Archive for the ‘Uncategorized’ Category

Time for computer science to grow up

March 2, 2011

“We end up living in a deadline-driven world, submitting a paper when we reach an appropriate conference deadline instead of when the research has been properly fleshed out. Many also just publish “least-publishable units,” doing just enough to get accepted into a conference.”

from: Time for computer science to grow up, Lance Fortnow, Communications of the ACM, 2009

Dijkstra’s 3 Golden Rules for Successful Research

November 13, 2010

1- Raise your quality standards as high as you can live with, avoid wasting your time on routine problems, and always try to work as closely as possible at the boundary of your abilities. Do this, because it is the only way of discovering how that boundary should be moved forward.
2- We all like our work to be socially relevant and scientifically sound. If we can find a topic satisfying both desires, we are lucky; if the two targets are in conflict with each other, let the requirement of scientific soundness prevail.
3- Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you.
Source (with some explanations): http://www.cs.utexas.edu/~EWD/transcriptions/EWD06xx/EWD637.html

First Montreal Spring School in Graph Theory

May 13, 2010

I am attending this one-month summer school in Structural Graph Theory, which is held in Montreal. It is a high-level school with world-class speakers, and I am really enjoying it. We have two classes everyday for four weeks, making a total of 40 lectues.

Paul Seymour talks about excluding induced subgraphs, and, in particular, will sketch a proof of the Strong Perfect Graph Theorem, which he (together with Chudnovsky, Robertson and Thomas) has proved in 2001. This was a huge result, with a 150-pages proof. Not only is he a great problem-solver, but also he is a great teacher. I really do enjoy sitting in his class. He is so smart, draws lots of pictures, and always proves what he wants in a bottom-up way; That is, unlike many others who first write a Theorem statement formally and then write the proof, he first describes intuitively why such a Theorem has to be true, and only then writes it down.

Maria Chudnovsky (the picture is a bit old) also talks about excluding induced subgraphs, but her lectures are independent of the Paul’s. She is also smart and a good instructor (she was Paul’s PhD student and must have learnt a lot from him).

Bruce Reed talks about excluding minors from graphs. In particular he talks about Robertson and Seymour’s Graphs Minor Project. He is a great researcher. Sometimes his lectures are confusing for me, in particular when he talks about planar graphs. Fortunately he has now turned to tree decompositions, which I am a little familiar with.

To summarize, I am so glad that I am attending this school. Structural Graph Theory is really nice (though hard to prove new results) and I enjoy sitting in the classes and working on the assignments. It is like I am back in the IMO training camp (7 years ago)! The city of Montreal is also very nice. Here you see a photo I took in the botanical garden, which I went to see on May 8th.

a nice probabilistic argument by Alon

April 12, 2010

These days I am reading “Probabilistic Methods for Algorithmic Discrete Mathematics.” Alon‘s probabilistic proofs are usually beautiful. This one (Theorem 6.1) that I saw today was not an exception. It is really simple to understand, but also very elegant. I can’t help admiring it. It is brilliant. That’s the reason that I like the probabilistic method: because it is full of beautiful proofs. I wish I could write a similar proof someday.

The difference between an optimizer and a mathematician

February 15, 2010

Optimizer (E.g. algorithm designer): This theorem is good because you can devise an algorithm using it.

Mathematician: This theorem is good because it has a nice proof, or it is surprising, or it generalizes many known ideas.

Graphics in LaTeX: TikZ and PGF package

January 26, 2010

I don’t want to look ungrateful, but one of the main drawbacks of LaTeX is that it’s not easy to handle graphics there. I’m used to use the built-in “picture” environment, but that’s a headache as soon as your figure becomes complicated enough.

Recently one of my friends told me about the TikZ & PGF package (TikZ is the shell, PGF is the core) and I looked at the manual today: it looks promising. For instance the figure you see at above has been generated using <50 lines of code. The manual is very long but I will try to read it as soon as I get some free time. You can download the package here and the manual from here.