Lecture summaries (2025)

1/28   The syllabus.  Introduction to the course.  Intuition behind manifolds: some manifolds, some manifolds-with-boundary, and some objects that are not manifolds.  Open sets and smooth functions.  Reference: Textbook 1.1, supplementary notes on topology of Euclidean space on the course webpage

2/3 Smooth functions on arbitrary subsets.  Diffeomorphisms.  The definition of a manifold.  Parametrizations.  Products of manifolds are manifolds.  Reference: Textbook 1.1