1. Foundational Mathematics, Mathematical Analysis, Advanced Algebra

2. Specialized Mathematics. Area 1: Analysis – including Real Analysis, Complex Analysis, Functional Analysis, and fundamentals of Partial/Ordinary Differential Equations; Area 2: Algebra – including Abstract Algebra (groups, rings, fields), Number Theory, and Combinatorial Algebra; Area 3: Geometry & Topology – including Differential Geometry, Topology (point set topology, foundations of algebraic topology), and Differentiable Manifolds; Area 4: Applied Mathematics – including Numerical Analysis, Optimization Theory, Probability and Mathematical Statistics, Computational Mathematics, and Mathematical Physics.