Advanced mathematics is an important basic course in colleges and universities, and it is extremely important for every college student to learn it well.
Here, I put forward some suggestions on how to learn this course well for students' reference:
First, grasp the three links to improve learning efficiency
Preview before class: know what the teacher is going to say and review the relevant content accordingly.
Second, listen carefully: pay attention to the teacher's explanation methods and ideas, analyze and solve problems, and take good class notes. Listening to class is a process of listening, remembering and thinking.
Review after class three: Be sure to recall what the teacher said that day and see how much you remember;
Then open notes, teaching materials, improve notes and communicate; Finally finish the homework.
Second, understand on the basis of memory, deepen in the completion of homework, and build a framework of knowledge structure in comparison.
Third, according to the idea of "new = old+poor" to understand and deepen the learning knowledge.
Four, "there are three people, there must be my teacher", to participate in the teacher's guidance, ask students, discuss with each other.
Five, the basic methods to deal with mathematical problems:
A division and summation method;
The second is the method of directly finding the curve;
Three identical deformation methods:
① arithmetic addition and subtraction; ② multiplication and division factor method; ③ Integral derivative method;
④ Triangular substitution method; ⑤ Number-shape combination method; ⑥ Relational iteration method;
⑦ Recursive formula method; (8) methods of mutual communication; Pet-name ruby attack before and after;
Attending the method of reflection and verification; ⑾ builder's method; ⑿ stepwise decomposition method.
Sixth, the combination of stage review and comprehensive consolidation.
Five principles of learning methods
Learning methods are closely related to the learning process, stages and psychological conditions, which not only includes the understanding of learning rules, but also reflects the understanding of learning content. In a certain sense, it is also a learning method with personal characteristics. Learning methods vary from person to person, but the correct learning methods should follow the following principles: step by step, careful reading, self-satisfaction, combination of knowledge and practice, and unity of knowledge and practice.
1。 "Step by step"-that is, people learn systematically and step by step according to the knowledge system of the subject and their own intellectual conditions. It requires people to attach importance to the foundation, avoid aiming too high and be eager for success. The principle of gradual progress is embodied in: first, we must lay a good foundation. Second, from easy to difficult. Third, we should do what we can.
2。 "Read carefully and think carefully"-that is, according to the dialectical relationship between memory and understanding, memory and understanding should be closely combined, and they should not be neglected. We know that memory and understanding are closely related and complement each other. On the one hand, only by understanding on the basis of memory can we understand thoroughly; On the other hand, only by memorizing with the participation of understanding can the memory be firm. "Reading" requires "three things": feeling in the heart, feeling in the eyes and feeling in the mouth. To "seriously think", we should be good at asking and solving problems, and use "self-questioning method" and "people's questioning method" to ask and ask questions.
3。 "Self-satisfaction"-that is, give full play to the initiative and enthusiasm of learning, tap their inherent learning potential as much as possible, and cultivate and improve their autonomous learning ability. The principle of self-satisfaction requires you not to study for the sake of learning, but to digest and absorb what you have learned and turn it into your own use.
4。 "Combination of Bo and Yue"-that is, combining the two according to the dialectical relationship between Bo and Yue. As we all know, the relationship between Bo and Yue is based on Bo. Under the guidance of Yue, Bo and Yue combine and promote each other. Insist on learning from others. First, read widely. The second is intensive reading.
5。 "Unity of knowing and doing"-that is, combining learning with practice according to the dialectical relationship between cognition and practice, avoiding learning without using it. As the saying goes, "the knower begins to do what he knows, and the walker becomes what he knows", which is effective only under the guidance of knowledge, and is blind without knowledge. Similarly, the knowledge verified by lines is true knowledge, and the knowledge divorced from lines is empty knowledge. Therefore, the unity of knowing and doing should pay attention to practice: First, we should be good at learning, practicing, learning and accumulating in practice. The second is practice, that is, applying the knowledge learned to practical work and solving practical problems.
Mathematics learning method
● Comprehensive review, reading thin books.
● Highlight key points and strive for perfection.
Basic training, repeat.
When learning mathematics, we must do a certain number of problems and practice the basic skills thoroughly. However, we don't advocate the tactic of "asking questions in the sea", but advocating simplicity, that is, doing some typical questions repeatedly, solving more questions and changing one question. To train the ability of abstract thinking, the proof of some basic theorems, the derivation of basic formulas, and some basic exercises need not be written, just like a chess player's "blind chess", you can get the exact answer by meditation with your brain. This is what we mentioned in the preface, 20 minutes to complete 10 objective questions. Some questions can be answered at a glance without writing. This is called well-trained, and people with solid basic skills of "Practice makes perfect" have many ways to encounter problems and are not easily stumped. On the contrary, when you do a problem, you are always looking for a difficult problem. In this way, when you go to the examination room, you may not encounter similar problems you have done before; Many candidates misjudge the questions they can do, which is classified as carelessness. Indeed, people will be careless, but people with solid basic skills will find out immediately when they make mistakes, and rarely make "careless" mistakes.