1. Advanced Mathematics: This is a basic course of mathematics department, including calculus, differential calculus of multivariate functions, multiple integrals, ordinary differential equations and so on. This knowledge is the basis for further study of other mathematics courses.
2. Linear algebra: Linear algebra is a branch of mathematics that studies vector space and linear mapping, including matrix theory, vector space and linear transformation. This knowledge is widely used in computer science, physics and other fields.
3. Probability theory and mathematical statistics: Probability theory and mathematical statistics are mathematical disciplines that study the regularity of random phenomena, including the basic concepts of probability theory, random variables and their distribution, parameter estimation, hypothesis testing and so on. This knowledge has important applications in finance, engineering, biology and other fields.
4. Discrete mathematics: Discrete mathematics is a branch of mathematics that studies discrete structures (such as sets, graphs, sequences, etc.). ), including set theory, graph theory, combinatorial mathematics and so on. This knowledge is widely used in computer science, information theory and other fields.
5. Real analysis and complex analysis: Real analysis and complex analysis are branches of mathematics, which study the properties of functions on real numbers and complex numbers, including their continuity, differentiability and integrability. This knowledge has important applications in functional analysis, partial differential equations and other fields.
6. Abstract algebra: Abstract algebra is a branch of mathematics that studies algebraic structure, including group theory, ring theory and domain theory. This knowledge has important applications in cryptography, coding theory and other fields.
7. Topology and geometry: Topology and geometry is a branch of mathematics that studies spatial properties and structures, including point set topology, algebraic topology, differential geometry and so on. This knowledge is widely used in physics, geometry and other fields.
8. Numerical analysis: Numerical analysis is a discipline that uses numerical methods to solve mathematical problems, including interpolation, numerical calculus, numerical solutions of ordinary differential equations, etc. This knowledge has important applications in computer science, engineering and other fields.