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Insolvability of the quintic in radicals
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Insolvability of the quintic in radicals
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Description
Identifier
Thesis
2192
Author
Kielski, Michael Edward, 1983
Title
Insolvability
of the
quintic
in
radicals
Publisher
Central Connecticut State University
Date of Publication
2011
Resource Type
Master's Thesis
Abstract
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
reproduciblesee
full
text
document
for
equation]
for
[not
reproduciblesee
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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