Learning Notes

Everything has a purpose. Learning has a purpose. Often time we doing thing the other
way around, learning without purpose. Purely learning you may say. Well, now I find out
with a purpose in mind, you learn better and faster. I think that is at least the way I should learn in the future. Motivation baby, Motivation!

8/2/2010

Doing research is really needed you to be disinterested. Proving things step by step
and showing your imaginations are true needed great patient. Oh my, I am still too
impacted and naive to be a genuine researcher.

Interpretation

It should be noticed that interpretation of types is very different from
the interpretation of terms. The connection between the two is the soundness
theorem: the interpretation of term is in the interpretation of types.

New thoughts on 7/15

I just realize that the applicative structure is just not expressive enough to
describe the axioms. I need a more expressive signature.

Learning note 7/15

1. Term algebra provides us an algebraic formalization on the term signature, so that
we can use tool from algebra to study term. So in a sense, Herbrand is a smart guy.

2. The only identities or equational classes in term algebra are those syntatical identities.

3. It is(is it?) possible to have a sigma-algebras which has it's own equational classes that can not be formalized by the identities in sigma-signature.

4. A spec=<\sigma,E> is only a form of algebraic specification, we can replace E by
a bunch of axioms.

Research

Maybe I am still used to letting another person remind me, hey! you have to finish the $#$%^ by the end of #@!@##$. But that's not the case when you are a phD student. Some may like this kind of being pushed feeling, but I don't. In my opinion, there's two kind of research, one is giving by others like your advisor, the other is your own research, which you are pretty much on your own. Sometimes, your advisor is just too busy to give you more instructions. For me, I am kind of feeling frustrated when I find out the fact that I am alone in this research. Yes, my advisor can give me advice, but I realize that he is any possibly closed to the answer than me. He may point out a problem or field that he think it's worthwhile to do, but he will pretty much let you explore this area by yourself. So don't expect too much from your advisor, he also has his own research to do, just like you except maybe ten times busier than you. But what if I am too frustrated by the research I've done so far and don't even have a clue where it will lead me to? Well, hang on there, you will figure it out eventually, always remember, nobody force you to do anything, you are on your own, you struggling in these years of PhD, but after all these years of struggling, you may form your own style of handling things and your own foundations for your future research.

Understand

People use different perspective to understand how things work! I find it out because today I was reading another student's code. And I find that I am the kind of person who tend to understand the complex aspect of it, is it good or bad? I realize the complexity of my code is way much than his.