) and worked to express them in a more formal way. You may find yourself wondering why we are going out of our way to complicate ideas you have understood since elementary school. The reason for the abstraction (and the reason for this course!) is so that we can explore just how far we can push these patterns. How far does our understanding of factorization in the integers stretch to other types of numbers and other mathematical objects (like polynomials)? In this chapter we will set the ground work for answering that question by introducing ideas that will assist us in streamlining our investigation into factorization.
