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Intermediate
Higher Education
en
Geometry and Topology in the Plane
MIT OpenCourseWare
Platform
· Cambridge, USA
About this course
An undergraduate mathematics course that introduces geometric and topological ideas in the Euclidean plane. Topics include polygons and winding numbers, billiards and phase space, principal frequency and symmetrization, smooth and immersed loops, algebraic curves and their intersections, two-dimensional complexes and Betti numbers, hyperbolic geometry, and curved geometries with geodesics and curvature.
Prerequisite Skills
Skills you should have before taking this course
linear algebra
Calculus
real analysis
Skills Gained
Skills you will develop by completing this course
linear algebra
geometry
topology
algebraic curves
hyperbolic geometry
differential geometry
complex analysis
mathematical problem solving
Spectral theory (principal frequency)
Combinatorial topology