Abstract Algebra

Appreciate the power of abstraction and the axiomatic method.

We begin with rings and fields to see how familiar properties of the integers can be extended to polynomial rings, and then to other rings and fields, before moving to groups. You will learn the definition of rings and fields at the same time as you will see the construction of various number systems and the ordered field structure of the real line in Calculus 2, and study vector spaces over the reals in Linear Algebra.