Author Information

Jesse Berglund


It is known that the general equations of fourth-degree or lower are solvable by formula and general equations of fifth-degree or higher are not. To get an understanding of the differences between these two types of equations, Galois theory and Field theory will be applied. The Galois groups of field extensions will be analyzed, and give the solution to the query “What is the difference between unsolvable fifth-degree equations and fourth-degree equations?”

Note on the Author

Jesse Berglund is a senior mathematics major. This research was conducted over the summer of 2010 as an Adrian Tinsley Program Summer Grant project under the mentorship of Dr. Ward Heilman.

Rights Statement

Articles published in The Undergraduate Review are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.

Included in

Mathematics Commons