1. Fundamentals of elementary mathematics: Advanced mathematics is developed on the basis of elementary mathematics, so it is necessary to master the basic concepts, formulas and theorems of elementary mathematics, such as algebra, geometry and trigonometry.
2. Calculus: Calculus is one of the core contents of higher mathematics, and it needs to master basic concepts and calculation methods such as limit, derivative and integral.
3. Linear Algebra: Linear Algebra is a subject that studies vector space and linear transformation. It is necessary to master basic concepts and calculation methods such as matrix, vector, determinant, eigenvalue and eigenvector.
4. Probability theory and mathematical statistics: Probability theory and mathematical statistics is a subject that studies random phenomena and data analysis, and it needs to master basic concepts and calculation methods such as probability, random variables, distribution function, expected value and variance.
5. Ordinary differential equation: Ordinary differential equation is an equation in which the derivative of the research function is equal to zero, and it is necessary to master the solution and application of first-order and second-order ordinary differential equations.
6. Partial differential equations: Partial differential equations are equations in which the derivatives of multivariate functions are equal to zero, and it is necessary to master the solution and application of first-order and second-order partial differential equations.
7. Real variable function and functional analysis: Real variable function and functional analysis are subjects that study the properties and transformation of functions on real numbers or complex numbers, and they need to master basic concepts and methods such as measure theory, integral theory and functional analysis.
8. Numerical analysis: Numerical analysis is a subject that studies solving mathematical problems by numerical methods, and it needs to master basic concepts and methods such as numerical approximation, numerical solution and numerical optimization.
9. Discrete mathematics: Discrete mathematics is a discipline that studies discrete structures and their properties, and it needs to master basic concepts and methods such as set theory, graph theory and logic.
10. computer programming: to learn advanced mathematics, you need to have certain computer programming ability and be able to use programming language for mathematical modeling and calculation.