1. Pure Mathematics

• Algebraic structures and number theory
• Topology and geometry
• Functional analysis and operator theory
• Mathematical logic and set theory
• Graph theory and combinatorics

2. Applied Mathematics and Mathematical Modeling

• Nonlinear dynamics and chaos theory
• Optimization and operations research
• Control theory and game theory
• Mathematical models in engineering and physics
• Computational fluid dynamics

3. Computational Mathematics and Numerical Analysis

• Finite element analysis and numerical methods
• High-performance computing in mathematics
• Computational algebra and symbolic computation
• Approximation theory and error analysis
• Machine learning and artificial intelligence applications in mathematics

4. Probability and Statistics

• Stochastic processes and Markov chains
• Bayesian inference and statistical learning
• Multivariate statistics and data analysis
• Time series analysis and forecasting
• Statistical modeling in artificial intelligence

5. Mathematical Physics and Differential Equations

• Partial and ordinary differential equations
• Quantum mechanics and wave equations
• General relativity and mathematical cosmology
• Solitons and integrable systems
• Mathematical methods in thermodynamics

6. Mathematical Biology and Bioinformatics

• Mathematical models in epidemiology
• Computational genomics and systems biology
• Population dynamics and ecological modeling
• Neural networks and cognitive modeling
• Biostatistics and clinical data analysis

7. Financial Mathematics and Actuarial Science

• Quantitative finance and risk assessment
• Stochastic calculus in financial modeling
• Portfolio optimization and asset pricing
• Actuarial models and insurance mathematics
• Cryptographic methods in financial security

8. Mathematics in Engineering and Technology

• Signal processing and wavelet analysis
• Cryptography and cybersecurity algorithms
• Artificial intelligence and neural networks in mathematics
• Mathematical methods in robotics and automation
• Image processing and computer vision