There are many postgraduate courses and time is tight. Any review is costly, because time is your biggest cost. Some people say that if you do tens of thousands of problems or more, you should be able to do math well. This question may be right, even the sea tactics have their special advantages. But you should know that the postgraduate entrance examination is not only about your math scores, but also about other subjects. What you want to pursue is comprehensive promotion, that is, an overall concept and a coordinated process. Therefore, since you can get the extreme value of review under the limited time constraint, you should find your right direction, take fewer detours and spend "worthwhile" time. So what topics can be done to represent the right direction? I think this is a realistic problem for many years, especially in recent years. In other words, only by "playing tricks" with the real questions over the years can we have a correct sense of direction. In the future, you can know what kind of simulation questions you want to do, and you can know which ones are well done, how many times you want to do them, and which ones are really too technical and a little biased. There is a view that the real questions over the years should be put at the end to check their review. This view may be applicable to people who have a super good foundation in mathematics, but it may not be suitable for most people who have an average or poor foundation and are exposed to postgraduate mathematics for the first time. The reason is obvious. Let's make an image metaphor: if you are asked to go to a strange place, do you look at the map first and then follow the direction of the map to find the place? Or just walk, then walk and find something is wrong, and then look at the map and constantly correct your direction? Obviously, the former is wiser than the latter. Even if people who use the two methods get the same score through hard work, the former may spend less time than the latter, which undoubtedly gains a relative time advantage in other subjects. Here we assume that a person with a good mathematical foundation is better than a person who knows the road very well. Because he is familiar with it, even if he goes the wrong way, he won't make too many mistakes and can correct the direction immediately. Even if the final direction is wrong, he may do well in the exam with a foundation in mathematics, but what about those with poor foundation in general mathematics? We have no time.
Second, many mathematical methods and ideas come from textbooks.
For the role of teaching materials, many people only understand it as laying the foundation. In fact, there is another level that the teaching materials reflect strong mathematical ideas. In fact, many people think that textbooks can only provide them with a foundation, and then the real mathematical methods and ideas should be learned by reading tutorial books. Actually, it is not. What I want to say here is the proof of theorems and inferences in textbooks. Many people may not pay much attention to this, and then always say that they can't prove the problem well. In fact, the proof of theorems and inferences in textbooks embodies strong mathematical methods and ideas and is very practical. First, the proof in the textbook can greatly deepen the accuracy and accuracy of your understanding of the theorem. Many people's mistakes in understanding theorems and inferences do not stem from their memory and understanding ability. But I'm not familiar with how this theorem comes from and what assumptions it has. Familiarity with the proof process of theorems and inferences is helpful to better understand the conditions, applicability and accuracy of theorems. For example, the function limit has a property called number preservation. Many people casually say that the limit is greater than 0 and f(x) is greater than 0, but they often forget that this is only true in a certain neighborhood where the independent variables tend to a certain number. Therefore, when using the property of preserving numbers, not mentioning the concept of neighborhood is a misunderstanding of this property, and you may lose points in the exam. If you are familiar with the proof of this theorem, you will be familiar with the accuracy of these properties. Therefore, it can be seen that deepening the understanding of theorem proving will also help to strengthen the rigor of our mathematical expression and let us take fewer steps. Second, the proof of the theorem itself helps to strengthen the further understanding of some mathematical concepts. The proof of some theorems is simple, but the proof of some theorems is a long list, which uses many mathematical concepts, and sometimes we may not understand them thoroughly. Through these proof processes, we can deepen our understanding and application of concepts. Third, the method of proof is worth remembering. The proof of many theorems embodies certain mathematical ideas, including many ideas and methods of proof, which are directly reflected in many problems we have done, including some real problems over the years. So, don't complain that you can't prove it, and don't always complain that you lack mathematical thinking. Prove the theorem first! ! ! Let me give you another example to illustrate. I remember 1998 that there was a proof question in mathematics, and the first question seemed to be. That question is the proof of road median. It is proved that the median value is obtained in the open interval. That question is particularly good. The good thing is that the zero theorem can also be used to "grope", and the function values at both ends can be multiplied by less than or equal to 0, so many people are excited to prove it with the zero theorem. As a result, I didn't get a penny. The reason is the understanding of the accuracy of the theorem. Only when the function values at both ends of the function are less than 0 can the median be obtained in the open interval, and the condition of the topic can only be deduced that the product of the function values is less than or equal to 0, then the median may be obtained in the closed interval instead of the open interval. So that problem can only be proved by differential mean value theorem. And it is not particularly complicated to prove. This question is particularly good, but it is not difficult for you to say it is difficult. It depends on the accuracy of your understanding of the theorem. If you understand correctly, you can get points, and if you don't understand correctly, you won't get points, so you will skillfully distinguish between these two types of candidates. What distinguishes them is their foundation, not their math skills.
Third, the sublimation of the book review debate.
I mainly talk about Chen Wendeng's books and Li Yongle's. I also read the answers on the forum, which can be summed up in one sentence: look at Chen Wendeng with a good foundation, and look at Li Yongle with a poor foundation. I think this answer is too general. Because what is a good foundation and what is a poor foundation, there is no clear answer. Then I'll give you a clear explanation now.
The person who is suitable for Chen Wendeng's review guide should be a person who has a clear and accurate understanding of basic concepts and theorems, can skillfully use them, is interested in mathematics, has some training in mathematical thinking mode and thinking mode, is good at analysis, is curious about knowledge and has strong ability to analyze mathematical problems. This kind of person will make rapid progress when he is Chen Wendeng's review guide.
People who are suitable for Li Yongle's review books should be: people who understand basic concepts and theorems clearly and accurately, use them skillfully, pay attention to basic concepts, theorems and problems, are bored or afraid of high-skill bias, want to keep the right direction all the time, know little about mathematics for postgraduate entrance examination, know little about mathematics in universities, rarely use mathematical knowledge and methods in their majors, and strive for victory steadily. This kind of person can use Li Yongle's review book to quickly find the right direction and improve quickly. Therefore, it can be seen that it is reasonable for everyone to say that Li Yongle's book has strong applicability and wide scope of application.
The characteristics and improvement modes of these two books are also different. Let me talk about them.
Chen Wendeng's review guide: Mathematical thinking is very strong, and many topics are partly from the topics of college mathematics competitions, but there are not many real questions over the years. Therefore, what can really make good use of Chen Wendeng's books is not a set of "willy-nilly", but a thorough understanding of the mathematical ideas behind the skills. Without this skill, you can't really understand the essence of Chen Wendeng's books. I can only do this. In my opinion, it is risky to learn mathematics not by copying, but by copying. For example, Chen Wendeng's book on definite integrals contains many such things. For example, there are many methods in the book: when encountering such a function, use such substitution to transform the integral interval and integral expression. Indeed, the following example does the same, because the example he cited must serve the method he cited, so I am sure it can be worked out. But not all the questions can be replaced in this way. The real understanding should be to analyze what role such substitution can play and why it comes to mind. Therefore, people without some mathematical analysis ability can't understand these essential contents. Therefore, Professor Chen once said that the review guide is written in depth, but it is thoroughly understood, and mathematics must be greatly improved. I especially agree with this sentence now. Many people have succeeded by following the method given by Chen Wendeng. For those who have read his books and got high marks, I think most of them are not made up, but really understand the essence of Chen Wendeng's mathematical thought. Therefore, for those who really want to get a particularly high score and have strong analytical skills and mathematical thinking, the promotion of Chen Wendeng's book is not only a little bit, but also an all-round promotion from methods to ideas. But if you only know how to do it, you can't say that you can't improve, but you will improve slowly, and the quality of improvement is not as good as that of people with good mathematical foundation.
Li Yongle's Book Review: My impression is one word: stability. Concepts, theorems and formulas are clearly explained, and the topics are mostly from real questions over the years. The sense of direction is very clear, and the mathematical methods and ideas embodied are directly related to the mathematics of the postgraduate entrance examination, which is very practical and has great guiding significance for the examination. The number of questions is reasonable and the difficulty is moderate, which avoids the discussion of eccentric questions and directly points to the discussion of the most common methods of postgraduate mathematics. For students with poor foundation as I just defined, they can quickly enter the review mode and state of postgraduate mathematics. Because the current postgraduate mathematics attaches great importance to the examination of basic ability and basic skills, I think the review effect brought by Li Yongle's review book will be more efficient. Therefore, for a person with poor foundation, Chen Wendeng's review guide is a spiral all-round promotion, while Li Yongle's review book is a rapid and rapid promotion. If a person wants to get a good score in the exam, but not a super high score (135 or above), it is enough to do Li Yongle's book. For those who must be above 65,438+0,35 in mathematics, perhaps Chen Wendeng's review guide can give you more inspiration for getting high marks in mathematics.
Another problem I want to emphasize is that any tutorial should be done by yourself. The more times you read, the more thorough your understanding will be. But don't watch it too many times. Sometimes the marginal effect of the last few times is not obvious. The so-called good foundation and poor foundation I just mentioned are based on reading textbooks and mastering the formula of concept theorem, and then I make a definition. Therefore, for those with a good foundation, it means reading all the textbooks. For those with a bad foundation, it is not very scientific to define the textbooks. If you look directly at Li Yongle's review book instead of the textbook, some places will still appear, which is very vague and difficult to understand, and will affect your quality improvement. Even if you read all the textbooks and are familiar with the formula of the concept theorem, you may not be able to fall into the ranks of the foundation I just defined. Therefore, scientifically positioning yourself is the key to choosing the review mode.