I know this is not really a research question, but I would like to ask it of research mathematicians, to see if there is a consensus. In a recent discussion on this topic, someone suggested that if you ask 10 different mathematicians you'll get 10 different answers ...
My question: What topics do people think should be taught in a first course in Geometry at undergraduate level? You can assume students have already covered basic Linear Algebra and Analysis. The course would be of 10-12 weeks, with 2 lectures per week (typical course length in the UK).
In contrast to say Analysis or Algebra, it seems not obvious to me at all. In Algebra I don't think I'd be sticking my neck out to suggest one would introduce groups, subgroups, cosets, Lagrange's theorem, normal subgroups, factor groups - the syllabus writes itself. In Analysis it would be convergence (sequences and possibly series) and continuity. (If you want to disagree with those suggestions, please start a different thread.)
