For many freshmen, advanced mathematics learning is somewhat difficult and the results are not satisfactory. Teachers have been thinking hard: although teachers have done their best in the teaching process, there are still many students who don't study well. What is the reason? According to the survey, these students are either not interested in learning or can't get to the point. Therefore, advanced mathematics learning must fully mobilize the enthusiasm of learners and master appropriate learning methods in order to gain something. 1 Learners should realize the importance of learning advanced mathematics, improve their interest in learning and change passive learning into active learning. As we know, many students don't realize the importance of learning advanced mathematics. They don't know the importance of learning advanced mathematics in university courses, and they have no enthusiasm for learning, let alone enthusiasm. Mathematics education plays an important role in foundation and quality education. New technologies and processes led by modern information such as modern information, space skills, nuclear energy utilization, basic engineering, microelectronics and nanomaterials +0 1 1. The quantitative analysis of modern humanities needs mathematics as the main basis. The rigorous definition method, meticulous logical thinking and comprehensive and systematic analysis of mathematics discipline are the concentrated reactions of dialectical materialism in mathematics discipline. It plays an irreplaceable role in the quality education of college students. Quality is manifested in four aspects: mathematical consciousness, mathematical language, mathematical skills and mathematical thinking. The improvement of quality helps students to form good ideological and moral quality, scientific and cultural quality and physiological and psychological quality, thus improving people's quality. This can be verified by examples. Take the Geology Department of Peking University as an example, one department has trained 48 academicians of Chinese Academy of Sciences. This is due to Li Siguang's thought of strengthening the foundation of mathematics and physics, because students are basically good at engineering mathematics, with strong logical thinking and clear mind. 1.2 Cultivating interest in advanced mathematics can stimulate enthusiasm for learning. "Interest is the best teacher." Psychologist Bruner believes: "Learning is an active process. The best motivation for students to learn is their interest in the textbooks they study. ""If they are interested in learning, they will like learning, and if they are tireless, they will find time to study. "Only when students are interested in learning can they direct and focus their psychological activities on the object of study, with vivid perception, concentration, keen observation, lasting and accurate memory, keen and rich thinking, strengthen the internal motivation of learning, arouse the enthusiasm of learning and stimulate intelligence and creativity. Improve learning efficiency. 1.2. 1 Improve the interest in learning advanced mathematics. First of all, we can understand the history of mathematics in China, and understand the process and reasons of the germination, development, prosperity and weakness of mathematics in China. We can also talk about the history of calculus discovery in higher mathematics. Through the understanding and feeling of history, we can experience the profoundness of mathematics, stimulate the appreciation of the beauty of mathematics and improve our interest in learning advanced mathematics. Mathematics is beautiful, but this kind of beauty is not easy to be perceived, and it is often mistaken for mathematics as boring. Branch growth and stock skills include Fibonacci series and golden section. The proportion of gold is as big as the universe, as small as microorganisms, and it is everywhere. Mathematics has the beauty of numbers, symbols, figures, ideas and ways, which is shocking and fascinating. You can consciously take the initiative to understand. Learning advanced mathematics should pay attention to the understanding and digestion of basic knowledge (basic concepts, basic theories and basic methods). There is a saying in Hua: "I study mathematics from the first, second, third, fourth, fifth and sixth volumes of primary school, and the research of knowledge should start from the foundation." "Young Newton also relearned the basic knowledge and basic formulas and made steady progress step by step. Many students in higher vocational colleges do not pay attention to the understanding and mastery of basic knowledge. They aim too high and too far, and the result is in vain. The basic theory is embodied in the content and demonstration of theorems and theoretical models abstracted from practical problems. Seriously thinking about the source of each theoretical model in the book and knowing from which actual situation it was abstracted will greatly improve the ability to solve comprehensive problems. Also pay attention to the proof part. Because the proof process is a logical reasoning process, it can exercise the brain well, deepen the understanding of the theorem and improve the operational ability. Deduction is the essence of high numbers, which requires repeated efforts. If you don't understand, ask more questions. The understanding of the basic way is reflected in the formation of knowledge-related networks. For example, all important concepts in high numbers are defined and studied by it. The common skills of replacing invariants with variables are embodied in the constant variational method for solving differential equations, the idea of differentiation and the linearization method for nonlinear problems. The ideas of breaking the whole into parts, breaking the whole into parts, and integrating division and summation are applied to the element method in the problem; From the special to the general, study the way of thinking, and so on. In the application of learning and methods, we should cultivate people's logical thinking, abstract thinking, spatial imagination and self-study ability, cultivate a scientific world outlook and rigorous scientific attitude, enhance the will to learn, and form a good personality quality. 3. In the study of advanced mathematics, we should adjust our psychological state, pay attention to learning methods, be not afraid of difficulties, and know that difficulties are relative. " Facing the cliffs, you can't see a crack in a hundred years, but if you chisel with an axe, you can get one inch, one foot, and one foot. Keep accumulating, leap will come, and breakthrough will come. "Establish three hearts: confidence, determination and perseverance. Overcome laziness, think more and summarize more. When you encounter difficulties in the learning process, you must not be discouraged, but strengthen your confidence and confidence in overcoming them. Explore learning methods. 3. 1 keep up with the teacher's teaching rhythm, so as to preview the lectures efficiently. Look at the textbook first, and ask questions if you don't understand. Be sure to listen carefully in class, outline the contents of the chapters and prioritize them. Write down the important content, not every word, just a few strokes, and grasp the essence. Summarize in time after class, pay attention to the accumulation of ideas, and sort out the experiences that emerge in your mind at any time, even if it is just your brain. In order to consolidate and deepen understanding, it is best to check your mastery regularly. 3.2 Learning with proper mathematical memory methods requires not only understanding, but also mechanical memory, such as symbols, formulas, basic definitions, problem-solving skills and methods. Finding a suitable memory method is helpful to the persistence of knowledge. Image memory, analogy memory and system memory are used. There are many symbols with high numbers, which are difficult to remember. Cause learning disabilities. You can examine the features carefully and remember the images. Many of them are the first letters of their English interpretation, such as differential, which can be understood as the first letter of English differential, and integer can be understood as the extension of the first letter of "and", which can deepen your understanding of the definition. Systematic memory is suitable for learning the relationship between chapters and knowledge. It is helpful to sort out and grasp the overall context of knowledge. Memory methods are complementary and can be used interchangeably. To solve the problem correctly and constantly correct your thinking, you must do the problem. When learning new knowledge, you may wish to refer to theorems or formulas, try to memorize knowledge points, and then try to practice independently from textbooks to check your mastery of knowledge. What can't be done is the fault in thinking, and some content learners can correct themselves. For the more difficult content, learners need to consult teachers or consult learning materials, find some well-known teaching materials, pay attention to inspection, find out the characteristics and transfer of knowledge, think from multiple angles and aspects, and cite concrete examples to think about too abstract content, so that their thinking will gradually be comprehensive and profound, their knowledge will be integrated, and their books will be read thin. Mastery is the best. But it is not recommended to do a lot of exercise. Exercises are not all valuable, especially many problems encountered in the sea of questions are low-level repetitions, which can not get useful enlightenment. Some comprehensive questions just rub some knowledge points together, but if they can be simply said, they are deliberately complicated, tortuous, circling and setting traps. Learners should stay awake. Think about some really enlightening questions and study the meaning of the questions. Generally speaking, the more you simplify the problem, the more profound and valuable conclusions you can get. When you finish a question, don't stay at the original level, ask more why, and it will often lead to a new realm. Sometimes you have to skip things you don't understand for a while and solve them later.