Ring Theory: We define PIDs and UFDs and describe their relationship. Prime and irreducible elements are defined, and conditions for implication are given.
(second version: corrections to definition of prime and irreducible; comment should be 'R UFD implies R[x] UFD, improved proof that, in UFD, irreducible implies prime).
Includes course on Group Theory (problems and solutions at website) and Ring Theory, and Field Theory. For Prerequisites on proofs and sets, see the Math Major Basics course.