Topology and Geometry

Topology is the study of properties of geometric objects which do not involve distance or angle; allowing consideration of such additional properties leads to Geometry.

  • 18.900 (Geometry and Topology in the Plane) provides an introduction to concepts and constructs in geometry and topology using examples accessible with only 18.0x preparation. Prerequisite: 18.03 or 18.06.
  • 18.901 (Introduction to Topology) explores the notion of continuity at its deepest level. Prerequisite: 18.100.
  • 18.904 (Seminar in Topology) is an introduction to algebraic topology: the fundamental group, covering spaces, classification of surfaces. Prerequisite: 18.901.
  • 18.950 (Differential Geometry) explores concepts of curvature, focusing on curves and surfaces. Prerequisites: 18.100 and Linear Algebra.
  • 18.952 (Theory of Differential Forms) gives a modern theoretical treatment of Stokes' theorem using differential forms. Prerequisites: 18.101 and either 18.700 or 18.701.
  • 18.994 (Seminar in Geometry) Prerequisites: 18.100 and Linear Algebra.