Freshmen often have doubts about "why do they still study mathematics when they go to college" and "what's the use of learning mathematics". Not only in the undergraduate stage, but also in the master's and doctoral stages, we should learn mathematics and learn higher-level content. If you are engaged in management and engineering, you should continue to study mathematics. Advanced Mathematics is a compulsory basic theory course, which plays a fundamental role for students to study various professional courses and engage in various management and engineering work after graduation. Especially in today's rapidly changing science and technology, mathematical methods have been widely used in various fields of science and technology. Therefore, for college students, a clear task is to learn advanced mathematics well and lay a good foundation for future study and work.
So, how do freshmen learn advanced mathematics well? The following are some opinions for your reference.
First of all, we should have a correct understanding of advanced mathematics.
Although advanced mathematics is only the foundation of modern mathematics, it can accomplish many practical tasks. By studying advanced mathematics, students' ability to analyze and solve problems can be improved, so as to master good learning methods and cultivate keen scientific thinking. Therefore, mathematics is called "gymnastics of wisdom". Regarding the application of advanced mathematics, I will give three examples to illustrate:
First, why should the shape of the cooling tower in thermal power plants be curved, rather than straight like a chimney? The reason is that the cooling tower has a large volume and a very heavy weight. If it is made straight, the building materials at the bottom can't bear much pressure (as we know, the highest mountain on earth can only reach 30,000 meters, otherwise the rocks at the bottom will melt). Making the edge of the cooling tower into a hyperboloid shape can just make the pressure of each section equal, so that the cooling tower can be made very large. Why hyperboloid? It can be solved in less than 5 minutes with calculus theory in advanced mathematics.
Secondly, everyone is familiar with computers, but without mathematical principles and methods, computers can be said to be a pile of "garbage". Because fundamentally, computers can only do addition, and the billion we often say actually refers to addition. Other complicated calculations can only be realized by transformation and addition, and this transformation process requires knowledge of advanced mathematics. Such as logarithmic calculation, in fact, using the series theory of calculus, logarithmic function can be transformed into a series of multiplication and addition operations.
Thirdly, "Wu Fa" put forward by Wu Wenjun, a famous mathematician in China, is a mathematical theory and method. People use it to solve many high-end scientific and technological problems such as machine proof of geometric theorem, machine tool design, circuit design, robot trajectory problem, surface stitching and so on, and it is world-renowned. "Wu method" plays a key role in these frontier scientific problems, so the word "mathematical technology" has appeared at present.
It can be said that mathematics is everywhere. Modern science cannot be called science without calculus (the main content of higher mathematics), and calculus is the function of higher mathematics.
Second, abandon the learning methods of middle schools as soon as possible, and understand and master the learning methods of universities.
After students enter the university from middle school, there should be a big change in their learning methods of advanced mathematics. The teaching methods in middle schools are qualitatively different from those in universities. The outstanding performance is that middle school students learn by imitation and single way under the direct guidance of teachers, while universities require students to learn creatively under the guidance of teachers. For example, the teaching of mathematics in middle schools is carried out completely according to textbooks. Only the teacher is required to speak and the students are required to listen in class, and no notes are required. Teachers speak slowly and seriously, and there are many examples of calculation methods. After class, students are asked to imitate what the teacher said in class and do some exercises. There is no need to delve into reference books such as textbooks (reference books are only selected for the college entrance examination to train problem-solving ability). Higher mathematics courses in universities are different. Textbooks are only one of the main reference books, and teachers often don't teach them exactly according to them. This requires students to take the key and difficult points mentioned by the teacher in class as clues, read a lot of textbooks and similar reference books, fully digest and master the contents taught in class, and then do exercises to consolidate their knowledge and conduct repeated creative learning.
Third, learning basic concepts and ideas is the most important, and mastering core ideas and methods is the goal.
The study in the university stage can't cope with the exam. It is important to learn the connotation of each course, that is, the way of thinking. In advanced mathematics, if you want to put forward or establish an idea and method, you must always have basic concepts and conclusions as the basis. If we don't have a good grasp of these concepts and basic conclusions, it will be difficult to master their internal core ideas and methods. The process of learning advanced mathematics is also the process of establishing new cognitive concepts. For example, the transition from finite mathematics to infinite mathematics is a cognitive leap. Freshmen often don't realize the importance of learning basic concepts and conclusions, but only understand them on the surface of words, ignoring the change of ideas, which leads to learning difficulties, loss of interest and even weariness of learning. In fact, the difficulty in learning advanced mathematics lies in the accurate understanding and flexible application of basic concepts and conclusions, as well as the establishment of dynamic change concepts. After breaking through this difficulty, many problems were solved.
Fourth, grasp four links to improve learning efficiency.
First, preview before class. Understand what the teacher is going to say, review the relevant content accordingly, be targeted and take the initiative to learn. Second, listen carefully. Listening to lectures is a process of listening, taking notes and thinking wholeheartedly. Pay attention to the teacher's explanation methods, ideas, and the process of analyzing and solving problems. At the same time, pay attention to the problems encountered in the preview and take notes in class. Third, review after class, step by step. On that day, you must recall the contents of the teacher's lecture, and then read the textbook content repeatedly with your notes, improve your notes, master the relationship between what you have learned, and finally finish your homework. When doing homework, summarize and refine the knowledge, ideas and methods learned, and build a knowledge structure framework through comparison; We should review and consolidate the knowledge we have learned frequently and carry out circular learning; Learn to sum up. Fourth, the overall grasp, can not break the chain. Advanced mathematics is a complete chain, one link is buckled. If any link is not mastered well, it will affect the whole learning process. We should pay special attention to the concepts of function and limit, which are the "foundation" of advanced mathematics and directly affect the subsequent study. If you don't master it as a whole, it is easy to "drown" in a large number of concepts, conclusions and problems.
Fifth, cultivate creative thinking and the ability to solve problems by mathematical methods.
When studying a course, we should consider its extension. Learning advanced mathematics can not only learn mathematical knowledge, but also cultivate their creative thinking and ability to use mathematics, especially the consciousness of mathematical model. Higher mathematics fully embodies creative thinking such as logical thinking, abstract thinking, analogy thinking, inductive thinking, divergent thinking and reverse thinking. Students should experience these ways of thinking well and improve their scientific thinking ability through the carrier of advanced mathematics. The so-called mathematical consciousness refers to the psychological tendency to use mathematical knowledge. It contains two meanings: on the one hand, when you face a problem to be solved, you can actively try to find a strategy to solve the problem with mathematical standpoint, viewpoint and method; On the other hand, when you accept a new mathematical theory (you may learn more branches of mathematics), you can actively explore the context and practical value of this new knowledge, and the mathematical thinking that runs through it will play a direct or subtle role. This requires students to establish mathematical concepts and improve their understanding of mathematics. The so-called consciousness of establishing mathematical model means that when we encounter a practical problem, we use what we have learned to establish the corresponding mathematical problem (mathematical model), which not only solves the mathematical problem but also solves the original practical problem. We will encounter many such application examples in the process of learning. Please summarize these examples carefully and summarize them into general methods. When studying other courses, we should deliberately think about whether these methods can be used to deal with the problems of this discipline.