Date of Award

2009

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Ali E. Özlük

Second Committee Member

William M. Snyder

Third Committee Member

Andrew Knightly

Abstract

Galois theory is an area of modern algebra which provides a framework for transforming problems involving fields into more manageable problems involving groups. The fundamental theorem of Galois theory asserts that there exists a one-to-one correspondence between certain subfields of a splitting field of a polynomial and the subgroups of its Galois group. This realization provides an elegant answer to the question of whether a polynomial equation over a base field is solvable by radicals. In fact, a polynomial is solvable by radicals if its Galois group is a solvable group. In general, the determination of the Galois group of a polynomial is not itself a trivial task, thus the determination of Galois groups provides a basis for the content of this thesis. More specifically, this thesis is concerned with the determination of Galois groups using resolvent polynomials from theory to implementation.

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