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Insolvability of the quintic in radicals

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Identifier	Thesis 2192
Author	Kielski, Michael Edward, 1983-
Title	Insolvability of the quintic in radicals
Publisher	Central Connecticut State University
Date	2011; *
Resource Type	Master's Thesis
Notes	The goal of this thesis is to trace the development in mathematical theory that led to the proof of the insolvability of the quintic. That is, there does not exist a general formula in radicals for equations of the form [not reproducible-see full text document for equation] for [not reproducible-see full text document]. There are of course solutions to equations of this form, in fact the fundamental theorem of algebra guarantees it, but a formula using only radicals to find the roots of the equation is an impossibility. The question as to why this is so has remained an allusive gem of mathematics until the early 19th century. Even then it was disputed for another forty years after being proven because of the seemingly unlikeliness of there not being a “nice” formula. After all, there were general formulas to find the roots of quadratics, cubics, and quartics so the question must be asked as to why there isn’t one for equations of the fifth degree and higher. This question has been a driving force behind the creation of Galois Theory which has ultimately redefined the way mathematics is structured. The ideas formed in order to find the roots of equations have permeated almost all areas of mathematics. Some mathematicians, such as Felix Klein, have suggested that these ideas, particularly group theory, be placed at the center of mathematical research because of their far reaching consequences. It is for this reason that the developments in early equation theory be closely examined and understood.
Subject	Quintic equations Equations, Roots of
Department	Department of Mathematical Sciences
Advisor	Waiveris, Charles
Type	Text
Digital Format	application/pdf
Language	eng
OCLC number	804653035
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Insolvability of the quintic in radicals

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