Let's talk about high numbers first. I think the basis of high numbers should be limit, derivative and indefinite integral. For derivatives, I personally think there should be no derivative that cannot be found, and there should be no derivative that cannot be found wrong. To achieve this state, you have to do more problems yourself and explore a set of experience by doing them. No teacher will give us much help in this respect. Indefinite integral is very important, it is a connecting link. I can't learn indefinite integral well, and I can't learn definite integral, differential equation, multiple integral, curve and surface integral and infinite series well. How can I learn indefinite integral well? According to the experience introduced by many postgraduate students, I have the same view.
On the one hand, we should know three operations of indefinite integral, the first is differential method, the second is method of substitution, and the third is partial integral, especially partial integral. As can be seen from the papers we have tested in the past, many questions of indefinite integral are done by partial integral. This year, Math II and Math III of the postgraduate entrance examination were tested by step-by-step integration method. These three methods can only be mastered by doing a lot of problems. In addition, more than 20 important indefinite integral formulas should also be firmly remembered.
We emphasize the importance of foundation, which does not mean that you can get high marks in mathematics by mastering these three parts. This is not the case. I think the most important thing is to be familiar with important test sites and scoring points. After reading the examination papers for more than 20 years, we can see that the curve and surface integral in Mathematics I is very important. Generally, this part accounts for 16, but there are some special cases. In 2007, it was 18, which accounted for 150 in the test paper. In 2008 and this year, the score was 14, the big question was 10, and the multiple-choice question or fill-in-the-blank question was 4.
What is the test of curve and area? It is clear to all that it is either the calculation of curve integral or surface integral. It should be noted that we are taking the postgraduate entrance examination. When we do curve integration, we must remember to use Green's formula, and when you do surface integration, we should think of using Gaussian formula. In taking Math I and Math III, infinite series is bound to be taken. Infinite series generally accounts for 65,438+06 points in taking Math I, generally 65,438+00 points or 65,438+02 points for a big question, another multiple-choice question or fill-in-the-blank question, 9 points for a big question, and 4 points for a fill-in-the-blank question or multiple-choice question, totaling * * * 660. The question type of the big exam is not to expand a function into a power series, nor is it the sum of several series or the sum of a power series.
For students who take the first, second and third grades, it is necessary to repeat the integral. Generally, it accounts for 12, and big questions account for 8 points. What kind of questions do big questions bring? Generally speaking, the test is the calculation of piecewise function, and the second is that the integral area is symmetrical about coordinates and the integrand function is even and odd. When these two kinds of questions are mastered, the general double integral is no problem.
There is also a differential method of multivariate functions, which is tested every year, generally accounting for 12, big questions accounting for 8, and sometimes it may account for 10. The common problems in this respect are: one is to find the maximum and extreme value of multivariate function, or to find the second-order partial derivative of an abstract compound function. The other is the proof of functional equations and inequalities, which often appear in the form of comprehensive questions. About the foundation of advanced mathematics, important grading points and test sites, important questions are all here.
Linear algebra is also composed of three parts: the first part is the elementary transformation of matrices, the second part is the discussion of solving equations with parameters, and the third part is the solution of eigenvalues and eigenvectors of square matrices. Especially the third one has to take the exam every year. Everyone thinks linear algebra is not easy to learn. Why is it not easy to learn? Because there are too many properties, this is one aspect of the problem, and more importantly, the repetition rate of these concepts, theorems and properties is low, which is difficult for everyone to master. But the postgraduate exam is the best of the three mathematics courses. Why is it not easy to learn it well? That's because the two major questions it takes every year are too fixed. If you really master the questions you have tested in the past and thoroughly understand them, can you still paint a tiger as a menace?
The basis of probability theory and mathematical statistics is three parts: the first part is the probability of events, including conditional probability and multiplication formula, total probability formula and Bayesian formula, Bernoulli probability type. The total probability formula is a key question type, which has not been tested for several years, so we should pay attention to it next year.
The second part, random variables and their distribution, should pay special attention to the calculation method of conditional distribution density of continuous variables, which was tested last year and this year. Next year, we should pay special attention to the calculation of edge distribution law and conditional distribution law of discrete variables.
The third part uses the numerical characteristics, mathematical expectation, variance, covariance and correlation coefficient of variables. As we all know, without these four concepts as the basis, our statistics will be irregular. At the same time, four concepts are also frequently asked questions. Generally, this kind of question is not less than 65,438+00 points, which means that we have mastered this part, and the score of probability theory is almost half. We must pay attention to it.
I have already told you the basics, test sites and scores of three math courses for our postgraduate entrance examination, and we candidates must pay attention to them. From what I said earlier, you may also realize how to review math.
One is to grasp the foundation, and the other is to grasp the solutions and skills of key problems. In order to make students remember the two points I emphasized, I gave them a poem:
The root of the mathematical foundation tree,
Skill training depends on the type of problem.
Study hard, practice hard, sharpen,
If you get high marks, you will succeed naturally.
Moderator: Before this interview, many candidates asked many questions. We tidied it up and wanted Mr. Chen to answer it. Xu Kai, a candidate, said, I would like to ask whether it is better to just read textbooks to do exercises or to cooperate with tutorial books at this stage.
Chen Wendeng: This classmate Xu, let me make a suggestion: At this stage, you should master the basics first and have a good look at the four books you have studied in the past. You should read the basics I emphasized at least three times and do all the questions above. As for the other chapters, you can never read them intensively. I hope this student will be deeply impressed by the important concepts, theorems and formulas after reading the relevant chapters. You should take a look at the important knowledge points and write them down. As for the following questions, because our textbooks can't be as comprehensive as tutorial books, I think textbooks are very useful as a basis, but they can't play much role as methods and skills to improve important questions.
Netizen, if you read the counseling book I wrote, I suggest you keep pace with me. For example, when I talk about limits, you should read the relevant chapters in the book immediately after listening to my class, and don't get ahead of me. In other words, I didn't talk about integrals before I talked about limits. You have already seen integrals. Don't fall behind. You won't see the limit until I talk about integrals. It's no use. Synchronize with me, and this effect will appear.
One of the goals to be achieved in the intensive stage is to thoroughly understand what the teacher said; There is also a need to master the solutions and skills of some questions emphasized by the teacher, and it is very important to focus on reviewing the questions. Because of this, this year I published a book "The Core Problems of Postgraduate Mathematics" in Beihang Press.
Moderator: There is a Zhang Yifan. He said, Mr. Chen, I'm going to take the second math exam next year. Is there a big gap between the real questions of postgraduate entrance examination and the exercises after class? Is there a difference between the test range of Math 1 and Math 2?
Chen Wendeng: The scope of Math 1, Math 2 and the exam is very clear to this student, which is different, but the difficulty is basically the same from my personal strength. Sometimes the problem of math 1 will also appear in math 2, not to mention linear algebra. As for the difference between real questions and exercises, from the perspective of real questions, it should be said that it is more comprehensive. As for the difficulty, it depends on what kind of books you compare, and compared with our university textbooks, the questions in our textbooks can't be compared with the real questions in our postgraduate entrance examination, but compared with the questions in some counseling books specially written for postgraduate entrance examination, some may be relatively flat, and some may not be so difficult. I hope that students will look at the real questions of the previous postgraduate entrance examination.
Moderator: Hello, teacher, I would like to ask whether linear algebra and probability theory generally have proof questions when taking the math exam for postgraduate entrance examination, and if so, what are they generally about?
Chen Wendeng: I can't elaborate on this. Linear correlation of vector groups, eigenvalues and eigenvectors of linear algebraic Aiko matrices; Probability theory and mathematical statistics, probability Generally speaking, if you want to test proof questions, then there are more questions about the probability of events and the numerical characteristics of random variables. I think some proof questions are actually the evolution of some calculation questions, not real proof questions, and not too theoretical. They are called proof questions, which actually depend on whether we can make theoretical deduction.
Moderator: Civilized candidates can remember very little after reviewing the book. What should they do?
Chen Wendeng: After reading it, I don't really remember it. That's because you don't always sum up. You should do this. After reading a chapter, make a summary, after each stage, make a stage summary, and finally make a big summary, because only by summarizing more can we form a knowledge framework and stretch the knowledge chain longer and longer. If something is not summarized, it will indeed form: the book is read and the topic is done. Therefore, we must attach importance to it, do more induction and summary, or it is better for Confucius to say, "Learn from the times and learn from the past."
Compere: What is the procedure for reviewing mathematics before the summer vacation? Can we start the problem?
Chen Wendeng: Don't worry too much about it. Before the summer vacation, I think you can have a good look at the four books you have studied in the past. It is necessary to write down some important concepts, theorems and formulas by yourself. Don't want to do the problem too early. It is best to finish the intensive class before doing it, because if you don't go to the intensive class first, you will spend a lot of time doing the problems and it is not worth it. I also want to remind some friends who are taking the postgraduate entrance examination that some people always want to hit the big luck. After doing a problem, they want to see if they got it right. Check the answers. Some netizens still lack confidence in themselves. This is not good, and it is very uneconomical to waste a lot of time in answering your questions. I think it's better this way. Finish the questions in a chapter and focus on the answers. Only in this way can we find out where we are not enough and how to fill the vacancy. If you are fragmentary, it is difficult to know what knowledge you have not mastered.
Moderator: A candidate named He Yuan asks you. He said that his math foundation has not been very good, from freshman to senior, but now the major he chose for postgraduate entrance examination is to take math test. Excuse me, Mr. Chen, do you have any good suggestions for candidates with weak foundation?
Chen Wendeng: Students with poor foundation don't need to look at mathematics so horribly. Some people say it's "talking about numbers turns pale". I don't think it's necessary. A few years ago, among the students we tutored in Wendeng School in Beijing, many students from Beijing Foreign Studies University, Second Foreign Studies University and China Youth Political College got high marks in mathematics (135 or more, and two students from China Youth Political College got full marks in mathematics). Originally, we thought that these schools didn't pay much attention to mathematics, but seeing that the candidates did well in the exam, I went to the other extreme, thinking that their schools also attached great importance to mathematics. In fact, their attention to mathematics is far less than that of economic science and engineering colleges, and there are fewer math classes arranged, and teachers have low requirements for students. But why did these students get high marks in mathematics? Some candidates told me that they gave full play to their two advantages: one advantage is their strong memory, and the other advantage is their strong imitation ability. Yes, if you don't have a strong memory, you can't remember all the words, let alone learn any foreign language, let alone imitate it. If you don't have strong imitation ability, you may turn English words into French, but of course not.
They say there are many things to remember in mathematics, and it is true. For example, formulas, theorems, and some important problem-solving methods and skills need to be memorized by rote. If you can't remember all this, it will be too late to make a temporary deduction when we take the exam. There is a proverb in China that "Practice makes perfect". If you think of something temporarily, you can never use it flexibly. Therefore, it doesn't matter if you remember, recite or have a bad foundation. As long as you have determination and confidence and give full play to the two advantages we just mentioned, memory and imitation, you will certainly learn math well.
Moderator: Another candidate asked you, he said that he bought your math review guide book. Do you know the above questions before you can get more than 70 points in the math test?
Chen Wendeng: This classmate, you underestimate yourself too much. If you really master our review guide, it is entirely possible to get a high score instead of 70. In 2006, I went to Hangzhou to give a lecture. During my lecture, a classmate of Hangzhou Dianzi University came up to me and bowed deeply to me. what did i say? The classmate said, Mr. Chen, I thank you for helping me with my math exam. I said, how many points did you get? He said I got 150. I said, how's your math? He said that I was taking the math test for the third time, and I immediately asked people, where did you listen to my class? His answer disappointed me. He said that Mr. Chen had never attended your class. Hearing this, my heart thumped. I don't know if this boy did well in other people's classes and wanted to mock me. I didn't expect this classmate to see through my mind. He immediately said, Mr. Chen, I didn't attend any class, so I read by myself. I said, whose book do you read? He said I would read your books, and I said I had several books. Which one do you want to read? He said that I only read one of your review guides. I said how many times have you seen it? He said that I had read it six times, and then he handed me the review guide in his hand behind him. When I took it, I saw that the book had changed beyond recognition. Two of the four corners were worn off, so I turned to look inside. The red pen and blue pen pencil hook in it to sketch the picture, which is messy. I told you at that time, classmate, you can't lend this book to your brother and sister. He said I wouldn't borrow it. I want to keep it. I feel very comfortable after listening to it. Traveling all over the country, I finally found such an admirer.
Compere: You have many admirers.
Chen Wendeng: I'm flattered (laughs). So I don't think I need to read many books, but I must study hard. Only by studying hard can I understand thoroughly and get good grades in the exam.
Moderator: "Carnation" He said, hello, teacher, I want to take the 20 10 postgraduate exam. I haven't studied mathematics in junior college before, but now I feel it is more difficult to take the math test. There is no remedial class here (he is a candidate in Guangxi). I don't know how to choose. I just want to ask questions about choosing remedial classes and tutors …
Chen Wendeng: As a student who has never attended an undergraduate course, I want to say that you are preparing for the postgraduate entrance examination. This enthusiasm should be encouraged, but you should be prepared for a protracted war. You want to make a crash course, shorten undergraduate mathematics from two years to one year, and catch up with others' level. It's not easy. What should I do at this stage? I guess this friend who took part in the postgraduate entrance examination may be a liberal arts student, so you should take a good look at calculus, linear algebra, probability theory and mathematical statistics. After reading these three books, you can buy a review guide for economics. I believe that if you do this, you can get a score of 890 in math.
Moderator: Just now I said that he has no remedial classes to choose from in the local area. Candidates like this should go to …
Chen Wendeng: Such a candidate may have no way out this year. It is also possible that our online school will start from September to June. 10. If the online school is opened, the majority of postgraduate students can have a look, because our online school is divided into several stages. The first stage is the basic remedial class, which is to make up for those students who have a weak foundation in mathematics and have never even studied mathematics. There will be an intensive class after that, which is very important.
Finally, the punching class, according to our understanding, prepares some enlightening examples for those important questions and important test sites, so that students can further improve their test-taking level.
Moderator: Now many candidates are faced with many choices of counseling institutions and tutors. Do you have any suggestions in this regard?
Chen Wendeng: At present, the postgraduate training market is shrinking, but the postgraduate remedial classes have mushroomed. It is precisely because of the emergence of many postgraduate remedial classes that this market is very chaotic at present. In order to safeguard the rights and interests of the majority of friends who take the postgraduate entrance examination, I hope that when choosing remedial classes, friends who take the postgraduate entrance examination should not only look at other people's advertisements. Some remedial classes are actually not qualified to run a school, and the level of running a school is relatively poor, but their propaganda ability is really strong. Next, I'd like to tell my friends about some scams in remedial classes. They try their best to build their own brand. They spend money on medals instead of running schools seriously. Some media are not true. In order to make money, they hold this award and that award. But in fact, they don't engage in questionnaires or real online competitions, but sell medals as commodities. This is a strange phenomenon. There are a lot of so-called excellent medals in the remedial classes that were not well run. This is the first one, and that is advanced. For example, just after the political examination every morning, there are large and exquisite advertisements on the campuses of colleges and universities in the afternoon. What warmly congratulates our school XXX on winning six major questions? Another training institution even exaggerated, saying that it didn't miss a question and won it all. If so, what's the use of holding remedial classes? Wouldn't it be easier to sell a book for several thousand dollars? Secondly, they do everything possible to beautify the teachers they employ. A few years ago, a remedial class packaged a man who failed in the postgraduate entrance examination for four years, saying that he was an outstanding young man in the contemporary era, with three talents in mathematics, a genius in academics, a wizard in teaching and a freak in thesis writing! Some tutorial classes named their teachers Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, You really don't know that these laurels belong to Newton? Leibniz's "There are cram schools" stubbornly described his teacher as a professor from Peking University and Beijing Foreign Studies University, and described his teacher as an excellent teacher in Beijing. Students, excellent teachers in Beijing must first teach in colleges and universities in Beijing. Only those recommended by colleges and universities are eligible to participate in the selection of outstanding teachers in Beijing. Some of our students are too gullible. If others say so, you will believe it. Won't you click on the website of the teacher's university? Isn't it exposed to point the fox's tail? The environment and time of class is also a black cloth that blinds students. It says that the teaching environment comes first, with air conditioning and tables and chairs. In fact, the places where classes are held are Baiyi Road and Xueyuan Road. Can it be like what they say? During class time, they bluff and show their strength, and many classes advertise. As long as the discerning person compares, the teacher and the class time will be clear. The kind of separation in students' fairy tales will not appear in reality. How can the same teacher teach in different classes at the same time? Moderator: Learn more. You can check on the websites of these schools.
Chen Wendeng: They are very good at using the reliability of data to deceive people. It is often seen that some remedial classes write in advertisements that the pass rate of attending their remedial classes is over 90%. Students, do you believe it? You know, there is no such data. The so-called high pass rate is just another trick they use to deceive people. They only know the number of people who have attended remedial classes, but they don't know the number of people who have taken the exam and those who have not. How is this pass rate calculated? You will speak for yourself. Using the Internet and newspapers to brag is also a common means for some remedial classes. I read an article in the newspaper. According to the remedial classes, in 2007, although the enrollment and economic benefits of many remedial classes declined, they still maintained the level of about 20,000 students. There were 1 10,000 students who participated in political counseling, but in fact there were only more than 3,000 students. Only more than 200 people were recruited in English and Mathematics respectively. The newspaper said it was more than 6,000 people, more than 5,000 people. The purpose of doing this is to deceive students and expand their appearance. What role can they play? Do they want to be contemporary Q? I want to tell the students who have participated in the professional course counseling that the scam is even bigger in this respect. They said they would find a proposition teacher to teach students, and they would be on-the-job graduate students who had just been admitted to graduate schools. I'm not saying that these in-service graduate students are not qualified, but that they have the ability to take exams, but they are not necessarily excellent teachers. Everyone knows this very well. Olympic champions are undoubtedly top players, but they are not necessarily excellent gold medal coaches. This is clear to students. There are also remedial classes that are even more deceptive. What kind of gold card, silver card and diamond card need you to pay 10,000 yuan or even 100,000 yuan to ensure that you can go to graduate school. Do you really have the ability to guarantee it? Don't talk about other institutions, just say that two students from Zhongcai University told me that they were cheated. Traditional education makes our nation respect teachers very much, but there are also some scum among teachers. One of them is a wang xing student from Beijing Institute of Technology. He claims to be the head of the department of mathematics and the dean of the graduate school. I have worked in Beijing Institute of Technology for 25 years and have been with this person for a long time. I have never heard that he is full-time. He said that he was a math expert who enjoyed the special allowance of the State Council, which was even more absurd. In the 1990s, the School of Mathematics and Foreign Languages of Beijing Institute of Technology did not have the right to review, so it had to be reviewed in Beijing. Starting from 1990, he submitted it four times in a row. Every year, his application materials say that there are several articles to be published in foreign journals. In the first year, experts thought he would be allowed to participate after the article was published. I didn't expect him to be cheated in this way, and finally the experts didn't believe him. This guy who always wanted to be a professor of mathematics, finally, I got a professor of management through contacts. The funny thing is that he is used to cheating outside. When he gave a lecture to students of Beijing Institute of Technology on the evening of February 28th, 2009, he even said that he was an expert enjoying special allowance from the State Council. Finally, he made a fool of himself in front of the students. When the students wanted to see his certificate, he said, "No".
Moderator: OK, just now, Mr. Chen took pains to tell our candidates how to distinguish these various advertisements and various deceptive tricks. I hope candidates can learn more about these institutions according to their own needs. Finally, I hope Mr. Chen Can will give us a few simple words!
Chen Wendeng: Dear examinee friends, your enthusiasm for postgraduate entrance examination deserves our encouragement and support, but you must be careful. Don't pin your hopes and lofty ideals on others. Believe in yourself and rely on yourself. Our slogan is: seeking truth from facts, being pragmatic and working hard. Finally, I send you a poem:
Awakening to the top of the brain,
Internal cultivation is more important.
Jianfeng Bao honed himself,
There is no need to jump the dragon gate.
Moderator: Thank you very much for your coming and your participation. This activity is over, thank you!