1, advanced algebra
Higher algebra is a subject that studies vector space, linear transformation and algebraic structure in mathematics. It involves abstract algebra, linear algebra and matrix theory. In higher algebra, the properties and operation rules of vector space are explored, and the influence of linear transformation on vectors, their eigenvalues and eigenvectors is studied.
In addition, advanced algebra also includes the study of algebraic structures such as group theory, ring theory and field theory, so as to deepen the understanding of abstract algebra concepts and theories. Advanced algebra is not only the foundation of mathematics, but also widely used in other fields such as physics, computer science and engineering.
2. Real variable function and complex variable function
Real variable function and complex variable function are important courses in graduate mathematics. They study the properties of functions in real and complex fields, including the concepts and skills of function limit, continuity, differentiability and integration, which provide the basis for subsequent mathematical analysis and practical application.
3. Probability theory and mathematical statistics
Probability theory and mathematical statistics are one of the most widely used mathematical disciplines. It studies the law of random events and the method of inferring the population from observation data. Learning content includes probability space, random variables, probability distribution, parameter estimation, hypothesis testing and so on.
4. Mathematical analysis
Mathematical analysis is a mathematical discipline that studies continuity and limit. Including real number theory, series theory, function sequence and function series, multivariate function, differential equation and so on. Mathematical analysis in postgraduate stage usually involves more in-depth theory and proof.
5. Partial differential equations
Partial differential equation is an important tool to study physical phenomena and natural laws in mathematics. They study partial derivative equations with many unknown functions, such as wave equation, heat conduction equation and Helmholtz equation. The course of partial differential equations for graduate students focuses on the establishment of theory and the exploration of solution.
6. Numerical calculation method
Numerical calculation method is a subject that uses computer to solve mathematical problems approximately. It studies numerical approximation, interpolation and fitting, numerical calculus, numerical solutions of ordinary differential equations, etc., and provides mathematical basis for numerical simulation and calculation of practical problems.