# The difference between studying math and economics

These words were written down while I was driven crazy by the theorems and their proofs in functional analysis. Just some jokes for fun. Merry Christmas!

Title: The difference between studying math and economics

Deduction 1: If you failed in studying economics, please doubt your textbooks and teachers; if you failed in math, please suspect your IQ first.
2. While you are proving a economic theorem, you can simply persuade yourself that "these conclusion are driven from math" so you can easily prove all of the theorems with the presumption that some conclusions are true; while you are trying to give a proof for a mathematical theorem, the author is doing his best to find the most basic assumptions and there is a long and meticulous proof waiting for you...
Deduction 2: Creativeness in economics in easy, since you can add an assumption anywhere you need; however, it is really difficult in math, since you cannot make any additional assumptions if unnecessary.
3. Studying the basic->intermediate->advanced level of economics is like building a house: the introductory level teaches the basic economic principles (build the framework); the intermediate level tells you how to analyze them with graphs (walling); the advanced level force you to use mathematical tools to prove the familiar principles strictly (decoration).
However, in math, it is like taking down a house: you should drop all decorations first with calculus; then find its frame with real analysis and functional analysis.
4. While studying economics, you should play with the dirty data in the real world everyday; when studying math, you can ignore anything in the real world and close yourself in your silent room.
5. Dealing with data in econometrics, an economic student will go shopping -- list all available econometric models and try them one by one; a math student will offer "VIP" custom service -- design a particular model according to the nature of the data.

Anyway, there are only some jokes just for fun! At last,

Merry Christmas!

# Keep off laptop [3rd week, Nov]

I don’t know exactly why, but I really feel tired when sitting in front of my laptop. I hate reading unlimited news in google reader, and I am also weary of replying emails… I should admit that the length of my reply is going to be shorter and shorter.

This week I only need to concentrate on my paper and its feedback, except for taking classes every day, mainly from the morning to the night. The weather becomes colder and colder, skipping the beauty of the fall and going directly to the winter. White snow covers almost every part of the ground, and causes some trees to bow down. Seeing the news on the television, no special feelings touch my heart.

Translating my transcript, writing a personal statement and even dealing with some stuffs are the primary tasks for me, although I still watched some dramas during spare time.

Money in, and money out. Time flows but never back. Less than 2 hours per day on average with my laptop, what can I do?

# back to the earth[3rd week, Oct]

I just come back to the earth from a week’s escaping. Sorry for leaving without a notice.

Well, just now when I open my Gmail, I found it impossible to read every mail carefully. I’m sorry if I ignored your email, and if it was really important, please send it to me again! I promise that this time I won’t miss anyone.

Meanwhile, Gmail tells me that “You are currently using 5886 MB (79%) of your 7383 MB“. I don’t know how and why… So shall I delete some “big” ones?

However, next week I will still be pretty busy, and although I WILL NOT disappear again, finding me without an email may be a hard thing. Writing my paper, preparing for the class… shall I apply for the lectures about latex in the following month? I’m not sure whether I have enough time to get well prepared for them. Too many stuffs to be done, an incontrovertibly busy week.

Well I should admit that I’d like to communicate with others in English rather than Chinese, even in the campus. So please forgive me if I write too much in English or if I reply you in English. You can tell me about your difficulties if you wish.

Finally, I should say that the feeling of being back to earth is really good!

# 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! ).