2. Number theory: the branch of mathematics that studies the properties and operation rules of integers, involving prime numbers, congruences and quadratic residues.
3. Combinatorial mathematics: a branch of mathematics that studies the selection or arrangement of elements in finite sets, involving binomial theorem, handshake theorem and so on.
4. Topology: a branch of mathematics that studies the properties and structures of space, such as compactness, connectivity and basic groups.
5. Algebraic geometry: a branch of mathematics that studies the relationship between algebraic equations and geometric objects, such as curves, surfaces and modular forms.
6. Stochastic process and probability theory: the branch of mathematics that studies stochastic phenomena and their laws, involving Markov chains, Brownian motion, Poisson distribution, etc.
7. Differential geometry: A branch of mathematics that studies calculus and geometric properties on manifolds, such as Riemannian geometry and geodesics.
8. Topological quantum field theory: a research field combining quantum mechanics with topology, involving topological order and topological phase transition.
9. Dynamic system theory: the branch of mathematics that studies the stability and periodicity of dynamic systems.
10. Computational Mathematics: Study numerical calculation methods and their applications in mathematics, such as numerical analysis, numerical algebra, optimization algorithms, etc.