The method of learning mathematics well from the zero foundation of liberal arts in senior high school
First, remember more. Here, taking more notes means that students take more notes in class, which is not too difficult for liberal arts mathematics, and the types of questions corresponding to each concept are relatively fixed, so what students need to do is to write down the key problems explained by the teacher in class and the key points and problem-solving ideas of some questions said by the teacher in class, which is very helpful for liberal arts students, because the mathematical foundation of liberal arts students is relatively weak, for teachers in class.
Second, focus on the foundation. Most of the reasons why liberal arts students have some difficulties in mathematics learning are because they didn't lay a good foundation of mathematics in junior high school or even primary school, and even didn't have a good understanding and memory of some basic knowledge of mathematics, so it will be more difficult to learn, so we must master our own basic knowledge of mathematics and lay a good foundation for ourselves, so as to have certain achievements in learning.
Third, practice more. What liberal arts students lack in learning mathematics is the logical thinking and calculation ability of mathematics, so they always can't get high marks when doing problems or exams. If they want to improve their computing ability and logical thinking, they need to practice more after class. Only after a lot of practice can they improve their problem-solving ability and mathematical logic thinking ability.
Suggestions on learning mathematics well from zero foundation of liberal arts in senior high school
One is to attend a cram school. This is a useful supplement to school teaching, which can be one-on-one tutoring or a small class of 4-8 people. If there are too many people, the effect will be greatly reduced.
Second, students learn from each other. Including the timely discussion and exchange of what you have learned in your daily study. For example, when you learn new knowledge of projection drawing, you can use recess or other time to ask your classmates for advice immediately about what you have not learned or what you have only, so as to solve problems anytime and anywhere.
The third is to ask the teacher for help. When studying and doing homework in each class, once there is something you don't understand, you can solve the difficulties and problems in learning in time through face-to-face counseling, telephone, email and other different ways, so as to ask if you have doubts. This is also a valuable experience for liberal arts students to learn mathematics well.
A plan to learn mathematics well from the zero foundation of liberal arts in senior high school
The first stage: laying the foundation (six months)
The first stage takes six months, and the main goal is undoubtedly to establish the foundation, which lasts for a long time and can be divided into two time periods.
Dig into textbooks
The first period lasts about four months, and the main task is to study textbooks. Textbooks can't be replaced by any other materials, and they are the basis of postgraduate mathematics. The officially recommended textbooks are Advanced Mathematics published by Tongji University Press, Probability and Mathematical Statistics published by Zhejiang University Press and Linear Algebra published by Higher Education Press. The first and second volumes of Advanced Mathematics published by Tongji University Press are detailed, which not only contain all the knowledge points of the number three postgraduate entrance examination, but also cover more non-test knowledge points, which has higher requirements for students. Personally, it is suitable for candidates who are interested in advanced mathematics or have more time. At the beginning, due to the pressure of specialized courses and limited time to study mathematics, I finally gave up this edition of teaching materials and chose a non-mainstream version specially written for students taking math exams. The content is relatively simple and easy to use, which is suitable for candidates who have never been exposed to mathematics in high school liberal arts universities. There is no need to be too entangled in the choice of teaching materials for postgraduate entrance examination, and the content is the same. No matter what the government and the people recommend, what suits you is the best. It is much more meaningful to start learning immediately after selecting the teaching materials than to spend time looking for the best teaching materials.
After choosing textbooks, many candidates may encounter problems such as enrolling in classes, skipping classes or self-learning. Personally, I suggest self-study. Most of the postgraduate classes are large classes, and the teacher's lectures are generally aimed at students with a certain foundation of advanced mathematics, which is obviously overburdened for zero-starting candidates. Skipping classes has advantages and disadvantages. It is good to be able to give feedback to the teacher at any time. The disadvantage is that teachers have strong teaching selectivity, narrow coverage and insufficient depth. So the best choice is self-study supplemented by appropriate classes. If you encounter difficulties in the process of self-study, you should consult your teachers and classmates in time, otherwise you will not be able to learn later.
Review the whole book
The second stage lasts about two months, and candidates begin to contact review books. You can choose a book review by Li Yongle or Chen Wendeng. Reviewing the whole book is a high summary of the knowledge points of the textbook. In addition, it also covers the problem-solving skills summarized by editors, which is of great help to the postgraduate entrance examination. The review book is mainly aimed at candidates with good review level, and the exercises provided are more difficult. Beginners will work hard, but don't lose heart. The focus should be on knowledge points and problem-solving skills.
The second stage: strengthening knowledge points and problem-solving ideas (half a year)
The second stage, which takes about six months, is the most important strengthening stage. The main goal of candidates in the process of strengthening is to master the review books. Many people think that the whole book is difficult to review because of its wide coverage, and they just need to look it up occasionally like a dictionary. But my personal experience believes that reviewing the whole book is of great help to the postgraduate entrance examination. This does not mean that mastering the exercises in the review book can help you take the postgraduate entrance examination. It's just that the summary of problem-solving methods in the review book comes from the hands of postgraduate experts, and their experience in doing problems between the lines is precious. Reviewing the whole book can be repeated many times to lay a solid foundation. After you fully understand the knowledge points of advanced mathematics and some problem-solving skills, you can choose the postgraduate course. However, candidates must be clear: the choice of postgraduate courses is not to let teachers teach all the knowledge points in detail, but to learn problem-solving ideas, simple problem-solving skills, correct writing methods and understand the real problem-solving routines. It is wrong to rely too much on the postgraduate classes, and it is also unreasonable to study entirely on your own. The knowledge taught by graduate teachers is particularly important.
These six months are the most important in the whole mathematics preparation, and they are the sublimation stage of mathematics understanding for postgraduate entrance examination. It is in this half-year period that the author deeply realized the consistency of mathematics in postgraduate entrance examination and mastered the foundation of advanced mathematics.
Teachers often teach students to lay a solid foundation for subject learning and stabilize the bottom of the pyramid. The same is true for the study of postgraduate mathematics. Both advanced mathematics and linear algebra have obvious basic knowledge blocks, and mastering these basic knowledge blocks will get twice the result with half the effort for the following chapters.
The content of advanced mathematics can be divided into four parts: limit and continuity, differential calculus (including the application of derivative and multivariate differential calculus), integral calculus (including double integral) and ordinary differential equations. Calculus and ordinary differential equations are based on derivation, and the basis of derivation is limit and continuity. The most important knowledge points of limit continuity are infinity, infinitesimal and limit continuity. Equivalent infinitesimal is the most commonly used knowledge point in calculation problems. Mastering several commonly used equivalent infinitesimals is conducive to saving time and improving the correct rate. Compared with equivalent infinitesimal, the continuity of limit has more universal significance, which can be used not only as a calculation problem, but also as an examination content of proof problem. In addition, it also involves the understanding of calculus, and the continuity of multivariate differential calculus is also its extension. The importance of the foundation of advanced mathematics is not only reflected in the study of complex knowledge, but also directly reflected in the arrangement of the scores of the postgraduate entrance examination papers. Whether you choose to fill in the blanks, the first step of the calculation problem is to find the limit, which shows its importance.
The basis of linear algebra is determinant and matrix. Compared with advanced mathematics, these two chapters of linear algebra directly cover the focus of the following chapters. The rank of vector group is the extension of matrix rank, and linear equations, similar matrices and quadratic forms are all matrix operations in essence. So master determinant and matrix skillfully, and then you don't have to be afraid.
Learning mathematics from scratch is not much better than being taught in detail and patiently by teachers. You need to learn to grasp the system and context of the postgraduate entrance examination mathematics, and distinguish between the foundation and the examination focus. It is not only conducive to learning new knowledge, but also helpful to solve difficult problems with large knowledge span, lay a solid foundation and learn to use it flexibly, so as to realize the connection and continuation of knowledge before and after.
The third stage: sorting out the real questions of the postgraduate entrance examination (four months)
The third stage is arranged for four months, focusing on sorting out the real questions of the postgraduate entrance examination. There are many versions of real questions in the market, among which Li Yongle's "Analysis of Mathematical Examination Questions over the Years" is highly appraised, which not only includes detailed explanations of real questions over the years, but also classifies real questions according to knowledge points, so as to facilitate the concatenation of knowledge before and after.
The use of "historical true questions" varies from person to person. At first, the author basically followed the following five steps:
First, set aside a few years of real questions with the same questions as in recent years for pre-test simulation;
Second, the real problem simulation over the years, in strict accordance with the examination time. If they haven't finished it after a while, they will correct the paper first, and then continue to study the problems they haven't done before;
Third, after correcting all the wrong questions according to the answers, record the wrong questions for future review;
Fourth, write down the knowledge points involved in each question;
5. Simply write down all the chapters of the postgraduate mathematics and put each question in the right place.
The fourth stage:? Topic sea? Tactics (two months)
In the final stage, set aside nearly two months to formally join the company? Topic sea? Stage. Personally, I have never been separated from studying mathematics? Topic sea? Tactics. ? Practice makes perfect? This is the best proof in mathematics learning. This stage is dominated by mock exams. In the initial stage, on the basis of careful summary in the previous stage, the real questions over the years are selected and simulated again. After mastering the real questions over the years to a certain extent, you can refer to Li Yongle's "400 Classic Questions of Full Reality Simulation". This book is very difficult. Even if all the problems can be solved, it is extremely difficult to finish it in three hours. When using "400 classic problems simulated by full reality", the time can be appropriately extended, and every problem can be solved. After completion, you need to correct and summarize the knowledge points as seriously as you do the real questions. After the training of "400 classic problems of full-reality simulation", we can select and sort out the simulation problems that are well evaluated by various institutions in the market. The simulation score is not important, the main purpose is to find the feeling of doing the problem. One week before the exam, you can start the simulation of the real questions reserved before. After receiving simulation training from various institutions, it will be much easier to do real questions.
The review schedule varies from person to person, but these four stages represent four levels respectively. No matter how much time is spent in each stage, mathematical ability should always be gradual.
I have always attached great importance to sea tactics, but for a long time, I practiced a lot but didn't improve my problem-solving level. Now that I think about it, the reason is improper answering skills. Of course, the postgraduate mathematics examines the mastery of basic concepts, theories and theorems, but in the final analysis, it pays more attention to operation methods than the context of theorems. From the arrangement of test scores, we can know that the scores of proof questions only account for a small part. Then, candidates who can calculate problems are obviously superior to those who can deduce.
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