(Topics include but are not limited to)
Topic 1: Pure Mathematics
nonlinear analysis 
Algebraic topology
catastrophe theory
Lie groups and Lie algebras
C * Algebra
functional analysis
differential geometry 
Complex analysis
Set theory
ordinary differential equation 
partial differential equation 
The inverse problem of partial differential equations in Banach spaces
Field and Galois theory
Convex analysis
Traversal theory
manifold
Modern Group Theory
Harmonic Analysis and Measurement Theory
Topological algebra
mathematical logic
Commutative algebra
harmonic analysis
Measurement theory
Topological algebra
Mathematical logic
Algebraic number theory
Analytical Number Theory
Probability and Statistics
Combinatorics
Module and Representation Theory
Non smooth analysis
Algebraic number theory
Analytical Number Theory
Module and Representation Theory
Topic 2: Applied Mathematics
linear algebra
Matrix theory
vector analysis
Complex analysis
differential equation 
Laplace transform 
Fourier analysis
Application Function Analysis
Error analysis and interval analysis
Mathematical Biology
Mathematical medicine
Mathematical Fluid Mechanics
Mathematics of heat and mass transfer
Optimization and Operations Research
Mathematical Psychology
Applied Information Economics
Applying multivariate statistical analysis
Application time series analysis
Applying Random Processes
Economic Data Modeling and Forecasting
Interest Theory and Applications
international finance
Database System and Application Development
numerical analysis
probability theory
mathematical statistics
Combinatorial mathematics
Computational Mathematics
information theory 
Topic 3: Computational Mathematics
Complex integral equations and numerical methods
numerical analysis
Integral equations and numerical methods
nonlinear equation 
Numerical Linear Algebra
Complex Analysis and Special Functions
Computational geometry
The Application of Computing Technology and High Performance Computing Science
Development of numerical calculation software
High Performance Computing Science
Fuzzy Mathematics and Mathematical Logic
Graph Theory and Combinatorial Algorithms
Computational Physics
Computational statistics
Computational Chemistry
Computational Engineering
fuzzy mathematics
mathematical logic
Algorithm Graph Theory and Combinatorics
Number Theory and Cryptography