I periodically find myself questioning my abilities as a mathematician (not to mention as a human being), but I am in one of those up-swing times right now - everything seems possible, and I just feel very very excited at the thought that I am going to get to do math for the rest of my life (inshah allah). So I thought I should list out some of the cool things I've learnt this semester.
(Oh btw, my blog-editor (Scribefire) has an on-the-fly spellchecker which flagged "allah" and "learnt" but not "oh" :)
Here goes :
1. Montel's theorem, Zalcman's lemma, Picard's theorem and the other awesome compactness conditions for meromorphic functions.
2. Covering spaces and their correspondence with the group of deck transformations.
3. Rudimentary notions of a Riemannian metric, and some wishy-washy stuff about the hyperbolic metric on the unit disc.
4. Weyl-Von Neumann theorem about self-adjoint operators (crazy!)
5. Definition of the extension of a C* algebra, and the introduction to Brown-Douglas-Fillmore theory.
6. Nuclearity, exactness, c.p. lifting theorems
7. Amenability of a group and its connection with nuclearity (together with a cool proof of amenability of an abelian group).
8. Just yesterday, some homotopy techniques in computing the K-theory of pull-backs (still fresh!)
So that's that. I hope, in times of desperation, I look back on this note and feel good again.
(Oh btw, my blog-editor (Scribefire) has an on-the-fly spellchecker which flagged "allah" and "learnt" but not "oh" :)
Here goes :
1. Montel's theorem, Zalcman's lemma, Picard's theorem and the other awesome compactness conditions for meromorphic functions.
2. Covering spaces and their correspondence with the group of deck transformations.
3. Rudimentary notions of a Riemannian metric, and some wishy-washy stuff about the hyperbolic metric on the unit disc.
4. Weyl-Von Neumann theorem about self-adjoint operators (crazy!)
5. Definition of the extension of a C* algebra, and the introduction to Brown-Douglas-Fillmore theory.
6. Nuclearity, exactness, c.p. lifting theorems
7. Amenability of a group and its connection with nuclearity (together with a cool proof of amenability of an abelian group).
8. Just yesterday, some homotopy techniques in computing the K-theory of pull-backs (still fresh!)
So that's that. I hope, in times of desperation, I look back on this note and feel good again.
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