An interesting proof of Menger's theorem

The proof is in

The Hahn-Banach theorem, Menger’s theorem, and Helly’s theorem

from What's New (Terrence Tao's blog).

I subscribed to his blog a while ago, but most of the time I have to skip his posts as I don't really understand the title.. but this one is of some interest to me as I did some study in graph theory this summer and used Menger's theorem in a proof.

In his post, Terrence has given a new proof to Menger's theorem by using a game-theoretic argument. I still need to spend more time later to understand the details, but this idea again, shows the beauty and unity of mathematics!

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Life is an opportunity to do something.

Goodbye ETS! Again!

OK... I need to say Goodbye to ETS again because I just took TOEFL this morning -- though most graduate school does not require TOEFL for students who get their bachelor's degree in an English speaking institute, but one reputable one insists that only students who get their bachelor's degree in a US college or university could be exempted from TOEFL. As I am applying for that school, I took TOEFL.

And I hope this will be the real end of my dealing with ETS...

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And I am aware of the fact that this blog has not been updated for a long time --- that's because blogging has a very low priority in my schedule and recently I have been consistently getting higher priority tasks (the starvation problem in Operating System).

And it is very likely that I will continue to be very busy until X'mas. So check back after that and I may have a summer + fall semester summary here.

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Life is an opportunity to do something.

Goodbye ETS

Just received my GRE score today and got to know my AW score is 5.0 (out of 6), which is quite acceptable for me. So finally I don't need to worry about this, which is good.

Recently I have been moving as my parents bought a house and it is such a hassle... most of my evenings and weekends are devoted to cleaning up and organizing stuff.. hopefully I can get over this soon...

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Life is an opportunity to do something.

Midterm Review

More than half of 2007 has passed, and it may be a good time to review my resolutions for 2007.

• Do well in MAT357 Real Analysis and ECO100 Economics (2006 Spring)
• I worked very hard for MAT357 and the result turned out to be good, and I indeed learned a lot from the course. Working on a homework for a whole weekend was a pain during the term, but somewhat memorable in retrospect. Specials thanks to Jay, Sheng, and Andrew for all the enlightening discussions.
• ECO100 was pretty easy and I seldom attended lectures after the first test due to the low entropy rate in lectures. But I did get a good understanding on the basic stuff and result was satisfactory too.
  
• Status update: DONE.
  
• Perform well at Altera
• It was a memorable 12 months. I learned a lot, worked hard and had lots of fun there.
  
• Status update: DONE
  
• Take GRE
• Status update: DONE (awaiting AW score for final approval)
• Have a good summer research experience
• The work in Professor Kschischang's group is very fun and so far I have made some progresses. But more to be done before any real achievement.
• Status update: IN PROGRESS
  
• Get my driver's license
• Status update: TBA
  
• Pick a good design project topic
• I choose Universal Portfolio, under the supervision of Professor Wei Yu. We have a very strong group, consisting people with strong technical or business background. I am very optimistic about our final result.
• Status update: IN PROGRESS
  
• Do well in the 2007 Fall
• I am looking forward to it!
• Status update: TBA
  
• Make profit in Forex trading
• Nope, no profit so far. And my trading is in a dormant state as I don't really know how to make profit consistently. I may resume this when I get more time and more experienced.
• Status update: DEPRECATED
  

In summary, so far not bad. But there is at least one more important task --- apply for graduate schools and I will work hard on it too.

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Life is an opportunity to do something.

Tentatively, I am done with GRE

Yes, I am tentatively done, and will be finally done with it if my AW score turns out to be OK.

I went to the test center at 1, and after certain registration stuff, I left all my belongs to a locker , went into the test room and started the exam.

At the beginning, there was a whole bunch of crap such as how to use the mouse, keyboard, etc. Then the test program started to gather certain information about the examinee. Interestingly, when asked to input my school name, the University of Toronto did not appear in the Canadian school list, while others like Waterloo, McGill or even Lakehead, Laval were all there. So I skipped that page.

Soon writing started and the issue topics contained one that I had practiced before, so I chose that one. The argument was something full of holes and very easy to attack. Hopefully I have done well in the AW part.

Then the Verbal part started. It seemed the so called GRE Blue Bible (寄托蓝宝书) has a pretty good coverage on the words for the Computer-Based Test, at least after working on the book, I knew most of the words in today's exam and made some educated guesses for the rest. The reading was kind of tough, but manageable. I ended up finishing the section 3 minutes earlier.

After that was the Quantitative part, which mainly consisted high school level math questions. I was quite careful when answering those questions as generally Chinese people get full marks in this section and there is no way to recheck answers after you submitted them.

When everything was done, there is an voluntary test section and not interested in writing one more issue, I skipped that after taking a glance at the topic.

Soon the final score came out after I confirmed that I wanted to report my scores. The score for the Quantitative part was 800, and the score for the Verbal part was 190 marks above my general expectation of 600. The result was definitely satisfactory and I have to admit that I am pretty lucky today.

Feeling relieved, I walked back home. It is good that I am done with GRE for now and can focus on something more important and fun -- summer research. Hopefully my next blog post can bring some more exciting news.

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Life is an opportunity to do something.

Google Calendar: Graduate School Application Important Dates

My friend Tom has created a Google calendar that has important dates (mainly deadlines) for graduate school application in the field of EECS for Fall 2008. If you are interested, you can subscribe it here to view all the events (given that you have Google Calendar):



And everyone is welcomed to add events to it. Just email me and I will add you to the editor list. The list currently only contains a few deadlines so there are still much room to contribute :)

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Life is an opportunity to do something.

What matters? (from Nan's blog)

Got the post below from Nan's blog at http://sunnansunny.spaces.live.com/Blog/cns!AC3B92D470C58072!931.entry

I find it very insightful and fully agree with what his advisor said. And I think it takes time and effort to reach that kind of level.

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What matters?

今 晚和老板聊天，开始是讨论我的一些想法的可行性，后来是关于博士论文题目，他对学术界的点评，包括教授、杂志，再后来老板开始谈他的人生经历，告诉我对于 确定博士论文题目不用着急，即使花上一年的时候找题目，也完全不是问题。好的开始是成功的一半。我摘录一部分写在下面。

My advisor:
"Some of my friends had to stay for one more year in order to go to college, but it turned out that it did not really matter."
"When I was force to join the Korean army, I thought it was really waste of time. I can read more books during that time, but it turned out that it did not really matter."
"When I was in Caltech, I met so many problems about finding the proper advisor and Ph.D. topic. I wasted two years and almost decided to quit. I even started to think about being a lawyer. But it turned out that it did not really matter."
"You really don't need to worry about your Ph.D. topic..."

Me:
"So what really matters?"

My advisor:
"Actually, what really matter is enjoying the moment."
"You know, Being No.1 will only make you happy for a day, after it, you won't feel happy. If I become tenured professor today, I will definitely be happy maybe for a week, but after that, I won't feel happy. Life continues going on. What makes you constantly happy is enjoying the moment, working hard and making contributions to the society..."

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Life is an opportunity to do something.

NSERC USRA 2007 Starts

Today is my first day, and obviously I am not working very hard, as I am writing this blog at this time. But I will gradually improve :)

I met with Prof. Kschischang this morning and we talked about my project over the summer. It will be a topic on network coding and it sounds really interesting. I think it will be a fun problem to work on.

Meanwhile, I also need to acquire some stuff to get started. Graph theory is useful for any general networking research, and I will read some tutorial papers on network coding too. There will be a lot to be explored and hopefully I can achieve something.

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Life is an opportunity to do something.

PEY Finished

Yesterday was my last day at Altera Toronto, meaning that my PEY (Professional Experience Year) is finished.

It was a speical year, as I took a break from school and worked in an industry setting. I have learned quite a bit practical stuff, got to know how a business operates, as well as gained some insights into the whole semi-conductor industry. I also had lots of fun there and made quite a few friends. Though there were still many things could be better, I don't regret spending this year at Altera. On the whole, it has been a good year.

Now is the time to delve into summer research...


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Life is an opportunity to do something.