An algebra course through a historical perspective with a particular focus on group theory and its applications, empahsizing on the one hand how central concepts in this subjet emerged as answers to concrete mathematical questions, and on the other hand how group theory has become central in mathematical fields far beyond algebra. The first half of the course will dive into Galois theory and the study of polynomial equations following Galois' original viewpoint. The second half of the course will study how Galois' breakthrough ideas have impacted mathematics and other disciplines as a whole; possible topics include the Erlangen program and classical Lie group actions in geometry, algebraic topology and a topological approach to Galois theory, or applications of group theory to molecular physics.
Prerequisites: Math 310 plus any proof-based math course (such as Math 318, 370, 371, 4111, 429. etc.).
Course Attributes: FA NSM; AR NSM; AS NSM