ABSTRACT
This chapter examines how modern mathematics became dominated by algebraic thinking. We begin building successive sets of numbers. We start with the natural numbers, proceed to the integers, the rational numbers, the reals, and end with the complex numbers. Each such step is motivated by a particular kind of problem that required the expansion of the concept of number. From there we jump outside of numbers to examine algebraic structures: groups, rings, fields, and vector spaces. In the process, we examine morphisms, homomorphisms, isomorphisms, and the concept of isomorphic. We then shift to a basic discussion of topology. We end with category theory as the capstone of mathematical abstraction (so far).
