Office: DRL 4C7
Course meeting times: MW 3-4:20 in DRL 4C6
Office hours: Monday 4:20-5:20, Tuesday 1-2, and by appt.
Text: Munkres Topology, 2nd edition.
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Instructor: Patricia Cahn Office: DRL 4C7 Course meeting times: MW 3-4:20 in DRL 4C6 Office hours: Monday 4:20-5:20, Tuesday 1-2, and by appt. Text: Munkres Topology, 2nd edition. |
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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, so if you have not taken 360/508 but have some proof writing
experience, you may still be prepared for the course (but please talk
to me first). 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.