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How to improve the scores of advanced mathematics quickly in one week?
First of all, we must master the basic concepts and theorems thoroughly, and it is absolutely impossible to skim them. For example, last year's final paper of Dolphin House had such a problem: the type of discontinuity of Dirichlet function at x=0, which many students did wrong. There are two main reasons: first, the nature of limit is still vague, and there is no difference between a function having a definition at one point and a function having a limit at one point; Second, there is no deep understanding of the types of discontinuities and the essential difference between the first type of discontinuities and the second type of discontinuities. If you do this problem step by step against the textbook, almost no one will make mistakes. Without the textbook, you may only have to choose among four options painfully. In addition, the concepts of differentiability and integrability are the same, and their error-prone points need to be explored during review.

Secondly, examples and exercises can't be ignored after class. Although the example is simple, the reason why it can be an example shows that it must have its classics. Please enjoy it carefully. Then there are after-school exercises. Although every small topic looks similar in a big topic, it is easy to ignore some details if you don't do it carefully. For example, is x=0 the vertical asymptote of y=arctan( 1/x)? When x tends to positive infinity and negative infinity, there is a limit of y=xsin( 1/x). Does it have two horizontal asymptotes? It can be seen that it is difficult to break through the leap of "quality" without reaching a certain "quantity" Therefore, although we will focus on recommending some after-school exercises in textbooks, it does not mean that it is enough to do these, but all topics should be done, only those recommended should be done seriously, and those not recommended should be done roughly. In addition, some of the total review questions in each chapter are the real questions of the postgraduate entrance examination over the years, and its importance is obvious to all.

Third, don't be arrogant. There are two kinds of low heart, one is to look at the questions and not do them, and rely too much on the answers; Second, doing the problem is just a simple mental calculation, and the calculation process is not carefully written. The consequence is that the former thinks he knows everything, but when he arrives at the examination room, he is dumbfounded when he sees the test questions, while the latter is more wronged. He does do every problem, but when calculating, he loses either one or the other, and the score he shouldn't lose can sometimes be as high as 30 points or more. From the test questions of 20 10, it can be seen that the calculation of some questions is still very large, and it is urgent to overcome the bad habit of being superior.

Fourth, we should make a reasonable review plan for ourselves. Some students may make a plan like this: in the first two months, look at the first volume and line generation of high numbers, and in the second two months, look at the second volume and probability of high numbers. What we want to point out is that it is not enough to watch it once. You may only have a preliminary understanding the first time, but this understanding will gradually deepen when you watch it the second time or even the third time. The author also has a deep understanding when learning a second foreign language recently. Every time you read a textbook, you will get some unexpected gains. So I suggest you divide these four months into 2-3 stages, and try your best to read the textbook 2-3 times in each stage. In addition, even in the intensive sprint stage, you should always come back and look through the textbooks.

Fifth, we must not exclude the guidance of others. I have seen such a reply on the forum: "Don't blindly worship, the key is to rely on yourself." It is true that there are some postgraduate institutions in society that mislead people's children, but it is also wrong to completely deny the important role of others' guidance. If you completely "go your own way", it is likely that many roads are detours, so that you can't complete the review task as scheduled. And selectively listening to other people's opinions, coupled with your own efforts, may have better results.