1. Establish a solid foundation: Mathematical analysis is a subject based on concepts such as real number, limit, continuity and calculus. Make sure you are familiar with these basic concepts before you study. You can review your math knowledge in high school if necessary.
2. Choose appropriate teaching materials and resources: Choose a suitable teaching material for mathematical analysis, such as Mathematical Analysis (Volume I) (Chen Jixiu) and Real Variable Function and Functional Analysis (Zheng). In addition, you can also use network resources, such as KhanAcademy, MITOpenCourseWare and other platforms to learn related courses and handouts.
3. Systematic learning: Mathematical analysis includes many sub-fields, such as real number system, limit and continuity, derivative and differential, differential mean value theorem, indefinite integral, definite integral, multivariate function differential calculus, multiple integral, series and so on. Start with the basic knowledge, gradually deepen, and master every topic thoroughly.
4. Do more exercises: The study of mathematical analysis is inseparable from a lot of exercises. By doing problems, you can test your understanding ability, find your own shortcomings and deepen your memory of knowledge points. At the same time, doing problems can also help you develop problem-solving ability and logical thinking.
5. Participate in discussion and communication: Discussing and communicating with classmates, teachers or online communities can help you better understand difficulties and doubts. In addition, working with others to solve problems can improve your teamwork and communication skills.
6. Review and summarize regularly: Learning mathematical analysis requires long-term persistence and hard work. Reviewing what you have learned regularly and summarizing your own learning methods and experiences will help to consolidate your memory and improve your learning effect.
7. Maintain patience and confidence: Mathematical analysis is an abstract and difficult subject. In the process of learning, you may encounter many difficulties and setbacks. Keep patience and confidence, believe that you can overcome these difficulties and finally master the knowledge of mathematical analysis.