First, pay attention to class.

It goes without saying that you should listen to the class carefully. So I won't say much. I'm only saying here that you must learn to take notes if you want to learn advanced mathematics well.

Taking notes will make the class more focused and help you review and consolidate effectively after class.

Some students can't take notes. As long as what the teacher said is irrelevant and detailed, they will remember it correctly. Their ears, eyes and hands are busy and exhausted.

Considering synchronous thinking, if this is the case, it is better not to remember.

There is no need to pursue completeness and pay attention to system in class notes. As long as there are choices and key points, general and technical problem-solving methods can be remembered.

Common and typical examples. And pay attention to the accumulation of problem-solving methods.

Especially the proof questions, because the proof questions are abstract, they often feel at a loss. However, when reviewing after class, we must properly sort out and supplement our notes, which is one of them.

This is a good note. If you can add your own experience and comments, it will be the best annotation.

If you preview well, you will know more specifically what to remember and what not to remember.

2. Review carefully.

In the whole learning process, review is the most important link. Some experts have studied the so-called "knowledge forgetting law", that is, the near is fast and the far is slow. The faster you learn, the more you learn.

The earlier you forget, the more you forget.

Therefore, what you have just learned should be reviewed in time after class, which is called "consolidating memory";

Midterm exam review is called "deepening memory";

Systematic review of the final exam is called "strengthening memory".

We summarize the law of knowledge forgetting as the exponential decay law of knowledge memory.

So we get the following two formulas. The first formula, specifically, is the "formula for reviewing memory". The initial learning amount is time, and a positive number is for reviewing memory.

Memory coefficient is the instantaneous memory of a certain moment. Then our comment will be

I'm correcting the coefficient. Repeated review can turn the coefficient into a small positive number, thus achieving the best memory effect. In extreme cases,

Memory will be "locked" and become the so-called "permanent memory".

Because we are constantly learning new knowledge while reviewing or on the basis of reviewing, the effect of repeated rolling review is knowledge.

Accumulate.

We can write this meaning into the second formula, which is called "reviewing old knowledge and learning new formula" or "knowledge accumulation formula". If you can review at any time like this.

This meticulous, then two years later, one's deceased father grind review, as long as

Just search and review in your "memory bank". Confucius, an ancient sage, said, "It's okay to keep pace with the times!" Modern secular people say, "Songs never leave your mouth,

The more you sing, the more spiritual you are; The more you fight, the better you get. "

3. Work hard.

Homework is an indispensable part of review. Review without homework is meaningless, and homework without review is inefficient. Reading, reading notes, doing homework, of course.

There needs to be an order of first and then, but proper alternation will be more effective.

If doing a good preview is a sufficient condition for improving the efficiency of classroom lectures, then completing homework in time is a necessary condition for reading advanced mathematics well.

The homework assigned by the teacher is the minimum homework requirement. If you can't find a clear feeling after finishing these homework, you should increase your homework appropriately.

Homework is for yourself. Copying homework is actually deceiving yourself.

The homework approved by the teacher must be carefully read, which is a respect for the hard work of the teacher and an excellent way to correct mistakes and avoid repeating them. Because most of the homework

It was originally approved by the teaching assistant. There may be some mistakes and others.

If you don't fully understand the teacher's comments on the exercise book, you must ask the teacher in time.

4. Answer questions overnight.

In the process of learning advanced mathematics, you will encounter all kinds of problems. The deeper you think, the more questions you have. Doubt is a good thing. Regardless of the size of the problem, it is "learning" when accumulated.

. If you don't think about it, you are just a tramp. Finally, don't say that there is nothing. Just trying to survive the risk may not be so lucky.

Learning should have a sense of anger, no anger, no anger, no hair, ask questions and answer them yourself. The "suddenly enlightened" under "meditation" is really called "boring"

Pity. "Of course, this is an ideal state, which can be sought and cannot be forced. we

There are many courses, but the energy is very limited, so we can't just focus on one course of advanced mathematics.

Ask yourself first, then ask your classmates. Learn from each other and brainstorm. Everyone has different bright spots, and once they collide with each other, they may produce gorgeous sparks.

Two heads are better than one!

It is the bounden duty of teachers to solve problems for students, and the time on duty for answering questions arranged by teachers is a valuable resource that you should make full use of. Any teacher who teaches advanced mathematics.

You can ask questions. Don't always expect the teacher to tell you the whole story when answering questions. A teacher who gives you hints and makes you think is definitely a good teacher.

If you think such a teacher is not enthusiastic enough, you are wrong.

At this time, you need enough patience, carefully follow the teacher's guidance and make a good budget. If you really understand it under the guidance of the teacher, it is of course the best.

Otherwise, don't understand is don't understand. Don't be embarrassed.

Ask, don't worry that the teacher will be impatient. The teacher will definitely give you the second step of guidance and the third step of inspiration. Until you fully understand it.

5. Extracurricular reading, reading is optional.

The learning requirements of engineering economics students for advanced mathematics are still very basic. Personally, I don't think it is necessary to read widely and study extensively. Carefully study the teaching of three advanced mathematics books.

Counseling books are very sufficient.

(1) textbooks, there is no need to study more.

Although the textbooks of domestic schools have their own characteristics, they are all compiled according to a unified outline, and the focus is exactly the same.

Some famous universities have made great strides in teaching reform, compressing many basic things into the syllabus and compiling many things outside the syllabus, such as the contents of differential geometry and the principles of operational research.

Theory and numerical calculation methods. We don't think it's necessary at all.

These books. Don't analyze and compare other textbooks except those designated by our school;

(2) Teaching guidance books should be read selectively and guided.

Many advanced mathematics study guides spend a lot of time explaining the so-called key points and difficulties. In my opinion, they are just simple repetitions and lists of textbooks.

There are also some study guides, doing a lot of so-called knowledge charts, contacts and programming. Some authors think they are too simple to reflect his new ideas. In my opinion,

Making it so complicated really makes people feel that they have entered a mystery of advanced mathematics.

Palace. How to learn advanced mathematics well through it? After learning this course well, these simple "knowledge charts, networks and programming" can be written by students themselves.

(3) At present, all kinds of review materials and problem sets of advanced mathematics are the most popular. But when you get this kind of book, please pay attention to the lack of typical examples

In-depth analysis, there are not enough examples to try to figure out, which is not very good for students.

As soon as school starts, some people actively buy books and buy them in piles. These people may have a particularly good foundation and great energy, and have read one book after another in the local area. Let's not go.

They kept up with their neighbors and bought many books. When reading a math book, you must think carefully. How can you read one book after another like a novel?

Buy it when you need it, read it carefully when you buy it, and don't collect it. You don't need to wrap a colorful cover. Only by turning the plastic-coated cover upside down is you really capable.

For students of engineering and economics, I feel that as long as they can "read two books", they will basically "have all the knowledge".

6. Preview can fully improve the efficiency of class.

Doing a good preview is an important part of learning advanced mathematics courses well. Preview can fully improve the efficiency of classroom lectures, and good preview habits can lay the foundation for improving self-study ability in the future.

A solid foundation.

Students' feelings about learning advanced mathematics are: "I can understand in class, but I can't do homework." In the final analysis, I still didn't really understand in class. One of the factors may be that I didn't prepare carefully.

For preview, everyone feels particularly tired, which is time-consuming and can't achieve good results (the so-called "get twice the result with half the effort"). This is because of the importance of preview.

If you don't master it well, think of preview as self-study. In fact, preview and self-study are both

Two different concepts.

Let's talk about the preview requirements of advanced mathematics courses in detail.

First of all, don't preview too much. According to the teacher's teaching progress, just preview the next teaching content. Too much to understand and digest.

For relatively simple content, you can take a closer look and think deeply when previewing.

A little bit.

It is of course the best to know and understand through preview, but generally speaking, the teacher's understanding will be deeper and more comprehensive than yours. Listen carefully to the teacher's analysis in class.

Teacher's understanding, he can help you produce a kind of "superposition" or "double" in understanding.

Increase "or even" leap ".

Many contents of advanced mathematics are difficult, so we can look at them roughly and think shallowly. Even so, I'm afraid I have to bite the bullet and put one.

Look at a complete content.

Preview doesn't require you to know everything. "Vague and seemingly incomprehensible" should be a normal phenomenon.

In class, the teacher will help you turn a vague shadow into a clear image, make your understanding "correct" and "complementary", and change "like understanding" into "real understanding"

; As for "don't understand", you will certainly hear more clearly in class.

Really, be more careful.

Some students think that taking notes in senior math class can't grasp the main points. Then please try to see if this feeling will improve after strengthening preview.

There is no doubt about the relationship between preview and the efficiency of attending classes. The gains and feelings of attending classes after preview are different from those without preview.

The teaching progress of advanced mathematics is very fast, and there are many things to learn in each class. It's really not easy to keep up with the progress without previewing.

It is true that many students feel that advanced mathematics can be learned quite well without preview. But I want to ask a question, "If you do a good job in preview, don't you?"

Is it possible to learn advanced mathematics better? "

In fact, in the near future, preview can improve the efficiency of class. In the long run, developing good preview habits can lay a good foundation for independent acquisition of new knowledge (self-study) in the future.

Students! Advanced mathematics is not terrible. The terrible thing is that you have no confidence and courage to learn it well. In fact, every subject has its own internal laws and structure, and its relationship with

These laws and structural ways of thinking, master the learning methods.

With your efforts, I believe you will be able to roam freely in the ocean of advanced mathematics.

Learning methods of advanced mathematics for freshmen.

At present, the one-year college entrance examination is over, and millions of high school students stand out among their peers through their own efforts, enter their dream colleges and universities, and start in a new chapter.

When studying in the environment, the major media in the society will keep repeating a topic: how can a high school student integrate into the new environment psychologically and physically as soon as possible and become a high school student?

Qualified freshmen? Moreover, freshmen appear from time to time in TV news or newspapers, falling asleep in the new environment of network or video games, but they can't keep up with the progress of college study and drop out of school.

Examples. The author believes that a senior high school student should not only adapt to the new study life from the environment and psychology, but also change his study methods.

noodle I have been engaged in advanced mathematics teaching in engineering colleges for more than 30 years. Advanced mathematics is a basic theoretical course in the teaching plan of engineering colleges and a compulsory course for freshmen.

Advanced Mathematics plays a fundamental role in the follow-up courses of various majors and the working conditions of such engineers and technicians after graduation from university. If school continues.

Only by mastering the knowledge of advanced mathematics can we successfully learn other professional basic courses, such as physics, engineering mechanics, electrician and electronics. And whether you can learn yourself well.

My own professional course. For another example, when you graduate and go to work, you should always apply mathematical knowledge to solve engineering and technical problems well. Because in the continuous development of science and technology,

Today, mathematical methods have penetrated into all fields of science and technology. Therefore, learning advanced mathematics well is a clear task for engineering freshmen.

Cheng, lay a good foundation for future study and work.

So, how do freshmen learn advanced mathematics well? The author talks about some superficial views on his own experience in teaching this course for many years for students' reference.

First, abandon the learning methods of middle school.

After entering the university from middle school, there will be a big turning point in learning methods. First of all, they feel very uncomfortable with the teaching methods and methods of universities, which is in advanced mathematics.

The reaction of this course in teaching is particularly obvious, because it is a big theoretical basic course, and students are used to imitation and simplification.

The learning methods developed for a long time from primary school to middle school education are difficult to change for a while.

The teaching methods in middle schools are qualitatively different from those in universities. Outstanding performance: middle school learning, students are imitating and learning alone under the direct guidance of teachers, while universities require.

Students study creatively under the guidance of teachers. For example, the teaching of mathematics in middle schools is carried out completely according to textbooks. In class, teachers are only asked to talk, and students are asked to listen, not to do it.

Taking notes, the teacher teaches slowly and carefully, and there are many examples of calculation methods. After class, students are only required to imitate what the teacher said in class and do some exercises. There is no need to delve into teaching.

Materials and other reference books (the college entrance examination chooses some other reference books in order to enhance the problem-solving ability of candidates, which is just the need to train the problem-solving ability), while the higher mathematics courses in universities are different.

Textbooks are only used as a main reference book. Students are required to take the key and difficult points mentioned by the teacher in class as clues, read a large number of textbooks and similar reference books and fully digest them.

Then do exercises after class to consolidate knowledge, which is repeated creative learning. This is a hard mental work, which requires not only study.

Students should study actively and consciously, and at the same time, they should be able to restrain themselves in a relaxed environment and master better learning methods in order to learn what they want to learn in a solid and professional way.

Lay a good foundation for the study of business courses.

Second, do three links well.

What is the best way to learn advanced mathematics? This varies according to everyone's study habits and ability to understand problems, but in general, we should do the following three links well.

First, preview before class. This process is very important, because only by previewing before class can we know what the teacher said is difficult to understand and what it is.

It's the point. Wait. In this way, when you listen to the teacher with some questions, the effect will be obvious, and at the same time, it will be lifelong beneficial for you to cultivate your self-study ability in the process of preview.

Yes It doesn't take much time to preview. Generally, a class takes about 30 to 40 minutes. You don't have to understand all the questions in the preview, just take them with you.

Go to class for these questions you don't understand. Second, listen carefully in class and take notes in class.

Everyone understands that it is necessary to listen attentively in class, but the importance of taking class notes is not appreciated by some students. They think it is all in the textbook, so there is no need to remember it, even some students.

The middle school teacher told us that we don't need to take notes in math class. In fact, this understanding is wrong, and it is also a bad study habit brought by middle school. First of all, you can say: The teacher is right.

The teaching of advanced mathematics course is definitely not a simple repetition of the contents in the textbook, but a large number of similar reference books, and combined with my own teaching experience and understanding, how to weigh it repeatedly.

Example teaching can make students better understand and master the speech before writing it. Therefore, it is no exaggeration to say that the teacher's teaching plan has both successful experience and past teaching.

Reference for training. Moreover, the content of a class is summarized into several organized points, some typical examples, proper selection of exercises and so on. These are not in the textbook.

Therefore, students must take good notes in class, and this good study habit, that is, diligent writing, is also of great benefit to the cultivation of their learning and working ability. Third, after class

Review, take notes and finish your homework carefully. Self-study after class, many people do their homework quickly, which is also a bad habit. In fact, we should further study the textbooks after class.

Or teaching reference books, after fully understanding the content of this lesson, sort out and enrich the class notes, add your own experience and experience in some places that need to be understood, and truly turn the knowledge in books into.

It is much better to finish your homework with the knowledge you have, and it is much faster to finish your homework than to make up your homework after class.

Third, be good at induction and go through the process of "from coarse to fine"

It is often said that reading and learning should be good at "from thin to thick, from thick to thin". In the study of advanced mathematics, this experience can be said to be very real. Because learning itself

It is the continuous accumulation of knowledge, so that the book will be "from thin to thick" and the content will be more and more, but people's memory is limited, so we should remember all useful things comprehensively.

It's hard to forget. What do we do? We need to sum up what we have learned, find out the internal relationship between them and things with the same essence, and then make them systematic and coherent.

Remember the most representative knowledge points, and the rest can be inferred and understood on this basis, that is, "from coarse to fine". So at the end of each chapter or unit

After the content is finished, you should summarize the basic concepts, theorems, basic formulas and calculation methods, and then memorize them with your brain in an orderly way, so that the knowledge you have learned is over.

It's all yours.

In short, university study is the last systematic learning process in life, which not only teaches us a relatively complete set of professional knowledge, but also trains students to go to social work.

Ability and social knowledge. As far as higher mathematics courses are concerned, it is necessary to cultivate students' ability of observation and judgment, logical thinking, self-study and problem-solving

The combination of abilities can constitute the ability to analyze problems independently and the ability to solve problems.