1. Elementary mathematics knowledge: including basic concepts and algorithms such as algebra, geometry and trigonometry. This knowledge is the foundation of advanced mathematics, and it is very important to understand and master the concepts and methods of advanced mathematics.

2. Function and limit: Many concepts and methods in advanced mathematics are based on function and limit. Therefore, it is necessary to have a clear understanding of the basic properties, images and algorithms of functions, as well as the definition, properties and calculation methods of limits.

3. Calculus: Calculus is one of the core contents of higher mathematics, including derivatives, integrals and differential equations. Learning calculus requires a deep understanding of derivatives and integrals of functions and skillful use of calculus to solve practical problems.

4. Linear algebra: Linear algebra is another important branch of higher mathematics, which mainly studies vector space, matrix and linear transformation. Learning linear algebra needs to master the basic operations of vectors and matrices and the solving methods of linear equations.

5. Probability theory and mathematical statistics: Probability theory and mathematical statistics are important application fields in higher mathematics, involving random variables, probability distribution, parameter estimation and hypothesis testing. Learning probability theory and mathematical statistics requires a clear understanding of the basic concepts and principles of probability statistics and the ability to use statistical methods to solve practical problems.

6. Numerical analysis: Numerical analysis is an important branch of higher mathematics, which mainly studies numerical calculation methods and error analysis of approximate solutions. Learning numerical analysis requires a certain understanding of the basic methods and skills of numerical calculation and the ability to use numerical methods to solve practical problems.

In addition to the above basic knowledge, learning advanced mathematics well requires good logical thinking ability, abstract thinking ability and problem solving ability. At the same time, through a lot of practice and practice, we can deepen our understanding and mastery of advanced mathematics knowledge and improve our problem-solving ability and skills.