Abstract Algebra: Using Sylow theory, we show that any simple, non-abelian group with 60 elements is isomorphic to A_5, the alternating group on 5 letters. As an application, we show that A_5 is isomorphic to the symmetry group of rigid motions of a regular icosahedron.
U.Reddit course materials available at ureddit.com/class/23794/intro-to-group-theory Master list at mathdoctorbob.org/UReddit.html
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.