Water stirs the sound of stone, and people stir up ambition. Put a piece of paper in the desk and write down the words that inspire you. When you are doing something, your competitors may be studying. Tell yourself that everyone is a genius, and you don't have to feel inferior for a little failure, and you don't have to be proud of a little success.
Mathematics is an abstruse and interesting course. If you increase your confidence in this course and are not afraid, you will easily accept this course, and you will also find that this course is not difficult, which is a very necessary condition for learning mathematics well.
Mathematics is characterized by highly abstract theory and strict logical reasoning. By studying mathematics, we should improve our ability of abstract thinking, logical reasoning, mathematical operation and solving practical problems. The content of any math class consists of four parts: basic concepts (definitions), basic theories (properties and theorems), basic operations (calculations) and applications. To learn mathematics well, we must study hard and work harder in these four parts.
Basic concepts should be clear and easy to understand, thorough and accurate, not specious and half-baked. Mathematical reasoning depends entirely on basic concepts, which are unclear, and many contents can't be learned, mastered and used. For example, in linear algebra, the linear correlation of vector groups has nothing to do with linearity, the ranks of vector groups and maximal uncorrelated groups, and the similar diagonal shapes of matrices. It is often difficult for beginners to grasp, which requires gradual deepening, repeated thinking and thorough understanding in the process of reviewing and doing problems.
Basic theory is the core of mathematical reasoning, which consists of some concepts, properties and theorems. Some theorems do not require every beginner to prove, but the conditions and conclusions of theorems must be clear, and they must be familiar with theorems and learn to use them. Some things must be remembered. For example, the elementary transformation of matrix is one of the important contents of linear algebra. Finding the inverse matrix of a square matrix, finding the rank of the matrix and solving the linear equations are all inseparable from the elementary transformation of the matrix. To understand the truth, why the above problems can be solved by elementary transformation, and what is the theoretical basis? Whether to do elementary row transformation or column transformation. For another example, the existence theorem of solutions of linear equations and the structure theorem of solutions, as well as the related theorems for judging whether vector groups are linearly related, must be kept in mind. In the study of probability theory, the knowledge of calculus is very important for understanding the theory of probability and statistics.
Mastering mathematical concepts and theories and learning to use them mainly depend on doing problems. After reading the content, you should do the questions and do a certain number of questions, which can deepen your understanding of the content and improve your ability to solve problems. Practice makes perfect, there is no shortcut. It is an accepted fact that "not doing problems means not learning mathematics". In the process of solving problems, we should constantly sum up ideas and methods, master the law of solving problems, and improve our ability to analyze and solve problems by doing problems, that is, gradually improve our mathematical literacy. My math teacher in college was a graduate student of Peking University (I was preparing to go to the United States to study for a Ph.D. in mathematics), and I was the top student in the college entrance examination in Fujian Province. He scored 120 (full mark) in mathematics and 99 in physics in the college entrance examination ... He told me that the experience of studying calculus is to do 40,000 problems to ensure that calculus passes (including the calculus part of the postgraduate entrance examination). -the importance of the problem is generally obvious.
To learn mathematics well, we must take all aspects of learning seriously. First of all, listen to the class and concentrate on it. If you can preview it, the effect will be better. When giving a lecture, you should grasp the teacher's analysis of the problem, take notes, learn to do it by yourself, and take notes while listening, especially the parts you don't understand. The second link is to review notes and do problems. After class, you should review your notes in combination with textbooks and notes. We should sort out the content of this lesson according to our own ideas. After reviewing the content, do the exercises. Don't look at the examples while turning pages. Finish the exercises in the workbook by catching mice and cats. This won't have any effect. It should be used as a question to test whether you really understand or not fully understand your study. Think over and over what you haven't fully understood until you fully understand it. Of course, I don't encourage a person like me to read books. It is better to find free video courseware, which will be more efficient. )
Followed by the stage summary. After each chapter, you should make a summary. Summarize the basic concepts and core contents in this chapter; What problems are solved in this chapter and how are they solved? What are the important theories and conclusions to rely on, and what are the ideas to solve the problem? Sort it out, summarize the main points and core contents, as well as your own understanding and experience of the problem.
Finally, the summary of the whole course. Make a summary before the exam. This summary will sort out and summarize the contents of the book, analyze what you have learned and grasp the relationship between chapters. This summary is very important, and it is a comprehensive arrangement of the core content, important theories and methods of the whole course. On the basis of summing up, I will have a deeper understanding of the contents of the book and analyze and solve some slightly difficult problems to test my mastery of all the contents.
If we can grasp the above four links, really study hard and never let go of a difficult point, we will certainly learn math well.
In the exam. . .
The Relationship between Examining Questions and Solving Problems
Some candidates do not pay enough attention to the examination of questions, are eager to achieve success, and rush to write, so that they do not fully understand the conditions and requirements of questions. As for how to dig hidden conditions from the problem and stimulate the thinking of solving the problem, it is even more impossible to talk about it, so there are naturally many mistakes in solving the problem. Only by patiently and carefully examining the questions and accurately grasping the key words and quantities in the questions (such as "at least", "a > 0", the range of independent variables, etc. ), and get as much information as possible, in order to quickly find the right direction to solve the problem.
The relationship between "doing" and "scoring"
To turn your problem-solving strategy into a fractional point, it is mainly expressed in accurate and complete mathematical language, which is often ignored by some candidates. Therefore, there are a lot of "yes but no" and "yes but incomplete" situations on the test paper, and the candidates' own evaluation scores are far from the actual scores. For example, the "skip" in solid geometry argument has caused many people to lose more than 1/3 points. In algebraic argument, the idea of "substituting pictures for proofs" is correct, even ingenious, but it is clumsy because it is not good at translating "graphic language" into "written language" accurately. Another example is the image transformation of trigonometric function in 17 last year. Many candidates "have a good idea" but don't know clearly, and there are not a few points deducted. Only by paying attention to the language expression of the problem-solving process can we grade the "can do" questions.
The relationship between quickness and accuracy
At present, in the case of a large number of questions and tight time, the word "quasi" is particularly important. Only "accurate" can score, and only "accurate" can avoid taking the time to check. And "fast" is the result of usual training, not a problem that can be solved in the examination room. If you try to be quick, you will only make mistakes in the end. For example, in last year's application problem No.21,it was not difficult to list piecewise analytic functions, but quite a few candidates miscalculated quadratic functions or even linear functions in a hurry. Although the following part of the problem-solving idea is correct and takes time to calculate, there is almost no score, which is inconsistent with the actual level of candidates. Slow down and be more accurate, and you can get a little more points; On the contrary, if you hurry up and make mistakes, you will not get points if you spend time.
The relationship between difficult problems and easy problems
After you get the test paper, you should read the whole volume. Generally speaking, you should answer in the order from easy to difficult, from simple to complex. The order of examination questions in recent years is not entirely the order of difficulty. For example, it was more difficult to manage 19 than to manage 20 and 2 1 last year. Therefore, we should arrange the time reasonably when answering questions, and don't fight a "protracted war" on a stuck problem, which will take time and won't get points, and the questions we can do will also be delayed. In recent years, mathematics test questions have changed from "one question to many questions", so the answers to the questions have set clear "steps", with a wide entrance and easy to start, but it is difficult to go deep into the final solution. Therefore, seemingly easy questions will also have the level of "biting hands", and seemingly difficult questions will also be divided. So don't take the "easy" questions lightly in the exam, and don't be timid when you see the "difficult" questions of new faces. Think calmly and analyze carefully, and you will definitely get the score you deserve.