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I have been interested in math for a long time but I almost gave it up in the last two years. So this is a place for me to get myself back in and revise things I have learnt before. That said, the blogposts are intended to make my mind clear instead of being expository.

Topics I would try to blog about/learn about recently:

Linear algebra: Kronecker product, Cholesky, SVD

AG: essentially Hartshorne chapter 1 & 2. I think I still have many things left ununderstood.

Complex analysis: A quick review

Multivariable Calculus: All the computations I should have learnt

AT : review

ANT: learn

3 Comments leave one →
  1. July 26, 2009 10:42 pm

    “That said, the blogposts are intended to make my mind clear instead of being expository.”

    I certainly don’t think the two are mutually exclusive though. For instance, when I post, I settle for a mix between the two- my goal is both to provide material on whatever subject I am talking about and to help myself understand said material better. Actually, trying to write the material in a readable fashion forces me to understand better the mathematics itself; it also provides me with a useful reference to look back to later, by which point I might have forgotten, say, the proof of Engel’s theorem.

    • soarerz permalink*
      July 26, 2009 11:04 pm

      You are right, though my primary aim would be to go through those stuff once more, so very often I would skip things I consider obvious, omitting some definitions sometimes (eg eigenvalue was not defined in the two posts about diagonalization) etc. If readers have not seen these stuff before they may not be able to follow. The posts are thus succinct summaries for my own use.

      BTW, are you actually following Humphreys’ book for your series of Lie algebra post?

  2. July 27, 2009 1:10 am

    Partially, but not entirely. It’s a mix of Bourbaki, Humphreys, my memory from Serre’s _Lie Algebras and Lie Groups_, and Fulton and Harris. As I get to semisimple Lie algebras and representation theory I will probably start to use Serre’s _Complex Semisimple Lie Algebras_ more. These are all nice books, but I find it difficult to focus on any one alone by itself.

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