Abstract Algebra

This is a modern course in abstract algebra with an emphasis on groups, rings, fields, vector spaces, and related algebraic operations like group actions. By studying the symmetric groups and Galois theory, we prove the impossibility of certain geometric constructions and the solution of the quintic or higher order polynomial equations (in a single variable) by radicals. Special topics include the study of the general structure of geometries over sets in terms of their transformation groups (Klein Erlangen Programme).