I've decided that I should make a diary of my progress in mathematics (both in my modules as a student at UCL and in my independent study and readings.) Currently, my UCL courses are: [examinable] Functional Analysis, Algebraic Topology, Algebraic Number Theory, Nuclear and Particle Physics; [non-examinable] Galois Theory, and Probability (from measure theory.) Just spent the day working through Algebraic Topology, particularly work with exact-sequences (and some diagram chasing!) and the homology of the "subdivided simplical circle". (This course is AT is "Via homology of simplical complexes" and doesn't assume ant general topology.)
Speaking of general topology, myself and some other UCL students have started an undergrad colloquium at the maths department. A friend an I gave a short talk and problem class on general topology to start it out (our department doesn't have a course in general topology, and my friend and I had done substantial reading on it - from Munkres and Dugundji.) We covered the definition of a topology, continuity, Hausdorff spaces, connectedness, and the quotient space (as best as we could given only an hour!) I typed up our notes from the talk and they're online:
Right, so....time for sleep...more maths tomorrow!