To learn advanced mathematics well, the most basic thing is to prepare well before class, take notes in class, pay attention to problem-solving methods and review well after class. These three steps are important links to learn advanced mathematics well.
Doing a good preview before class is an important part of learning advanced mathematics well, which lays the foundation for the next two steps. We should have a general and systematic understanding of each chapter, grasp the structure, initially form the framework of knowledge system in our minds, have a general and comprehensive understanding of its content, and then gradually refine and deepen it, from shallow to deep, from easy to difficult, so as to grasp the overall situation, strategize, distinguish between primary and secondary, and make our study targeted, so as not to be led by the teacher. Everyone can know the meaning of the knowledge points that the teacher wants to say, so that the classroom can receive better results.
Doing well in class notes is an essential part of learning advanced mathematics well, which provides information for the next review. It is skillful to take notes in class. You should remember what is not in the book, general and some technical problem-solving methods, and common questions, which will provide good information for your future exam review. Many students don't like taking class notes, which is bad for their study. Because everyone's energy is limited, it is impossible to remember everything the teacher said in class in every class, but often the content in the exam is what the teacher said in class. If you don't take notes, there will be no information when reviewing, and your mind will be blank, so you won't be able to start the exam. Students, do you think this is not a price loss? Moreover, taking class notes not only provides you with review materials for the exam, but also won't sleep in class. You can also practice your calligraphy by taking notes. It's the best of both worlds. Why don't students enjoy it?
To learn advanced mathematics well, we should also pay attention to problem-solving methods, especially when solving proof problems. Many students are afraid, because some proof questions are abstract and general, which makes students with poor foundation unable to start, so we should pay attention to the problem-solving methods. "Bridging" method is the best way to solve the problem of proof. Put out what is known and what needs to be proved first, and then connect it internally through bridges, so that it can be solved quickly. In the process of solving calculation problems, we should pay attention to summing up the methods of solving problems and draw inferences from others. There are many solutions to many problems. In this way, you should pay attention to generalization, find the simplest solution, be concise and spend less time.
Reviewing in time after class can consolidate what you have learned and make you understand what you have learned further. Doing homework like this is handy. How to review in time? On the day when you finish a lesson, you must go back and read what you have learned. Combining book knowledge and class notes, I will make an in-depth study of what I have learned, find out what I don't understand in time, read books repeatedly and understand slowly, so that I can slowly digest what I have learned into my own things. In the next week or two, you will go back to review what you have learned before. As the saying goes, "review the past and learn the new." You won't be so nervous when it comes to the exam, because you already have a plan. Students! Advanced mathematics is not terrible. The terrible thing is that you have no confidence and courage to learn it well. In fact, every subject has its own internal laws and structures, and the thinking methods that are adapted to these laws and structures. With a good learning method, plus your own cleverness and hard work, I believe you will be able to roam freely in the ocean of advanced mathematics.