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How to stimulate students' interest in advanced mathematics
Li Rui of the School of Science has to study advanced mathematics in almost all majors, and mathematics will be used at all levels of society. The importance of mathematics is obvious, but there are still many students who lack the enthusiasm and initiative to learn advanced mathematics, especially in our school, which focuses on practical teaching and pays insufficient attention to theoretical things. Moreover, mathematical theory gives people the feeling that it is boring and complicated, so most students are in a state of forced and helpless learning, just for the sake of. In view of the present situation, how to stimulate students' interest in learning in higher mathematics teaching and make them like and love mathematics; How to make a math class lively, interesting and easy to understand? Based on my practical teaching experience in recent two years, this paper makes some preliminary discussions on how to stimulate students' interest in advanced mathematics. 1. The limit theory of mathematical thought in ancient literature is the first advanced mathematics course for students who have just entered the university. In fact, the concept of limit has existed in China since ancient times. Zhuangzi said: A hammer of one foot can take half of it every day and last forever. It is a series with 1 as the first term and 1/2 as the common ratio. Its limit is zero, but it will never reach zero, which contains the limit and philosophical thought in mathematics. There is also the eternal quatrain in Li Bai's "Yellow Crane Tower Farewell to Meng Haoran on the way to Yangzhou", "I sail far away from the sky and only look at the Yangtze River." It is also a vivid metaphor of extreme thoughts. My friend is gone, the boat is gone, only a faint solitary sail. A river still flows eastward. It is also said that when the distance (n) is getting bigger and bigger, the figure of friends is getting smaller and smaller. Here, the idea of mathematical limit is integrated with the artistic conception of literature, which enriches students' imagination and emotional experience. Therefore, when talking about the content of limit, we can use such a literary sentence as an example. Students not only understand the essence of limit, but also enliven the atmosphere, thus stimulating students' interest in mathematics in the first class of mathematics. If the definition of limit is taught to the students in the first class in mathematical terms, they will not only find it complicated and difficult to understand, but also be unwilling to continue studying in the future. Second, interspersed with the historical background of mathematics Speaking of Green's formula in mathematics, I will tell students the story of mathematician Green. Green dropped out of school as a child and taught himself while working. When he was young, he wrote his first insightful math paper. Although he didn't pay attention to it at first and didn't give up, it even aroused his enthusiasm for learning mathematics. Later, he went to Cambridge University with the support of his friends, and later published many mathematical papers, which had a great influence on the mathematical community at that time. Through such a short story, on the one hand, I have a deep memory of Green's formula, on the other hand, I get inspiration from the extraordinary experience of mathematicians. And I think this method is very practical for students in our school. Calculus theory in mathematics is an important content widely used in all walks of life, but sometimes the process of solving it is very boring. At this time, we can talk about the historical background of calculus at an appropriate time, which is the story of Newton and Leibniz. Telling the founding history of calculus in teaching can also make students understand that mathematics comes from application. Thirdly, humorous language permeates mathematics. It is more important for college mathematics to let students understand mathematical ideas. Make students unconsciously affected. Advanced mathematics sometimes has two classes in a row, and even three classes in a make-up class, so it is particularly important to infiltrate humorous language in life into mathematics. Many times, such as the third and fourth periods in the morning and the first and second periods in the afternoon. At this time, students will feel sleepy. No matter what they say on the platform, they may not be able to listen. So at these times, I will tell students some math jokes or anecdotes, such as this math joke: One day, a mathematician felt that he had had enough of math, so he ran to the fire brigade and announced that he wanted to be a fireman. The fire chief took the mathematician to the backyard alley of the fire brigade. There is a warehouse, a fire hydrant and a hose in the alley. The fire chief asked, "Suppose the warehouse was on fire, what would you do?" The mathematician replied, "I connected the fire hydrant to the water pipe, turned on the tap and put out the fire." The fire chief said, "Exactly! Last question: suppose you walk into an alley and the warehouse is not on fire, what would you do? " The mathematician pondered for a long time in doubt and finally replied, "I will set fire to the warehouse." The fire chief shouted, "What? Why did you set fire to the warehouse? " The mathematician replied, "In this way, I will simplify the problem into a problem that I have solved." Although this joke is absurd, it standardizes the students' listening state and impresses them deeply. In fact, teaching a course successfully is also an art. Only after arousing students' interest, can we further study the teaching methods and thoroughly understand the connotation of mathematical theory, so that students can truly understand the importance of mathematics and learn this basic course well.