This advanced class combines a traditional abstract algebra curriculum with topics in linear algebra and geometry. Topics include: introductory group theory; Sylow theorems; isometries of the Euclidean plane; symmetries of wallpaper patterns; isometries of the hyperbolic plane and Kleinian groups; elementary Lie groups and their discrete subgroups; Lie algebras; spectral theorems and decomposition theorems for finite-dimensional vector spaces; multilinear algebra; Galois theory; rings and modules; and introductory representation theory. Exploration of these topics will extend over both the Fall and the Spring term. There will be opportunity for students to pursue individual research questions. Registration is first-come, first-serve, starting when 4000-level registration opens on May 17. To register, see the instructor in Dickinson 213 on Mondays 1:00pm – 2:00pm, Tuesdays, 1:00pm – 2:00pm, and Fridays 2:00pm – 3:00pm, or email firstname.lastname@example.org.