In the middle school stage, there may be no further studies or few, but it is very important. It may be more helpful for you to find a math manual, look at the sequence in it, and deduce and restore it, and it won't take too long.
Listen carefully in class and practice more after class.
You can try to reason about the theorems in the textbook yourself. This will not only improve your proof ability, but also deepen your understanding of the formula. There are many exercises. Basically, after each class, you have to do after-school exercises (excluding the teacher's homework).
The improvement of math scores and the mastery of math methods are inseparable from students' good study habits. Therefore, good math study habits include: listening, reading, exploring and doing homework.
Listening: We should grasp the main contradictions and problems in class, think synchronously with the teacher's explanation as much as possible, and take notes when necessary. After each class, we should think deeply, sum up and make a lesson.
Reading: When reading, you should carefully scrutinize and understand every concept, theorem and law. For example, you should learn from others by connecting with similar reference books to increase your knowledge and develop your thinking.
Inquiry: Learn to think, explore some new methods after solving problems, learn to think from different angles, and even change conditions or conclusions to find new problems. After a period of study, we should sort out our own ideas and form our own thinking rules.
Homework: review before you do your homework, think before you start writing, and grasp a large piece of a class of questions. Homework should be serious and writing should be standardized. Only in this way can you learn math well.
Suggestions on learning advanced mathematics.
Compared with high school mathematics, advanced mathematics is very different, mainly by introducing some brand-new mathematical ideas, especially the infinite division, limit and so on. Formally speaking, the learning methods are also very different, especially in large classes, and it is difficult for teachers to tutor alone, so the requirements for self-study ability are very high. The specific learning methods vary from person to person, but there are some basic rules that everyone must abide by. I specifically say the following points:
1。 Book: textbook+problem set (required), because learning math well is absolutely inseparable from doing more problems (a bit like high school, hehe); It is suggested that the problem set should be related to the postgraduate entrance examination, which will also help you prepare for the postgraduate entrance examination in the future.
2。 Remarks: try to have it. When I say notes, I don't mean copying the blackboard intact. It's boring, and you don't have to use a small notebook alone.
You can write it in a book. The key is to have your own summary of each chapter in your notes, similar to an outline (sometimes in a teacher or reference book, you can refer to it), and it is best to have various questions+methods+error-prone points.
3。 Lesson: I suggest you preview before listening. Actually, I never attend classes, except exercises. It doesn't matter if I don't understand. Many college courses are reread after class in combination with teachers' notes. But remember, don't make a surprise attack before the exam, it is absolutely impossible. You should keep up with it at ordinary times and try not to make mistakes step by step.
4。 Learning high numbers well = thorough basic concepts+firm basic theorems+basic network knowledge+basic knowledge+basic problems well. Mathematics is a concept+theorem system (and reasoning), and it is very important to understand concepts, such as limit and derivative. You should have a vivid understanding of them.
In order to understand, you should also remember their mathematical descriptions. You don't need to remember them. You can give examples to the book yourself, draw a picture (image understanding is actually very important), and then do more questions and learn from it. It is suggested that you mark all the concepts with colored pens, so that it will be clear at a glance when reading a book (the theorem is boxed).
The basic network is the knowledge outline summarized in the above-mentioned notes, so we should also pay attention to it.
Basic knowledge is what high school teachers often call "quasi-theorem", that is, there are things that can be used as theorems or inferences that are not in books, and some of our own little experiences. These things are informal, but very useful.
I understand all the questions, such as the solution of various limits.
Well, all this has been done. My high number should not be bad, at least I can cope with the exam. If you want to improve, you can do some math problems for the postgraduate entrance examination and experience it. Actually, that's all.
You can also read some books about the application of advanced mathematics. In fact, mathematics is originally from the application, and you will know that it is really useful (I don't know what your major is)
Finally, talk about how to improve your understanding ability (a family statement)
1。 Give specific examples. If you know derivatives, give yourself an example, such as f (x) = 820302x2+811211(the square of x).
2。 Visualization of metaphor. For example, imagine the graph of a binary function as a straw hat on the girl next door.
3。 Primary analogy. For example, comparing binary function with univariate function, Taylor formula is quadratic function, which is easy to understand.
4。 Multi-book reference method. Go to your library and borrow some advanced mathematics textbooks written by different authors. Although the content is the same, different authors often express the same question from different angles. It is often much easier for you to understand the same problem from many different angles and examples. Give it a try!
5。 I don't know the temporary jump method. If you don't understand the process of proving and deducing some theorems for the time being, it doesn't matter, just let it be for the time being, write down this doubt and solve it later.
Having said so much, I don't know which ones are useful to you. By the way, there is no shame in asking questions. Ask your classmates and teachers. The meeting is the purpose. If you have any questions, leave me a message.
In addition, we must establish a good learning attitude towards linear algebra. The content here is abstract, so it needs more time. Moreover, the study at this stage is a good opportunity to exercise your abstract thinking and logical thinking, which is of great help to your future professional study. I hope you can grasp it.
As for probability statistics, it pays more attention to reality and prefers calculation. You should master some knowledge of number theory and some mathematical theories well, which is also close to your major's mathematics.
In short, to learn college mathematics well, the most important thing is to lay a good foundation.
Finally, I wish you success in your studies!