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In Real Analysis you learned about metric spaces — any set of objects endowed with a way of measuring distance — and the topology of sets in such spaces (open, closed, bounded, etc). In this course we flip this on its head: we explore how to develop analysis (limits, continuity, etc) in spaces where the topology is known but the metric is not. This will lead us to a bizarre and fascinating version of geometry in which we cannot distinguish between shapes that can be continuously deformed into one another. Not only does this theory turn out to be beautiful in the abstract, it has become a vital part of data analysis and is also connected to many areas of math and physics. This course is excellent preparation for graduate programs in mathematics.
Format: lecture; Taught remotely, but synchronously. While recordings of lectures will be made available, all participants are expected to make their best effort to attend the class over Zoom. In addition to class meetings, there will be tutorial sessions with a TA once per week.
Grading: no pass/fail option,
yes fifth course option
homework, tutorials, and exams
MATH 350 or 351; not open to students who have taken MATH 323. Familiarity with basic group theory recommended, but not required.
Juniors and seniors