Freshmen have just entered the university from middle school. They don't understand the characteristics and importance of advanced mathematics, it is difficult to master a set of scientific learning methods, and they don't know enough about the importance of learning advanced mathematics, which leads some students to learn this course badly. Advanced mathematics is a compulsory theoretical basic course for freshmen of science and engineering. It plays a fundamental role in the study of follow-up courses of various majors, the working status of such engineers and technicians after graduation from university, and the study of advanced mathematics courses. For example, only by mastering the knowledge of advanced mathematics in the school can we learn other professional courses smoothly. Such as physics, control science, computer science, engineering mechanics, electrical and electronics, communication engineering, information science, etc. In order to learn our professional courses well. For another example, when you graduate and go to work, it is bound to be applied to mathematics knowledge frequently to solve the problems in engineering technology well. Because today, with the continuous development of science and technology, mathematical methods have widely penetrated into all fields of science and technology. Therefore, a clear task for engineering students in their study is to learn advanced mathematics well and lay a good foundation for their future study and work. So, how do freshmen learn advanced mathematics well? The following views are for students' reference only. First, abandon the learning style of middle school and adapt to the environment as soon as possible. After entering the university, a high school student should not only adapt to the new study life in the environment and psychology, but also change his study methods. After entering the university from middle school, there will be a big turning point in learning methods. First of all, I feel very uncomfortable with the teaching methods and methods in universities. This is especially obvious in the teaching of advanced mathematics, because it is a basic theoretical course for freshmen. Students are used to imitation and a single learning method. This is a long-term education from primary school to middle school, which is difficult to change for a while. The teaching methods in middle schools are qualitatively different from those in universities. Middle school students learn through imitation and singleness under the direct guidance of teachers, while universities learn creatively under the guidance of teachers. For example, the teaching of mathematics in middle schools is completely carried out in accordance with the contents of textbooks. Teachers talk in class, students listen, and students are not required to take notes. Teachers teach slowly and seriously, and there are many examples of calculation methods. After class, students are only required to imitate what is said in class to solve the exercises after class. There is no need to delve into textbooks and other reference books (some reference books are selected in the college entrance examination to enhance students' problem-solving ability, just to train students' problem-solving ability). However, in the study of higher mathematics courses in colleges and universities, textbooks are only the main reference books, which require students to study the textbooks after class, read a lot of similar reference books, and then complete the exercises after class. In this way, creative learning is repeated. This is a hard mental work, which requires students to study consciously and repeatedly. Be able to restrain yourself in a relaxed environment. College life is a major turning point in life. Universities pay attention to cultivating students' ability to live independently, think independently, analyze independently and solve problems, instead of having a dependent environment like middle schools. 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. Middle school is teacher-led learning, students only need to follow the teacher's baton, while universities mainly rely on self-study, and teachers only play a guiding role. Freshmen should adapt to college life as soon as possible and make a good start, which is beneficial to their four-year college career. 2. Pay attention to the differences and connections between middle school mathematics and advanced mathematics. The center of middle school mathematics curriculum is the transformation from concrete mathematics to conceptual mathematics. The purpose of middle school mathematics course is to prepare for college calculus. Learning mathematics always goes through a gradual process from concrete to abstract and from special to general. From numbers to symbols, that is, the names of variables; The relationship from symbols to functions, that is, the relationship between objects represented by symbols. The first thing higher mathematics should do is to help students develop the concept of function-the expression of the relationship between variables. This has promoted students' understanding from constants to variables, from description to proof, from specific situations to general equations, and began to understand the power of mathematical symbols. However, the main content of higher mathematics is calculus, which inherits the cultivation of middle school, and the two are inextricably linked. 3. Adapt to the teaching characteristics of advanced mathematics as soon as possible In order to adapt to the teaching reform of advanced mathematics in the 2 1 century, the teaching of advanced mathematics has also undergone great changes. On the basis of traditional teaching methods, more concrete and visualized modern educational technology is adopted, which is not available in ordinary middle schools. Therefore, students should not only pay attention to the differences and connections between advanced mathematics and middle school mathematics after entering the university, but also as soon as possible. Seriously teach the first class of advanced mathematics and do it in strict accordance with the teacher's requirements. If we can persist in previewing before class, listening to lectures in class, reviewing after class, finishing homework carefully, summing up what we have learned after class and deepening our understanding of what we have learned, we can master what we have learned, so it is not difficult to learn advanced mathematics well. Some students just can't grasp themselves. At first, they saw that the content of advanced mathematics was very similar to that learned in middle school, so they took it lightly and thought it would be good to have a look. Either they don't attend class or they don't finish their homework. As a result, the following chapters can't be understood and can't keep up, and even some students can't keep up, and their final grades are not ideal or even fail. 4. Mastering the correct learning methods Because of the characteristics of advanced mathematics, students can't master it all at once. Some contents, such as the continuity and discontinuity of functions, the substitution method of integral, and the method of step-by-step integration, are still difficult to master at the moment, and each student needs to ponder, think, train and persevere repeatedly. By comparing the positive and negative examples, we can learn some truth from them, and let us go from ignorance to a little knowledge to basic mastery. Here, I only talk about the methods of learning advanced mathematics in combination with general learning methods for reference.

First, be diligent, thoughtful and practice more. The so-called learning includes learning and asking questions, that is, learning and asking questions from teachers, classmates and themselves. Only by "asking in learning" and "asking in learning" can we digest the concepts, theories and methods of mathematics; The so-called thinking is the content of learning. After thinking and processing, the essence and essence are obtained. Hua Qin's thinking, rough-to-fine mathematics learning method is worth learning from. The so-called practice, as far as advanced mathematics is concerned, is to do problems, which is the characteristic of mathematics itself. Generally speaking, exercises are divided into two categories. One is the basic training exercise, which is usually attached to each chapter. This kind of problem is relatively simple and not difficult, but it is very important, that is, to lay the foundation. The second is to improve the training practice, with a wider range of knowledge, not limited to this section of this chapter, and to use a variety of mathematical tools in solving. Mathematics practice is an extremely important link to digest and consolidate knowledge, otherwise it will not achieve the goal.

Second, pay close attention to the foundation and proceed step by step. In any subject, the basic content is often the most important part, which is related to the success or failure of learning. Advanced mathematics itself is the foundation of mathematics and other disciplines, and it has some important basic contents, which are related to the overall situation of the whole knowledge structure. Taking calculus as an example, the limit runs through the whole calculus, and the continuity and nature of the function run through a series of theorems and conclusions. Derivation and integration of elementary functions are related to various disciplines in the future. Therefore, we should work hard from the beginning and firmly grasp these basic contents. When learning advanced mathematics, we should study and practice step by step. Third, classify and summarize, from coarse to fine. The general principle of memory is to grasp the outline and remember it in use. Classified summary is an important method. The classification method of higher mathematics can be summarized into two parts: content and method, and illustrated by taking representative problems as examples. When classifying chapters, we should pay special attention to some conclusions drawn from the basic content, that is, some so-called intermediate results, which often appear in some typical examples and exercises. If you can master more intermediate results, you will feel relaxed when solving general problems and comprehensive training problems.

Fourth, read a reference book intensively. Practice has proved that under the guidance of teachers, we can accurately grasp a reference book and read it intensively. If you can read a representative reference book well, you can easily read other reference books.

Fifth, pay attention to learning efficiency. Mastering mathematical methods and theories often requires practice to make perfect. It is impossible for a person to master what he has learned through one study, and it needs to be repeated many times. The so-called "learning from time to time" and "reviewing the old and learning the new" all mean that learning has to be repeated many times. The memory of "Advanced Mathematics" must be based on understanding and skilled problem solving, and rote learning is useless.

Six, master the learning rules 1. Book: textbook+problem set (required), because learning math well is absolutely inseparable from doing more problems. It is suggested that the problem set should have a book related to postgraduate entrance examination, which will also help you prepare for postgraduate entrance examination in the future.

2. Note: as much as possible. 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 down in the notebook. 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. Class: I suggest you preview before listening. It doesn't matter if you don't understand. Many college courses are reread after class in combination with teachers' notes. But remember: don't make a sudden attack before the exam, it will never work. Keep up with it at ordinary times and try not to make mistakes step by step.

4. Learn high numbers well = basic concepts+basic theorems+basic networks+basic knowledge+basic questions. Mathematics is a concept+theorem system (and reasoning), and it is very important to understand concepts, such as limit and derivative. You should not only have a vivid understanding of them, but 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 experience. 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 useful, such as the solution of various limits. All these have been done, and the high scores should not be bad, at least it is no problem to 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. It's not as difficult as you think. You can also read some books about the application of advanced mathematics. In fact, mathematics originally comes from application, and you will know that advanced mathematics is really useful. In a word, university study is the last systematic learning process in life. It should not only teach us relatively complete professional knowledge, but also cultivate students' working ability and social knowledge to go to society. As far as the course of advanced mathematics is concerned, it is necessary to cultivate our students' abilities of observation and judgment, logical thinking, self-study and problem solving. When these abilities are combined, they can form the ability of independent analysis and problem solving. Here, I hope everyone will attach great importance to the study of advanced mathematics and explore a set of effective learning methods for themselves.