Galois Theory - MATH5725

The theory of fields holds the key to questions which frustrated mathematicians for hundreds of years, including the impossibility of squaring a circle or trisecting an angle with ruler and compass, or finding a formula for solving quintic equations. The key to their study involves the Galois group which, loosely speaking, captures the symmetry of the field. Topics covered will include, fields, Eisenstein criterion, field extensions, algebraic extensions, groups of field automorphisms, normal and separable extensions, finite fields, Galois correspondence, solvable groups, solving equations by radicals, ruler and compass constructions, Kummer extensions, Artin-Schreier extensions.

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