Group Representations

Group representation theory studies abstract groups by realizing their elements as linear operators, turning questions about symmetry into linear algebra over a group algebra whose module structure encodes everything. You'll spend the term computing character tables, decomposing representations via Maschke and Schur, and pushing into modular territory with Jacobson radicals, Cartan matrices, and Brauer characters — assessed through homework, a midterm, an oral presentation, and a final. Building on graduate algebra, it's the standard gateway to finite group theory, number theory, and Lie-theoretic work, and the modular half connects directly to active research in block theory.