MATH 476 - Representation Theory

A course in matrix representations of groups, a topic which unites the powers of group theory and linear algebra. Topics include: symmetry in linear spaces, modules, group actions, characters, tensor products, and Fourier analysis on groups. Applications are chosen from: ranked data, molecular vibrations, quantum mechanics, random walks, number theory, and combinatorics. Important ideas from linear algebra are revisited from a more sophisticated point of view. These include: linear transformations, abstract vector spaces, change of basis, subspaces, direct sums, projections, and eigenvalues and eigenvectors. Prerequisite(s): MATH 376 . Odd numbered fall semesters. (4 Credits)