Modern Algebra 1.

Catalog description

PR: Adequate background in abstract algebra including group, ring, and field theory, and adequate background in linear algebra. Focuses on Galois theory - the study of roots of single variable polynomials - an application of group theory to the study of field extensions. Covers group actions, Sylow theorems, solvable groups, field extensions, splitting fields, Galois group of a polynomial, fundamental theorem of Galois theory, solvability by radicals, and further topics if time permits.