1. Higher-order derivatives and differential equations: The calculation of higher-order derivatives and the solution of differential equations are one of the difficulties in graduate mathematics. This requires a deep understanding of the nature and derivative law of functions and flexible application.
2. Spatial analytic geometry: Spatial analytic geometry involves concepts such as vector, line and surface and their relationships. In the process of solving problems, we need to master the algorithm of vectors, the expression method of equations of straight lines and planes, and be able to carry out spatial geometric transformation.
3. Probability theory and mathematical statistics: Probability theory and mathematical statistics are another difficulty in postgraduate mathematics. This requires a deep understanding of concepts such as probability, random variables, distribution functions, and mastering the methods of probability calculation and statistical inference.
4. Extremes and maximums of multivariate functions: Extremes and maximums of multivariate functions are one of the difficulties in postgraduate mathematics. This requires a deep understanding of the concepts of derivative, partial derivative and gradient of multivariate functions, and the application of Lagrange multiplier method and KKT condition to solve the maximum problem.
5. Series and Fourier series: Series and Fourier series are one of the difficulties in postgraduate mathematics. This requires a deep understanding of the convergence and divergence of series, and the ability to expand periodic functions into infinite series with Fourier series.
The above are just some difficult problems in the mathematics of postgraduate entrance examination, and there are other complex variable functions, ordinary differential equations, linear algebra and so on. For these problems, candidates need to improve their problem-solving ability through systematic study and a lot of practice.