Mathematics is a special course in the postgraduate entrance examination, which has the dual nature of professional course and public course. It is a compulsory course for postgraduate entrance examination in engineering, economics, management and other disciplines. The content of the examination involves three parts: advanced mathematics, probability statistics and linear algebra, which are divided into four types: mathematics I, mathematics II, mathematics III and mathematics IV. Different majors have different requirements for mathematics. The scope, difficulty and emphasis of the four different types of examinations are different. For example, probability statistics is not taken in Math II, and the contents of higher mathematics are less than those in Math I, while Math III and Math IV have higher requirements for probability statistics. Therefore, first of all, candidates should be clear about the requirements of their majors for mathematics in order to review them in a targeted manner. For most candidates who need to take three public courses, mathematics is the most difficult to learn and the most difficult to take. Therefore, over the years, mathematics has the lowest average score in almost three public courses. The full marks of these three public courses are 100 for politics and English and 150 for mathematics. So if you grasp it well, you can fall far behind others and gain an absolute advantage in the total score. If you don't grasp it well, you will lose the best chance to defeat the enemy.

First, the characteristics of the subject and the misunderstanding of review

Postgraduates have many mathematics contents, wide knowledge, strong comprehensiveness and high skill. Especially as a proficiency test, the postgraduate mathematics often organically combines the knowledge points of advanced mathematics, linear algebra and probability statistics, which increases the difficulty of mathematics review. Many candidates report that it is still difficult to make breakthrough progress even if a lot of review time is allocated to mathematics and a lot of problems are done. Our survey shows that there are some misunderstandings in the review of the majority of candidates.

1? Passive confrontation is inefficient.

For a long time, the argument that "postgraduate entrance examination is difficult, mathematics is difficult" has been widely circulated and deeply rooted in people's hearts. Many candidates have been afraid of mathematics before they know the content and type of the exam, and set their goals and expectations very low. "Just crossing the line can almost become a more common mentality. This is reflected in passive response rather than active preparation in review. In fact, mathematics is a subject that needs in-depth study. If you want. First of all, we must eliminate fear and build up confidence in winning. Only in this way can we turn passivity into initiative and experience real fun in mathematics learning and problem solving. For this part of the candidates, please refer to the first section of this chapter "successful mentality".

2? Only skill, no understanding.

Fundamentally speaking, this is a manifestation of speculative psychology. Learning is hard work. Many candidates don't want to work hard and unilaterally pursue other people's ready-made methods and skills. They always want to learn more routines, and they can answer questions according to the pictures of cats. As everyone knows, the methods and skills are based on their deep understanding of basic concepts and knowledge. Each method and skill has its specific scope of application and premise of use. Mathematics for postgraduate entrance examination is a high-level contest, and seemingly the same questions may have essential differences. Therefore, pure imitation is absolutely impossible. This requires us to give up speculative psychology and understand the ins and outs of each method step by step.

3? Look at the problem and do it.

Due to the tight review time and heavy tasks, many candidates bought materials, but they just read books in a hurry and didn't practice. It seems that they can do it at a glance, but they are either confused in logic or don't know how to write at all. Mathematics is a rigorous subject, and there can be no omissions. Before we have established a complete knowledge structure, it is bound to be difficult to grasp the key points in the topic. Ignore nuances. The fundamental purpose of solving problems is to deepen our understanding of the whole knowledge through problems and organically link them. Through hands-on practice, we can also standardize the answering mode and improve the proficiency of problem solving and operation. You know, a question as big as three hours is a test of calculation ability and proficiency, and now the paper is graded step by step. How to make an answer is effective, which can only be achieved through our own continuous exploration.

4? Only pursue high difficulty, not heavy foundation.

The study of basic knowledge is no exception to any subject. Most of the mathematics for postgraduate entrance examination are intermediate and easy questions, and only about 20% are difficult and skilled questions. The problem is only the further synthesis of simple questions. If you are stuck on a problem, it must be because you don't understand a certain knowledge point enough. Or the train of thought of a simple question is vague. Ignoring the foundation leads candidates to lose a lot of points on many simple questions. It is really not worth giving up the 70% that can be determined for the uncertain 30%. Postgraduate entrance examination is not an olympiad, and neither difficulty nor skill is the key to success. Therefore, in the review process, we must proceed from reality, lay a solid foundation, and have a deep understanding, so that even if we encounter some problems, we will break them down smoothly. This is the fundamental solution.

5? The sea tactics are not summarized.

We say that we want to do a topic because we want to deepen our understanding of the whole knowledge through the topic and connect it organically. Math learning is inseparable from doing problems, but it is by no means equal to doing problems. Abstraction is one of the most important features of mathematics. In the review process, it is very necessary for us to spread out a certain number of exercises and deeply understand the connotation and extension of abstract knowledge points. But don't forget, our most fundamental purpose is to understand knowledge points and form our own organic knowledge structure. Therefore, our idea of doing the problem must be from understanding to doing the problem to induction and then back to understanding. In addition, it is necessary to do some problems to increase proficiency, but if it exceeds this limit, it is completely unnecessary to make doing problems a mechanized labor. These bases can also be one of the bases for us to judge whether we are doing sea tactics.

6? Do the questions, turn over the books, and don't remember the formulas.

There is also a common habit of the majority of candidates, that is, they don't remember the formula, look back at the book when doing the problem, leave it alone after checking, and recite it before the exam. We know that mathematics is logical, and formulas and theorems are inextricably linked, so we should remember with understanding in the usual review process, rather than simply reciting. On the one hand, the memory based on understanding lasts longer; On the other hand, I understand that in case it doesn't happen, we can deduce it ourselves (although time may not allow us to do too much). Mechanical memory is easy to forget and make mistakes. In this case, we won't know if we use it wrong, so it's not wrong to lose points!

Second, one's deceased father grind math solid review plan

The last part leads the majority of candidates out of various misunderstandings in review. The main task of this part is to teach candidates a targeted and operable specific solution. We advocate attaching importance to basic and daily accumulation, and oppose quick success and instant benefit. However, due to the late preparation time of some candidates, here, starting from reality, a test-taking breakthrough plan besides a solid review plan is given as a backup plan. You can choose according to the actual situation. Just as quick martial arts must have its dead point, quick learning is fundamentally faced with the problem of insufficient chassis. If there is enough time, I sincerely hope that the majority of candidates will choose to prepare slowly and steadily. Let's talk about material selection first.

1? Data selection

There is an independent part in this book to discuss the strategies and methods of data selection. This part focuses on the data and ideas we used in math review according to the previous candidates' experience.

1) examination outline and examination analysis

The examination syllabus drawn up by the State Education Commission strictly stipulates the scope and difficulty requirements for all kinds of professional candidates to take the examination, which should be one of the most authoritative and useful reference materials for all candidates and the basis for candidates to make plans. Examination analysis is a kind of historical reference material, which is compiled together with the outline. On the one hand, it is to further analyze the knowledge points of the outline, on the other hand, it is to analyze the real questions and candidates' papers, so as to facilitate candidates to locate themselves more accurately.

2) Real questions over the years

These questions are of great significance for understanding the questions of postgraduate entrance examination, understanding the ideas of setting questions, grasping the key points of propositions, strengthening answering skills and training answering norms. Nowadays, counseling books are usually interspersed with books or give some real questions in the form of appendices, but the whole set of real questions containing detailed answers and grading rules still plays an irreplaceable role, because the real questions of postgraduate entrance examination not only meet the strict answering specifications from each question, but also meet the expected difficulty and discrimination on the whole, so the whole set of real questions can better reflect the characteristics of the proposition. In addition, it is worth noting that there are often no standardized answers in the current counseling materials, and standardized answers can make the thinking clearer. Judging from the answer, there are not many key steps required for each question, and the final exam time is tight and the task is heavy. It is wise not to write useless steps, but to the point.

3) Teaching materials

Textbooks are the key to our first review. The basic textbooks given below are all the best versions in the past.

Tongji Edition of Advanced Mathematics: The explanation is detailed, the examples are moderately difficult and involve a wide range of contents. It is a widely used textbook in colleges and universities, and there are many supporting textbooks.

Tsinghua Edition of Linear Algebra: The explanation is informative, detailed and in-depth, suitable for students with plenty of time (recommended).

Tongji edition of linear algebra: light and short, concise and easy to understand, suitable for students with poor foundation.

Zhejiang University Edition "Preliminary Probability and Mathematical Statistics": The basic exercises after class are covered.

4) Tutoring materials

The advantage of reading textbooks is comprehensive and meticulous, but it often takes too long and the focus is not prominent. For students who take the postgraduate entrance examination, they often feel like falling in a fog. We will review the counseling materials at each stage later, which are basically sorted by time.

The Tsinghua version of Advanced Mathematics has recently been published and is available in all major bookstores. It follows the curriculum and is very effective in improving mathematical thinking. A Course of Linear Algebra, written by Hu Jinde, is very compatible with Tsinghua's textbook. The Course of Probability and Statistics is very popular with everyone, and Li Yongle is also using it.

Chen Wendeng's Mathematics Review Guidance and Mathematical Problem Collection and Simulation Test, and Li Yongle and Fan Peihua's Mathematics Review Complete Book are the two books most used in the market now. Among them, Chen Wendeng's book Probability Theory and Linear Algebra is relatively basic and can be used in the first round of review. Advanced mathematics is partly difficult and suitable for the second round. In addition, math problem collection and simulation test.

5) sprint books

The 400 classic simulation questions edited by Yuan Yintang and Li Yongle have many knowledge points, strong skills and standardized topics. Li Yongle's sprint 135 points is short and pithy, which can be used to review and penetrate knowledge in the final review. Besides, the better simulation questions are EB's and Chen Wendeng's.

2? The first stage is to lay a solid foundation and review comprehensively (April-August)

Main objectives: to thoroughly understand the requirements of the postgraduate entrance examination syllabus, to achieve accurate positioning, to review the knowledge points involved in the syllabus in detail, to lay a solid foundation, to train mathematical thinking, to master some basic problem-solving ideas and skills, and to prepare for the next stage of problem-solving breakthrough.

It can be seen from the content distribution of examination papers over the years that all the contents mentioned in the examination syllabus are likely to be tested, and even some less important contents can appear in the form of big questions. It can be seen that any opportunism will only harm yourself in the end. It is wise to refer to the examination syllabus and review it comprehensively without leaving any omissions. Therefore, the main idea of our review is to take the exam outline as the key link and study math textbooks carefully from beginning to end. First, don't focus on the key points and difficulties, but review the knowledge points equally against textbooks and counseling materials. For some important concepts and formulas, we should remember them on the basis of understanding and do some simple exercises by the way. These after-class exercises and tutoring material exercises are very helpful to summarize some related problem-solving skills, and also help to remember and consolidate knowledge points.

As you can see, this round of review time accounts for about half of the total review time, which lays a solid foundation for our later problems. According to the above ideas, this round adopts the following review mode, and candidates can choose according to the actual situation. The selection principle can refer to some suggestions in material selection.

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Textbook+Examination Outline+Tsinghua's Advanced Mathematics Tutoring, Hu Jinde's Linear Algebra Tutoring and Yao's Probabilistic Statistics Tutoring Book.

Textbook+Examination Outline+Advanced Mathematics Tutoring in Tsinghua, Mathematics Review Guide in Chen Wendeng, Probability Statistics and Linear Algebra.

Textbook+Examination Outline+Li Yongle and Fan Peihua's Mathematics Review Book, and Chen Wendeng's Mathematics Review Guide Probability Statistics and Linear Algebra.

Several problems to be paid attention to in review;

1) emphasizes learning rather than reviewing.

For most students, because of the early learning time of advanced mathematics, and the original learning difficulty is not great, plus forgetting, I am afraid that there is not much mathematics knowledge left now. So at this time, we should emphasize learning, take the initiative to re-learn to do and think.

2) Selection of audit sequence.

One thing to mention is that mathematics contains three courses. You may forget calculus after learning probability and forget probability after learning linear algebra. So you should review it repeatedly and gradually shorten this cycle. We don't advocate that these three courses go hand in hand. After all, the three courses are different. If you want to learn a course, you will feel like riding a tiger before you go forward, and then you will spend more time cleaning up the mess. As for the three courses,

3) Pay attention to detail and depth.

In the process of learning, we must try our best to fully understand and master the knowledge points. Because the exam syllabus is not in the order of chapters in the textbook, we can study for a period of time first, and then evaluate the review of knowledge points according to the syllabus.

4) the problem of outline

Because the examination syllabus and mathematics examination analysis were published late, the syllabus has not changed much over the years because of the consistency of investigation. Therefore, at this time, you can refer to the outline of previous years to review the knowledge points. When the new syllabus comes out in July and August, we can compare and supplement it.

5) Emphasize active personal participation and organize notes.

It is very important to write your own feelings in the learning process, and try to dig deep into the connotation of examples in the form of captions or notes. It is also important to review the first three rounds. It would be easy if we had our own notes in the last round of review. Some students say that the best way to learn linear algebra is to deduce it yourself, which makes sense. In fact, if we adopt this attitude in learning everything, we will certainly learn well.

3? In the second stage, I will be familiar with the types of questions (September-165438+1October).

Main objectives: be familiar with the questions of postgraduate entrance examination, strengthen the connection between knowledge points, distinguish important and difficult points, shorten the review period as much as possible, master the overall knowledge system, and master theorem formulas and problem-solving skills skillfully.

After the last round of review, we have mastered the knowledge points quite well, but there is a problem that the knowledge points are isolated, the connection between them is not strong, and forgetfulness often occurs in the review. These are not terrible, because we are all involved in the previous work, and it should not take too long to return to the original state. Moreover, if we really forget it seriously, it shows that we have shortcomings in relevant knowledge points and can also provide a basis for our review.

The examination syllabus has three levels: knowing, understanding and knowing the content requirements; Generally speaking, the content to be understood and the methods to be mastered are the focus of examination. In previous years' exams, the probability of these problems is very high. The same test paper, this score is more. People who "guess the questions" often have to work hard in this respect. Generally speaking, they can guess several points, but when it comes to comprehensive questions with secondary content in the main content, "guessing questions" will not work. Not only should we work hard on the main content and methods, but more importantly, we should find the connection between the key content and the secondary content. Use key content to enhance the overall content. The main content is thoroughly understood, and other contents and methods will be readily solved. In other words, grasping the main content is not to abandon the secondary content and isolate the main content, but to naturally highlight the main content from the analysis and comparison of the relationship between the contents.

View mode:

Exam syllabus+Chen Wendeng's math review instruction, math problem collection and simulation test, Li Yongle sprint 135.

Exam syllabus+Chen Wendeng's Mathematics Review Guide and Mathematical Problem Set and Simulation Exam, as well as Li Yongle and Fan Peihua's Mathematics Review Encyclopedia's Probability Statistics and Linear Algebra.

No matter which mode you adopt, you should start to summarize at this stage, and you must record your mistakes and experiences in doing the questions and understanding, so as to prepare for the whole brain reappearance one week before the exam. Some mistakes are habitual. If you correct them at that time, you will forget them after a long time. It is easy to make them again during the exam!

Candidates should be fully familiar with the postgraduate entrance examination questions according to the counseling book. The reference books given above all have detailed answers, even the answers are right below the questions. We require candidates to answer the questions independently, and they must do it themselves first, and then correct it according to the answers. There are several mistakes in some reference books. Candidates should not blindly believe the answers, but have firm confidence. In mathematics learning, we don't advocate "sea of questions" tactics, but advocate refinement, that is, doing some typical problems repeatedly to achieve multiple solutions to one problem. One question is changeable. To train abstract thinking ability, prove some basic theorems, deduce basic formulas and do some basic exercises, you only need to meditate with your brain and get the correct answer without writing, just like a chess player's "blind chess". This is called well-trained, "Practice makes perfect". People with solid basic skills have many ways to meet problems and are not easily stumped. On the contrary, when doing questions, many candidates will misjudge the questions they can do and attribute them to carelessness. Indeed, people who are careless but have solid basic skills will find out immediately when they make mistakes, and rarely make mistakes "carelessly".

Key content:

At this stage of mathematics review, the focus must be moved back, because the test sites, key points and difficulties of mathematics are mostly in the middle or the last chapters of each book, and the comprehensive questions and big questions of life system mostly appear in the later chapters. In Mathematics 1, the emphasis of advanced mathematics is on definite integral, multiple integral, line-surface integral and infinite series, and the emphasis of advanced mathematics in Mathematics 2, 3 and 4 is on differential mean value theorem. Definite integral, etc. The most important parts of linear algebra are linear correlation of vectors, linear equations, eigenvalues and eigenvectors, quadratic forms and positive definite matrices. There are many types of questions in these chapters, and the connection and transformation of knowledge points are very concentrated, which is convenient for doing comprehensive questions. The review of probability statistics focuses on the following chapters of one-dimensional random variables and their distribution. When reviewing advanced mathematics, we must organically combine limit theory, differential calculus and integral calculus. Flexible use. When reviewing linear algebra, we must take the linear equations as the core, and use the knowledge we have learned to analyze and solve problems flexibly, not in isolation. For example, determinant, matrix, vector and linear equations are the basic contents of linear algebra. They are not isolated and separated, but are closely related to each other. When reviewing probability statistics, candidates should flexibly use what they have learned, establish a correct probability model, and synthesize it.

4? The third stage of simulation training (65438+February-65438+1October).

Main objectives: make a general test of the previous review by using the set of questions, practice the standard of answering questions, keep the test paper clean, increase confidence, practice the allocation of examination time, enhance the ability of improvisation, and focus on reviewing the ambiguities of the first two stages and the places that are not well mastered.

After the above two rounds of preparation, candidates' ability and thinking reserve are enough to cope with the postgraduate entrance examination questions. At this stage, candidates should start practicing simulated or real questions. In this process, pay attention to the distribution of answering time and the adjustment of examination room mentality. No matter how their mock exam results are, they should keep a good attitude: if their grades are high, don't be complacent. After all, the pressure and environment in the real examination room are different from those in peacetime. Don't be discouraged if your score is low. Seriously sum up your experience and lessons. Generally speaking, simulation questions are hard to be true.

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True questions+400 classic simulation questions edited by Yuan Yintang Li Yongle+other simulation test papers.

Pay attention to this question:

In this stage of review, we need to pay special attention to the research on the standard of answering real questions. Because of the large number of exam questions and tight time, many students will feel that time is not enough. Once again, the study of real questions is mainly to grasp the whole test paper and the standard of answering questions. According to the standard, try not to write what needs to be written, which can save time on the one hand and standardize thinking on the other. Only by developing good habits at ordinary times can we be conscious of the exam and not panic. Because the real questions are limited, we should repeat this training process until we are satisfied.

The second question is to make a good summary. Good examples, mistakes and new solutions should be recorded. There are basically no knowledge points that can't be learned at this stage, but the problem is that the knowledge points are still chaotic, and the understanding and solutions of individual knowledge points are not fully grasped. At this time, no books can help you, only you can record, summarize and summarize them bit by bit.

5? The fourth stage is to strengthen memory and keep the state (1 monthly exam)

Main objectives: strengthen memory, adjust mentality, keep in shape, and actively take exams.

Due to the hard review for a long time, in the final review stage, candidates will inevitably feel psychologically and physically tired, and this is the most critical time for review. At this time, what we summed up in our original pages and notebooks will be of great use. Because it is our own summary, we think these things are more targeted, which can quickly restore the state and deepen the memory. On this basis, it is best to do some less intense simulation questions or real questions according to the examination time to keep the feeling. It is very important to prepare for the exam actively with a good review attitude.

At this stage, we need to pay attention to several issues:

1) First, adjust the routine.

Both students on campus and candidates studying alone will face this problem. This stage is no longer an important period for learning and reviewing knowledge. The key is to adjust your life rules to adapt to the upcoming exam and give full play to your best condition in the examination room. It usually takes about a week to adjust your schedule and excitement. Candidates must have a clear understanding of this issue.

2) Do not do simulation questions before the exam.

We talked about the role of simulation questions before. At this time, we should do more basic questions, or real questions we have done in the last two years, to avoid unfamiliarity and maintain confidence. At this stage, the psychological mood of candidates is the easiest to fluctuate, and doing some simulation questions before the exam may pull the mood to the bottom at once. If candidates encounter this situation, they should also come out quickly. The quality of simulation questions in the market is uneven, which is not equal to the real questions. In retrospect, it is very tangled.

3) Don't buy new tutoring materials.

At this stage, many businesses will release a large number of materials with various names, but in fact, after so many years, the content of counseling materials is not much different, and gradually they have their own characteristics and reputation, so it is impossible to have any breakthrough counseling materials in the short term. So, don't be fooled by fancy appearance and touching slogans. Most of the new materials are just the original ones, so there is no need to buy them again, let alone see the new ones.

4) Stop reading sprint books.

Generally, there are many simulation questions in this kind of books, and there are methods and skills to solve them. As the exam approaches, it is of little significance for candidates to do these things. We have been training in different degrees in the first three rounds. At this time, the best way is to look at the problem-solving ideas, answering skills, common mistakes and so on. This is more targeted. There is no one who knows himself better than himself, and what we sum up by ourselves is bound to be more useful to ourselves.

5) Don't trust lectures on topics.

There will be a pile of lectures and materials on the topic before each exam. Practice has proved that this phenomenon is a pure commercial behavior, which is not only not conducive to improving the performance of candidates, but also wastes money and valuable review time. Recently, there has been a phenomenon of selling "real questions" on the Internet. Many students are deceived and must take warning.

Third, the breakthrough plan of entrance examination mathematics

Thirdly, the plan to break through the exam quickly is only a backup measure for students preparing for the postgraduate entrance examination in September or even later. If there is enough time, I sincerely hope that the majority of candidates will choose to start preparing slowly. Because it is a rapid breakthrough, candidates will have more opportunities for quick success and instant benefit. This practice does not violate the principles we mentioned earlier, but requires us to have a correct attitude and do a good job of self-control. Let's talk about the choice of materials first.

1? Data selection

1) Examination outlines and real questions over the years. No matter how tight the time is, the outline should be one of the most authoritative and useful reference materials for candidates. The real questions over the years are of great significance for understanding the types of postgraduate entrance examination questions, understanding the ideas of writing questions, grasping the key points of propositions, strengthening answering skills and training general norms.

2) Chen Wendeng's Guide to Mathematics Review, Collection and Simulation of Mathematical Problems, and Li Yongle and Fan Peihua's Mathematics Review Book. As mentioned earlier, Chen Wendeng's book is highly inductive, requires high methods and skills, and is suitable for students with good foundation. Li Yongle's book is relatively basic, but the counseling effect is not inferior, and students with poor foundation can use it.

3) 400 questions of classic simulation edited by Yuan Yintang and Li Yongle.

4) "Introduction and Summary of Postgraduate Mathematics Knowledge", candidates can make full use of the refining potential of this book system and quickly grasp the weak links for strengthening.

2? The first stage is to select materials and start directly.

Main goal: to deeply understand and break through the examination questions.

Because time is tight and the task is heavy, we must carefully select the review materials and spend all our energy on the cutting edge. If we are fully prepared, the effect is still very good.

View mode:

Exam syllabus+Chen Wendeng's math review guide and math problem collection and simulation test.

Examination syllabus+Li Yongle's and Fan Peihua's math review books.

Some people say that as long as Chen Wendeng's book is done three times, the postgraduate entrance examination will certainly pass smoothly. There is some truth in this. Our main job is to make the materials we choose thoroughly twice or even three times. If you choose Chen Wendeng's books, you can use math problem sets and simulation problems appropriately, some key problems can be done by hand, and the rest can be done as you see fit.

In particular, I would like to emphasize the following points:

1) Candidates should not enter the misunderstanding. We say that reading questions can only be used after we have done math review guidance. Doing this when the foundation is not good can easily lead to a low-minded exam and should be avoided.

2) If you don't have enough time to take notes during the review, list the ideas and ideas in the review and the expansion of the topics in the book directly on the page, and use different colors for each review. For example, you can use a pencil for the first time, a blue pen for the second time, a red pen for the back, and so on. This seems to be a clear-cut, look at the work you have done, and you will be more practical.

3) Because of the short time, we choose less materials, not light tasks but heavy tasks. This requires us to dig deeper every time we do a problem, to understand abstract knowledge points with the least exercises, and to cope with changeable exams.

4) The focus of review must be moved back, because the test sites, key points and difficulties of mathematics are mostly in the middle or the last chapters of each book, and the synthesis and major problems of life system are mostly in the later chapters. Moreover, the following topics basically need the previous knowledge to pave the way, so you can review from the back to the front in the later stage of review, and you can only be familiar with the knowledge structure and focus on memorizing and contacting the previous chapters.

I hope it helps you.