Senior Honors Theses

Publication Date

Spring 5-2010

Major

Mathematics

Primary Subject Area

Mathematics

Keywords

Evariste Galois, Field Extensions, groups

Disciplines

Algebra | Logic and Foundations

Abstract

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible to trisect an angle using only a ruler and compass.

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