Learn the fundamental objects in algebra, especially representation theory, with hands-on experience in computing representations and constructing sophisticated proofs for some powerful (and quite beautiful!) results. Practice focuses on the basic structures of simple Lie algebras over the complex numbers, as well as the theory of highest weight representation including Verma modules and enveloping algebras, concluding with Weyl's character formula for finite-dimensional simple modules. Additional topics include root systems, Cartan subalgebras, Cartan/triangular decomposition, Dynkin diagrams, and the Killing form.   

This is an alternating years course.