### MATH 3231: Abstract Algebra II

**Description:** The main goal of this course is to discuss Galois theory, which is the study of relationships among roots of polynomials. For example, we will use Galois theory to prove that there is no formula analogous to the quadratic formula for the roots of *x ^{n}* -

*x*- 1 when

*n*is at least 5, or in fact for the roots of most polynomials of degree at least 5. More generally, Galois theory provides a correspondence between two different topics in algebra: fields and groups. Our study of fields will use linear algbera in interesting ways. For example, we will see how to show certain polynomials are irreducible using the concept of dimension. Only towards the end of the course will group theory be needed in a serious way, at which point what we need from group theory will be reviewed.

**Prerequisites:** Math 3230.

**Offered:** Spring (odd years)

**Credits:** 3

**Sections: **Fall 2018 on Storrs Campus