This course covers the fundamentals of manifolds, including topology, interior, exterior, boundary, closure, Hausdorff spaces, quotient spaces, projective space, second-countable space, continuity, compactness, locally Euclidean spaces, examples for manifolds, projective space as a manifold, and smooth structures. The course aims to teach students the concepts and properties of manifolds, providing them with the skills to understand and work with these mathematical structures. The teaching method involves theoretical explanations and examples to illustrate the concepts. This course is intended for individuals interested in advanced mathematics and geometry.
Overview
Syllabus
Manifolds - Part 1 - Introduction and Topology.
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure.
Manifolds - Part 3 - Hausdorff Spaces.
Manifolds - Part 4 - Quotient Spaces.
Manifolds - Part 5 - Projective Space.
Manifolds - Part 6 - Second-Countable Space.
Manifolds - Part 7 - Continuity.
Manifolds - Part 8 - Compactness.
Manifolds - Part 9 - Locally Euclidean Spaces.
Manifolds - Part 10 - Examples for Manifolds.
Manifolds - Part 11 - Projective Space is a Manifold.
Manifolds - Part 12 - Smooth Structures.
Taught by
The Bright Side of Mathematics
