Diff Geom25: Manifolds, classification of surfaces and Euler characteristic

Here we give an informal introduction to the modern idea of manifold, putting aside all the many logical difficulties that are bound up in this definition: difficulties associated with specification, with the use of infinite sets, with the notions of functions etc. Even those students who aspire to understanding mathematics correctly ought to be at least aware of the standard formulations, and if one is teaching a course at a major university these days one is limited by the curriculum and the orien br, br,