1. Elementary mathematics knowledge: Advanced mathematics is based on elementary mathematics, and it is necessary to master the basic concepts, operation rules and formulas of elementary mathematics. This includes knowledge of algebra, geometry and trigonometry.

2. Calculus: Calculus is one of the core contents of higher mathematics, which studies the rate of change and cumulative quantity of functions. Learning calculus requires mastering basic concepts and calculation methods such as limit, derivative and integral.

3. Linear algebra: Linear algebra is a branch of mathematics that studies vector space and linear transformation. Learning linear algebra needs to master the basic concepts and operation methods such as vector, matrix, determinant, eigenvalue and eigenvector.

4. Probability theory and mathematical statistics: Probability theory and mathematical statistics are branches of mathematics that study random phenomena and data analysis. Learning probability theory and mathematical statistics requires mastering basic concepts and methods such as probability, random variables, probability distribution and statistical inference.

5. Discrete mathematics: Discrete mathematics is a branch of mathematics that studies discrete structures and discrete objects. Learning discrete mathematics requires mastering basic concepts and methods such as set theory, graph theory and logical reasoning.

6. Mathematical analysis: Mathematical analysis is a branch of mathematics that studies functions, limits, continuity, differentiability and integrability on real numbers and complex numbers. Learning mathematical analysis requires mastering basic concepts and methods such as real number system, limit theorem, continuity, differential and integral.

7. Numerical calculation: Numerical calculation is a method and technology of mathematical calculation by computer. Learning numerical calculation requires mastering basic knowledge and skills such as numerical approximation, numerical solution, algorithm design and programming.

In addition to the above basic knowledge, learning advanced mathematics also requires good logical thinking ability, abstract thinking ability and problem solving ability. At the same time, through a lot of practice and practice, deepen the understanding and application of mathematical concepts and methods, and improve the ability to solve problems and innovate.