Fall 2026

Topology is the study of continuous functions: informally, a function is continuous when a little mistake in the input corresponds to a correspondingly small mistake in the output. Continuous functions are seen in calculus, but this course vastly expands the notion. First, and at length, we introduce metric spaces, which aren't usually sets of numbers but still have a notion of distance between any two points. Then we expand to general topological spaces, which have no intrinsic notion of distance at all, but have a qualitative notion of "nearby". These seemingly abstract theories are grounded in applications, from the existence of solutions to differential equations to the formulation of general relativity to certain questions about fuzzy tennis balls.