1, basic mathematics (differential geometry, mathematical physics, partial differential equations, functional analysis, algebra, algebraic geometry, complex analysis, dynamical systems, topology, harmonic analysis, number theory, etc. );
2. Applied mathematics (applied partial differential equations, computational geometry and scattered data fitting, industrial applied mathematics, mathematical methods of neural network, nonlinear science, complexity and computational system biology, actuarial science, etc. );
3, operational research and cybernetics (stochastic control and financial mathematics, distributed parameter control, operational research, etc. );
4. Computational mathematics (inverse problem of mathematical physics and its numerical solution, numerical algebra, scientific calculation, operation and optimization calculation, etc. );
5. Probability theory and mathematical statistics (stochastic analysis, stochastic process and its application, stochastic dynamic system, mathematical statistics, etc.). ).