1. Sequence and sequence: Understand the basic concepts of sequence and sequence, such as arithmetic progression, geometric progression, convergence and divergence, etc.

2. Limit and continuity: master the concept, nature, calculation method of limit and the continuity of function.

3. Calculus: Be familiar with basic concepts and methods such as derivatives, integrals and differential equations, so as to provide a basis for studying the properties of series and solving problems.

4. Real numbers and complex numbers: Understand the basic concepts, operation rules and applications of sequence numbers.

5. Power series: master the definition, properties and convergence radius of power series, as well as the expansion and application of Taylor series.

6. Function term series: Understand the concept, properties and discrimination methods of function term series, such as Dirichlet discrimination method and Abel discrimination method.

7. Fourier series: be familiar with the basic concepts, properties and applications of Fourier series, such as expanding periodic functions into Fourier series.

8. Series summation: master the methods of series summation, such as partial summation, staggered series summation, absolute convergence, conditional convergence, etc.

9. Application of sequence: Understand the application of sequence in mathematics, physics, engineering and other fields, such as solving differential equations, signal processing, probability theory and so on.

10. Mathematical analysis and proof: Have certain mathematical analysis ability and proof skills, and be able to use mathematical knowledge to solve practical problems.

In a word, learning the knowledge framework of sequence requires a solid mathematical foundation, including the knowledge of sequence and sequence, limit and continuity, calculus, real number and complex number. At the same time, it is necessary to have certain ability of analysis and proof in order to better understand and apply the knowledge of sequence.