 [研究生生活]Write to a student from School of Mathematics & Statistics |
Write to a student from School of Mathematics & Statistics
-- dedicated to those who pursue after the academic development
Mephisto, April 4th 2005
It is inevitable for us college students to have some trouble in the process of gaining good knowledge, I think. To commence be doubtful of the capability to deal with the complexity, the intellect to comprehend the abstract or advanced theory just for a trivial frustration in study is unwanted. We should know this phenomenon is normal and we should accept it willingly. From the day when we entered the ivory tower, the classic theories founded in the recent 3 centuries confronted with us, which are abstract and systematic to master in a short period, which own their subjects' developing history we need time to learn about, and which is different from the knowledge in the elementary schools or secondary schools we should distinguish from it. For example, Newton and Leibnitz discovered the Calculous, which showed us the infinitesimal conception. Another example is Turing's computable model theory, which and the Church's recursion theory were viewed as the theoretic rationales for the birth of the computer. These were the big breakthroughs in that day. If they can mastered easily by an average man, they will not be what they are. And it decided that we cannot grasp them in one day, i.e., we should learn them step by step in order to make a very solid foundation.
As a matter of fact, learning the knowledge for the textbook is relatively easier compared with the research. Why? When we are in the phase of learning, the only thing we’d better do is imitation. But in the researching, we face the open problems, which may have no standard answer, and there is no one who can tell you what to do and how to do. Many people told me that there is no oracle in the frontier of science. So as a student not a researcher is fortunate, because we can find so many classic textbook, good reference books, and famous papers, because our teacher can tell us the solution how to do an exercise even how to study well. When I was an undergraduate, studying the Calculous, my teacher recommended me a series of exercise books complied by Gemmidovic.
However, judging from the score you got I can tell you be a top student in your class. And little by little the courses you touched or will touch are further than ever. Now we can see that the problem of computing on the rational domain is so simple that we can say that this knowledge we will understand in a few hours because you have own enough ability to deal with this kind of problems. When you climb the summit you will discover the problem once viewed as hard is easy and another new challenge will burden on your shoulder. That is the case.
Having known your configuration on the courses, it is unreasonable indeed. I only suggest you schedule all the things soundly and give up some non-significant doings. Since you select to proceed and preserve your leading position, I think, giving up the weekend not to relax but to study is a must, giving up the money not to purchase luxury but to use it in copying or printing the papers or other helpful books and giving up some course temporarily just for concentrating on the most important courses, which you can complement later. Communicating with the successful man is another means to guide you go onto a shortcut.
When it comes to my experience, I just want to tell you to read a good book as many times as possible. More than one year before, I noted the model checking technique for the first time and at the same time the fixed-point theory occurred to me. Some papers on this abstract and complex theory were searched and gained, since this is a brand-new field for me, a layman. In the first a few weeks, I even did not know what the papers said, including the strange formulae printed on which. I analyzed the main causes must be that the authors are the experts in the model checking areas and they write the paper to communicate with others assumed their readers must be the peers. I know I want to do model checking but I still have not power enough to fulfill it. Till now I still cannot understand the fixed-point theory completely and I was little worried about it since I have read this theory for many times, but every time I went into it I made some new cognition on it. And when we faced a problem, there are different sceneries from different viewpoint or different hierarchies. As it is well known that the mathematical induction method is a general method to prove some proofs. Today I will tell you that mathematical induction proof is just a concrete form or special instance of the well-founded induction method, don’t be astonished, my pal, because maybe we stand at respective spot.
English learning is also important. Once it have wasted me much energy, and I really found its huge effect when I began to do the research and the large amount of English literature often make me depressed. I can recollected that at that time I just read one or two pages in a whole afternoon, however, after a long-term training for reading and writing English now I can cover 30 pages or more in one night almost no barriers. Through reading and writing theses in English, I leaned about the authors’ mode in thinking and their precise and rigorous work in research.
At last, I wish you to bring up happily, and I wish you can steer the canoe in the ocean freely and eventually reach the other shore as you desire.
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Hi, I'm blueshirt, a master candidate from Central China Normal University. My main interests are Formal Methods and Software Testing.
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