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) A survey of a broad selection of concepts in modern geometry and topology, with an emphasis on intuition and example computations. While this class is more theoretical than an 18.0x, it does not require the ability to analyze or construct abstract proofs. It should be particularly suitable for students who aren't sure yet whether they want to, or have time to, go significantly further in the general 18.9xx direction. Prerequisite: 18.03 or 18.06.
- 18.901 (Introduction to Topology) The first part introduces topological spaces, which is a very general context in which the notions of continuous map or compact subset make sense. The second part of the course studies the fundamental group, a basic algebraic structure that describes the structure of paths in a topological space. Because of the level of abstraction, it is important that students taking 18.901 have already developed the ability to construct proofs in an axiomatic framework. Even where it is not a requirement, the class can be useful for students who want to go deeper into certain parts of analysis or geometry. Prerequisite: 18.100.
- 18.904 (Seminar in Topology) Topics vary. Generally, aims to build on the content of 18.901 while exploring a broader range of subjects in topology. 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.