Applied Mathematics: Linear Algebra, Matrix Theory, Vector Analysis, Complex Analysis, Differential equations, Laplace Transform, Fourier Analysis, Numerical Analysis, Probability Theory, Mathematical Statistics, Combinatorial Mathematics, Computational Mathematics, Information Theory, etc
Pure mathematics: nonlinear analysis, algebraic topology, mutation theory, Li group and Lie algebra, C * algebra, functional analysis, differential geometry, complex analysis, set theory, ordinary differential equation, partial differential equation of Banach space, field and Galois theory, harmonic analysis and measurement theory, topological algebra, mathematical logic, algebra number theory, analytic number theory, modular and representation theory, etc
Computational mathematics: complex integral equation and numerical method, numerical analysis, nonlinear equation, numerical linear algebra, complex analysis and special function, computational geometry, application of computing technology and high performance computing science, numerical computing software development, fuzzy mathematics and mathematical logic, graph theory and combinatorial algorithm, etc