First, only by firmly grasping the foundation and closely following the definition can we deeply understand new knowledge.

Mathematics is a unified and holistic subject, and all knowledge points are closely related. Some people say that the study of college mathematics has little to do with the study of junior high school and senior high school. This statement is scientific. Mathematics is a rigorous subject, and the study of mathematics should have a gradual process. Therefore, learning mathematics should pay attention to the foundation.

Let's look at the following example: find the tangent of y=x at the origin.

With the knowledge of middle school, we can easily draw a graph with y=x, but from the image, y=x should have no tangent at the origin. Actually, it is not. We can use the method of high school to calculate the slope k=0 of the tangent of y=x at the origin, that is, the tangent is y=0, but we don't know why at that time. Now that we have learned the geometric meaning of derivative and differential, it is easy to explain this problem with the definition of tangent. The definition of tangent is: the limit of secant. In this way, y=0 is indeed the tangent of y=x at the origin. Therefore, mathematics learning is a basic learning. Only by firmly grasping the foundation and having an attitude of asking questions to the end can we learn mathematics well, not only knowing why, but also knowing why.

Second, classification, summary and comparison

We have learned a lot of similar mathematical knowledge, but they are essentially different. At this time, we need to put them together, find out the similarities and differences, classify and summarize them, and then compare them. For example, in higher algebra (linear algebra), the comparison between determinant and matrix: a number multiplied by determinant is to multiply this number by a row of elements in this determinant, and a number multiplied by matrix is to multiply this number by every element in this matrix.

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Another example is: in spatial analytic geometry, the comparison of methods for establishing straight lines and planes in space; Induction and comparison of equidistant formulas from point to line, line to line and line to surface; Comparison between sequence limit and function limit in mathematical analysis (advanced mathematics); Comparison of continuity, derivability and derivability of functions; Rolle theorem, Lagrange theorem and Cauchy mean value theorem. We may be confused when learning these things separately, but when we pull them together and put them on the same piece of paper, their differences and connections will be clear. This is not only easy to learn; I remember it clearly, too.

Third, look for the known from the unknown and understand the unknown.

This is commonly used by everyone. Every time we have a new lesson, the teacher leads from the known to the unknown, and then we look for the known knowledge from the unknown to understand. In fact, this should be done not only in class, but also after class. The more solid you learn, the more "known" you will find, and the more in-depth you will analyze when you do the problem, so as to achieve Excellence and get twice the result with half the effort.

Fourth, special knowledge and special memory. Use examples to help remember. Draw inferences from others.

This is also an important way to learn mathematics. There is a lot of knowledge about mathematics, some of which need special memory. At this time, we can use examples to help remember. Through a thorough analysis of an example, we can remember the knowledge points well, and then we can draw inferences from other similar problems.

For example: symbolic function sgn x

dirichlet function

riemann function

When learning a function, we should make its image clear and learn it clearly, and learn the function through the combination of numbers and shapes. For example, when we remember that "the function f is derivable at point X and continuous at point X; But the opposite is not the case. " When putting forward this proposition, just give an example: the function y= is continuous at x=0, but it is not derivable. When it is reflected on the image, the image is not smooth at the point (0,0).

In addition, to learn mathematics, we should learn more, practice more and think more. We should avoid being too arrogant and impetuous. It is also necessary to finish our homework carefully. At the same time, we can also recognize our own shortcomings and deficiencies, clarify the vague knowledge points and improve our knowledge system.

A Brief Talk on Mathematics Learning Methods

0494051119 Liu Ying

From kindergarten to the present university, we all have deep contact with mathematics. Because of my love for mathematics, I have deep feelings for mathematics. I believe everyone is familiar with the learning methods of mathematics. Whenever you learn math, the method is the same. The most important thing is perseverance! The following is my summary of mathematics learning methods:

First, seize the classroom.

Science study focuses on weekdays and is not suitable for surprise review. The most important thing on weekdays is class time. Listen attentively and stay close to the teacher. At the same time, it should be pointed out that many students tend to ignore the mathematical ideas and methods taught by teachers and pay attention to the answers to questions. In fact, the way of thinking is far more important than the answers to some questions.

Second, high-quality homework.

The so-called high quality refers to high precision and high speed. When writing homework, I sometimes repeat the same type of questions. At this time, it is necessary to consciously examine the speed and accuracy. Every time you finish this kind of problem, you can have a deeper thinking, such as the content of the examination, the mathematical thinking method used, and the rules and skills of solving problems. In addition, we should carefully complete the thinking questions assigned by the teacher. If you don't give up easily, you must carry forward the spirit of "nails", think quietly whenever you have time, and inspiration will always come to you suddenly. Most importantly, this is an opportunity to challenge yourself. Success will bring self-confidence, which is very important for studying science. Even if you fail, this question will leave a deep impression on you.

Third, do a good job in preview, think more and ask more questions.

Do a good job in preview, and target the questions you don't understand as the focus of the lecture. For the laws and theorems given by the teacher, we should not only know what it is, but also know what it is, so as to get to the bottom of it. This is the best way to understand. You should be skeptical about studying any subject, especially science. If you have any questions about the teacher's explanation and the content of the textbook, you can always ask them and discuss them with your classmates and teachers.

Fourth, sum up and contrast, and clear up ideas.