Fundamentals of group theory: homomorphisms and the isomorphism theorems, finite groups, structure of finitely generated Abelian groups. Structure of rings: homomorphisms, ideals, factor rings and the isomorphism theorems, integral domains, factorization. Field theory: extension fields, finite fields, theory of equations. Selected topics from: Galois theory, Sylow theory, Jordan-Holder theory, Polya theory, group presentations, basic representation theory and group characters, modules. Applications chosen from mathematical physics, Grobner bases, symmetry, cryptography, error-correcting codes, number theory.
MA 535: Algebra
Department