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MAST30026 Lecture 1: What is space? (Part 1)

I started with three dictionary definitions of "space" and briefly discussed them, before moving on to a survey of the standard abstract notions of space used in mathematics, including metric, topological and Hilbert spaces. In the remainder of the lecture I discussed the connection between symmetries of the plane and the abstraction of inner product spaces. Part 2 of this video finishes off the contents of the lecture notes. Lecture notes: http://therisingsea.org/notes/mast300... The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For details see the class webpage.