21-752 Algebraic Topology

12 units, Carnegie Mellon University

Topology is a less rigid variant of geometry that studies shapes of spaces. Algebraic topology associates algebraic invariants, such as groups or rings, to such spaces. This is achieved by building a space from simpler ones or by algebraically keeping track of how to map a simple space into a given space. This course will cover the fundamental group and covering spaces, homology theories, and the cohomology ring of a space (time permitting). (Three 50 minute lectures)

Prerequisites: 21-651 (min B) and (21-355 (min B) or 21-235 (min B) or 21-455 (min B)) and (21-373 (min B) or 21-237 (min B))

Offered: Spring 2026

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