Had a much better day in the library today, maybe it was because I had some inspiration!! (hehe... I will leave that to all of your imagination!) Re-copied and paraphrased some of the proofs presented in the lecture notes.
I think those of you who have spoken to me will know that I am a pretty strong advocate of copying your own notes when it comes to mathematics. Yeah, when a lot of abstract and complicated proofs are presented, copying does help you think through what you are writing down and better understand that proof. That's why I am re-copying everything for this module. Just had a test on this module last Friday, it was ok. After the test was done, A/P Chew presented some possible solutions. And mine mostly fit his, so I guess I would do okay.
Functional Analysis; this was one module in which I did not touch a single tutorial question as I had no clue what was going on! To have scored a B+ for the first test was really God's amazing grace. But then, it was more becuase everyone did badly, rather than my own merit; I almost failed that test! Ironically, this is one module who name intimidated me the first time I looked through the maths prospectus in year one. I never considered taking it, until a friend told me it was one of the better modules, true enough it is.
It is the 4th analysis module that I am doing. It's interesting that most mathematics undergrads really hate analysis, me included, and while most do only 1 analysis module, I've taken 4! And I intend to take MA4266: Topology, next semester, which will make it 5!! Somehow have a knack for it. Don't know why.
Anyway, the module is about linear functionals, (functions whose codomain is the real number line and the function is linear, not straight line, but linear, ie f(ax +by) = af(x) + bf(y)) on Banach Spaces and Hilbert Spaces. And of course the main part of the course focuses on the 4 big theorems in Functional Analysis, Hahn-Banach, Closed-Graph, Open-Mapping and Banach-Steinhauss Theorems. Just revisted the proofs of most of those theorems today. Very interesting. It's good that this module is a "soft-analysis" module, so I can avoid episilon-delta like proofs during the exam.
Covered most of the module today. That's good. Still need to cover 2 more sections. Then I should be ok with this module. Will see how I fare when I study at home on Friday.
PS: Read something interesting just now on another blog. Maybe I will say something tomorrow.
