Tag Archives: mathematics

A few books want to read

Fortunately or accidentally, I only have two classes this term. Meanwhile, they separate them into four days, so I only have two-hours class every day from Monday to Thursday. Compared to my previous schedule, it is too relaxing.

An advantage now is that I have enough time to read and think. Today I found Becker's book by chance, when I was browsing the literature on "social economics", or socio-economics. It is quite exciting, and I have realized how deep the water might be- before I was only using my naive intuition that there is something I can contribute soon.

The book I'm talking about now is

Gary S. Becker and Kevin M. Murphy, 2001, Social Economics: Market Behavior in a Social Environment.

Before I was paying more attention solely to network economics, and it turned out to be that they were quite similar to each other in most sense; however, socio-economics is for sure more broad.

Moreover, I took a few hours finishing reading another book,

Salsburg, D. (2002) The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century

From the name, you can see that this book is about basic statistics. To save time, I read its Chinese translation. Not very long, but very exciting - maybe I have been, and will always be attracted by mathematics and statistics. Especially the later one, perhaps due to the fact that I have so many friends in this area, is one field beyond economics that has influenced me the most, and more on the level of conception and methodology than techniques or actual methods.

@Roma Things remain to be clear

@Roma. Things remain to be clear

While reading this book, it reminds me another book I read before, which is about the famous economist Keynes,

Robert Skidelsky, 2005, John Maynard Keynes: 1883-1946: Economist, Philosopher, Statesman

What impressed me most at that time was not Keynes' contribution to economics - although nobody can neglect that, but his ideas on probability.  Until now, I still have the wish that one day I want to read Keynes' original book on probability somewhere.

I want to read Becker's book only for the reason that I need an idea for my history paper. One question I have been seeking for the answer for a while: why do we need to care about the network structure? Before, I was only arguing that the "summation is a naive way to draw the group's characteristics"; now it seems that I need to really re-think about this argument. In addition to sum or mean, people have developed distribution to help understand the world; furthermore, from central limit theorem, normal distribution can be utilized in most scenarios. Therefore, under what particular case will summation cause a severe problem?

Another thing I'm thinking about now is after reading the "Lady tasting tea", a term still remains to be explained more clearly: frequency school and Bayesian school's debate on the definition of probability. On one side we are lucky today that following Baye's idea will not be regarded as heterodox any more; on the other side, although his idea itself is very simple, how to make a perfect use of it is still a very tricky and should be dealed with carefully.

I'll stop here for now, and see whether I can gain some new senses soon. This year is too short- I need a longer time to make all things clear.

Intuition vs strictness

Just finished a very interesting class. Thijs was talking about contraction map, which should be the forth time for me to see it in class (-_-!), but there was another "big guy", who was so good at math (perhaps due to the reason that he was from and had been taught in France) that he could not stand the assumption that some economists made for the applications here. Then, I got the honor to listen to their "debate". Haha...

Maybe there are only two kinds of economists in the current academia: those who are extremely good at mathematics, and those who have been granted wonderful intuitions by somebody (maybe the god? but they may refuse to acknowledge the existence of any god). Well, if you would like to count the union and complement of those two sets to be really strict, there must be the third and forth sets - in the forth set, let's simply define it as a collection of outliners who are talent at neither math nor economic intuitions, but succeed anyway from some perspectives…. I’m so sorry but the only people who can be categorized like that I can think of now, are those so-called "media mogul" and live on their speech instead of academic contributions. But let’s ignore them here to make the world simpler 🙂

As I just said, the student in class who asked those technical questions was very good and strict at math – actually that might be the way to define whether you are really good at math: apart from those mathematical intuitions, the level of strictness shown from the way you speak can tell people what kind of formal math trainings you have received. In contrast, I don’t really know how good Thijs is at math, but he usually prefers the way to explain things intuitively – and his intuition is amazing! I don’t think it is common to find a macro guy who has that kind of great sense, or the feeling of “touch”. Then, if you combine both together, you can expect what great talk will emerge!

But to be honest, when I was listening to their opinions, although the natural reaction at that time was to smile and enjoy the debate, after it, especially now, I’m feeling somewhat upset. Which one can be cultured? The ability of math? Sure, but how long will it take if you failed to start from the very beginning? Intuition? I have no idea whether people born with that talent or it depends on the way you learned economics. Sometimes I’m worrying about I’m standing at somewhere in the middle – not really good at math, and haven’t been granted the direct sense of the real economic world. Thus, is there still any possible way left for me to do some decent work in the world of economics? Maybe it was fortunate that my foresight was not too bad: at least, I named this blog as “explore the world of economics”. Whatever I have explored, they will not put any actual constraint on myself.

1 hour on the Platform

Last Monday I listened to Peng's (Peng Shige) Lecture about the measure of financial risks. Similar to previous lectures, there are numbers of official news reports. However, I'd like to share my personal feeling with you.

I have no better choice but to admit that Prof Peng is really an authority, not only because of his great contribution to the professional field of mathematics and finance, but also for his zeal of research and the wonderful explanation of his thought.  He has the ability to make the only an hour's lecture magic, to lead us fall in love with his "nonlinear expectation operator". It is a pity for me that after having stayed for numerous years in SDU, I know nothing about Peng's research. I think without long time precipitation of thought, it is impossible to have such deep realizations.

One word he mentioned that night really impressed me, it was: dirty work. Nowadays there are so many dirty works that make us apathetic.

Today I have said too much just because last Wed's afternoon I had an exercise class of intermediate microeconomics for one hour as a TA. I was confident about my knowledge of micro economic theory, since I could understand the book called "microeconomic theory " by Mas-Cololl,Winston,Green as least. But when illustrate these with my words and make them clear to the audience, I learned the hardness of the process. I spent more than 5 hours in front of my computer on making the handout. Since pictures were helpful, I installed Illustrator and Flash to make the visual effects better. I was willing to use these as supplements to help them understand the economic thoughts behind the mathematical formulas. Although time is needed to examine whether I have succeed, I'll work on. Personally speaking, intermediate microeconomics is too important for the whole development of the economic study.  At least, I have already achieved my initial goal, which is also the reason I used to persuade my advisor to leave me this chance: to examine my knowledge of intermediate microeconomics.

The next class will be two weeks after, and I have to work hard to prepare. I just hope that my advisor won't be disappointed about his decision and trust, and also for those who take time to attend the class it is worthy that time. At last, I have no excuse to fail. It is really worthy that much.
In the end, and also on the one-year's memorial day, I want to speak out these words: I'll do whatever in return to your guidance.

Thank you so much, dear Yue, my advisor.

[NEW] You can download all presentations here: http://www.cloudlychen.net/papers.html#impre

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Stochastic calculus [4th week, Sep]

Today when I was checking my emails, I noticed one ad from The Wharton School of the University of Pennsylvania. There was no doubt that it is the most famous business school throughout the world.  But in fact, at the first glance, I didn’t realize that it is Wharton. I just thought that “oh, a school of Upeen“.

Followed its link, I was redirected to its official website, and read the introduction of its applied economics doctoral program. Although I did know that upeen would never give me an admission, I still looked carefully at the details of the program’s requirements. Of course, I paid much attention on the mathematical requirements. Some familiar words came into view, like

(1) at least two courses in calculus, (2) linear algebra, (3) differential equations, and (4) probability and statistics. We also recommended that you have taken: (1) real analysis, (2) econometrics, (3) stochastic calculus.

Ok… I have one year left to meet your requirements. However, the fact is, even if I can satisfy all the basic requirements of this program, I am still not competitive enough and I have no money to pay for the tuition. Thus, the final result mentains the same: It has nothing to do with me. Moreover, I would prefer the training of theoretical economics rather than applied economics.

Here I want to say something about “stochastic”. Some days ago one junior attracted my interest, not for his intelligence, but for his love of mathematics as a student of economics. I had met hundreds of schoolmates who had a good knowledge of math, either took some classes from the school of mathematics or taught themselves. But most of them were forced to enhance their math ability by the pressure from graduate schools or their advisors. Therefore, the real situation was, they did have some calculation skills after professional math trainings, but seldom did they really have the understanding of the spirit of math.

That boy was different. He didn’t got high marks in every class, thereby losing the most valuable testimony of outstanding performance at study. “The only choice for me is to take part in the entrance exams for postgraduate schools ( which is called ‘Kao Yan’) since my lack of English and GPA “, he laughed at himself when I encouraged him to go abroad. But he told me that he had audited most of the core courses in school of math. That day we talked about a question about matrix, or more specifically, Markov chain. He offered a new solution way, which was really out of my thought. I didn’t catch his meaning at first, so he explained it patiently. After that, he recommended me to listen to the course of stochastic process in school of math. To speak honestly, I had some knowledge about stochastic process so I told him. At first he was a little surprised, but soon he gave me an advice for the reason that my understanding of stochastic was not deep enough. Then he gave me a list of the courses and asked whether I would come to the class or not. Unfortunately, the time was conflicted with an other class on Tuesday afternoon. He said that it didn’t matter, since I would go to another half  of the course on Thursday and the course was pretty easy. OK, I will certainly do that.

Of course, as an exchange, I provided some suggestion for the economic courses…

Now what I want to say is, why “stochastic” is so important in economics? It seems that every one has an unique answer, so do I. But today the word “stochastic calculus” really makes me confused. After searching on the Internet, I have a basic conception of it. But why it sounds so familiar? …

Yes, Shige Peng （彭实戈）! And his backward stochastic differential equations! I see… I see…

Appendix:

Some Chinese materials about Stochastic calculus ( Author unknown, sorry! ).

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