Instructor: Patricia Cahn
Office: 4C7
Office hours: Wednesday 12-1, Friday 3-4, Monday 12-1 (Math 460/500 only), and by appointment.
Textbook: Munkres' Topology, second edition.
Course description: This course covers point-set and algebraic
topology. In point-set topology, we generalize the ideas of
open sets, continuity, connectedness and compactness from
analysis. Topology can be viewed as qualitative geometry; rather
than paying attention to distances, curvature, and other quantitative
properties of a space, we study the connectedness of the space, whether
it has "holes," and so on. In algebraic topology, we build tools for
converting problems in topology, where there is little structure, into
problems in algebra, where there is a lot of structure.
Topics covered: Point set topology: metric spaces and topological
spaces, compactness, connectedness, continuity, extension theorems,
separation axioms, quotient spaces, topologies on function spaces,
Tychonoff theorem. Algebraic topology: Fundamental groups and covering
spaces, and related topics.Prerequisites: Officially, Math 240/241, Math 360 or 508, or
permission of the instructor. Unofficially, you need to have experience writing
proofs. You also need some group theory (370 or 502), but this
may be taken concurrently, since we won't be using it until the second
half of the course.