1. Mathematical analysis (3 semesters). The main contents are limit, continuity, differential, integral, series and so on. Contact high school function knowledge. Giving the definition of limit is the first difficulty and the basis of subsequent study. We should be able to understand its connotation. This is a challenge and a leap in thinking. Careful analysis, using many estimation methods, scaling skills and so on. Different from the emphasis on calculation in advanced mathematics, analysis pays more attention to reasoning and proof. Many seemingly obvious conclusions need to be strictly proved. The key point is to learn all kinds of problem-solving skills on the basis of mastering the definition. There is nothing to say. You must do a lot of questions. 2. Advanced Algebra (2 semesters). The main contents include polynomial, determinant, matrix, linear equations, linear space, linear transformation, Euclidean space, quadratic theory and so on. It has little to do with high school knowledge, and many definitions are brand new, from a higher perspective. Of course, first of all, we should be able to transition from elementary algebra to advanced algebra, master new concepts and learn new methods. Because the content is more abstract than mathematical analysis, the difficulty lies in the understanding of concepts. 3. Analytic geometry (1 semester). The main contents are quadric surface, affine geometry, projective geometry and so on. Some schools combine this course with advanced algebra because many tools and methods are interlinked. When it comes to connection, mathematical analysis occasionally uses some knowledge of determinant and polynomial, and advanced algebra and analytic geometry occasionally uses some knowledge of formal differential. Differential geometry in the later course is a course that uses differentiation to deal with geometric figures.