First, review in combination with the outline

Outline is not only the rule that proposers should follow, but also the basis for our review. In 2009, 20 10, 20 1 1, the outline for three consecutive years has not changed a word, and even if it changes, it will not change too much. You just have to follow the syllabus for the first three years. Careful students may have noticed that the outlines of different knowledge points have different requirements, such as understanding, comprehension, mastery and calculation. So how should we treat it? Don't pay attention to the difference between these words in the review of the basic stage. It can be seen from the content distribution of examination papers over the years that all the contents mentioned in the examination syllabus may be tested, and even some less important contents may appear in the form of big questions. It can be seen that it is easy to lose points and lose in the examination room by using the review method of betting and guessing questions. You should refer to the exam outline and review it comprehensively, leaving no omissions.

Second, pay attention to the quality of the problem.

In the process of learning in the basic stage, the topics in the textbook must be done. Do you have to do all the questions in the textbook? According to statistics, there are more than * * 1900 topics in advanced mathematics textbooks, more than * * 400 topics in linear algebra textbooks and more than * * 230 topics in probability and mathematical statistics textbooks. To learn mathematics, we should practice the basic skills thoroughly, but we do not advocate the tactic of "asking questions about the sea". In fact, we already know the number of questions to be done above. To advocate refinement at this stage is to do some typical problems repeatedly, so that one problem can be solved many times and one problem can be corrected. The ability to train abstract thinking, the proof of some basic theorems, the derivation of basic formulas and some basic exercises all need to get correct answers without writing, just like a chess player's "blind chess", just thinking with his brain. 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, people who are always looking for problems when doing problems may not encounter similar problems when they go to the examination room. Many candidates miscalculate the questions they can do, which comes down to carelessness. It is true that people are sometimes careless, but people with solid basic skills can find mistakes immediately and rarely make "careless" mistakes.

Third, pay attention to the review effect.

Review is not simply memorizing all the knowledge. It is to grasp the essence of the problem and the essential connection between content and method, try to reduce what you want to remember, try to make yourself understand what you have learned, grasp the connection of the problem more, and memorize less knowledge. Moreover, if you remember it, you must remember it firmly. Facts have proved that some memories will never be forgotten, and some memories can be obtained by using their own connections on the basis of remembering the basic knowledge. In the process of reading textbooks, on the one hand, we should improve the review efficiency, and don't compare with others. Be able to describe concepts and theorems in your own language and avoid "a little knowledge"; Don't blindly do problems without paying attention to timely summary, so as to realize a leap from quantitative change to qualitative change; Don't rush to do the "postgraduate examination paper" before, and then do the second stage review after reviewing the three courses of mathematics, so the effect will be better.

Deeply understand the concepts and theorems required by the examination syllabus, master the exercises after class skillfully, turn over the textbooks frequently when encountering ambiguous problems in the future, and fully understand the context of the textbooks, which is of great help to the speed and quality of doing the questions.

Of course, as you said, mathematical logic and mathematical thinking are very important in mathematics. If you don't understand, I think you should sign up for a class, mainly to train your logical thinking. All the students in our class are in the new oriental math class reported by the state league. First, the map is cheap, which can save hundreds and send an enhanced version; Most importantly, they are taught by professors from Peking University and Beijing Institute of Technology, as well as online guidance and psychological counseling. It feels good. If you are interested, you may wish to have a look.