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. 4. Ordinary differential equations (1 semester). The main contents include the elementary solution of ordinary differential equations, higher order ordinary differential equations, linear differential equations, stability of solutions, boundary value problems and so on. It is a follow-up course of mathematical analysis, which uses a lot of calculus knowledge and has its own unique solution to master. 5. Abstract algebra (1~2 semesters). The main contents are groups, rings and domains. It is a follow-up course of advanced algebra. As the name implies, abstract algebra is more abstract and has a higher perspective than higher algebra. The operation of abstract meaning on sets is defined, and then algebraic structures such as groups, rings and fields are defined, and their properties are studied. It only involves proof reasoning, and it is important to be familiar with concepts. 6. Real variable function (1 semester). The main contents include Lebesgue measure, measurable function, Lebesgue integral and so on. Subsequent courses in mathematical analysis. The integral in mathematical analysis is Riemann integral, while the Lebesgue integral in the study of real variable function is a generalization of Riemann integral. This course is analytical and requires strong analytical skills. 7. Probability theory (1 semester). The main contents include probability space, distribution of random variables, numerical characteristics, limit theorem and so on. Follow-up course of real variable function. Different from the probability knowledge in middle school, the probability theory of university mathematics department is an analysis course. The background of real variable function and strong analytical ability are required. 8. Complex variable function (1 semester). The main contents include complex number, analytic function, complex integral, complex series, analytic continuation and so on. Subsequent courses in mathematical analysis. Mathematical analysis studies real functions, while complex variable functions study complex variable functions. It also involves many proofs and calculations, and has a unique method. It can also be used in turn to solve some difficult problems in mathematical analysis. 9. Topology (1 semester). The main contents are topological space, fundamental group and homology group. The follow-up course of abstract algebra also needs a certain analytical background, which is more comprehensive. The research method is mainly algebraic knowledge, the research object is topological space, and it has its own theory. Personally, I think topology is quite interesting. 10. Differential geometry (1 semester). The main contents are curve theory and surface theory. Subsequent courses in mathematical analysis and analytic geometry. A branch of geometry, which studies the shape of general curves and surfaces by using analytical differential tools and finds out the invariant system that determines the shape of curves and surfaces. 1 1. Partial differential equation (1 semester). The main contents are the solutions, generalized solutions and numerical solutions of three kinds of second-order linear partial differential equations. Subsequent courses of ordinary differential equations. Synthesis also needs some backgrounds of mathematical analysis, advanced algebra and complex variable functions. Also known as mathematical and physical equations. It has certain physical significance. 12. Function analysis (1 semester). The main contents are normed space, linear operator, three theorems (Hahn-Barnach theorem, open and closed image theorem, * * * Ming theorem) and so on. Follow-up course of real variable function. The peak of undergraduate analysis course in mathematics department is very comprehensive, which requires a solid analytical foundation and algebraic background. If you want to study mathematics further, you must learn it well. 13. Other elective courses: Graph Theory, Combinatorial Theory, Operational Research, Mathematical Modeling, Finite group representation theory, Lie Algebra, Stochastic Process, Banach Algebra, Abstract Function, Mathematical Software, etc.