(The following topics include but are not limited to)
nonlinear analysis 
Algebraic topology
catastrophe theory
functional analysis
differential geometry 
linear algebra
Matrix theory
Vector analysis
Complex analysis
ordinary differential equation 
numerical analysis
probability theory
mathematical statistics
Operations Research
Game theory
control theory
Combinatorial mathematics
Data analysis
statistics
applied mathematics
Calculation of geometric parameters
mathematical modeling 
Set theory
mathematical logic
Algebraic number theory
Analytical Number Theory
Function theory
discrete mathematics 
Symmetry and integrable systems
Complex function
Real variable function
Special functions and orthogonal polynomials
The Application of Computer Mathematics
The Mathematical Theory of Artificial Intelligence