Course Description

Mathematics 403a/b Field Theory

Automorphisms of fields, separable and normal extensions, splitting fields, fundamental theorem of Galois theory, primitive elements, Lagrange's theorem. Finite fields and their Galois groups, cyclotomic extensions and polynomials, applications of Galois theory to geometric constructions and solution of algebraic equations.

Prerequisite: Mathematics 308a/b or the former Mathematics 303b.

3 lecture hours, half course.

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