1. Number and operation: including natural number, integer, rational number, real number, complex number, addition, subtraction, multiplication, division, exponent, logarithm and other operations.
2. Algebra: a system that studies symbols and rules, including algebraic expressions, equations, inequalities, functions, matrices, vectors, etc.
3. Geometry: A discipline that studies the properties of shape, size and position, including concepts such as point, line, surface, body, angle and distance, as well as Euclidean geometry and non-Euclidean geometry.
4. Probability statistics: the discipline that studies random phenomena and data collection, analysis and interpretation, including probability, expectation, variance, standard deviation and statistics.
5. Calculus: the study of rate of change and accumulation, including limit, derivative, integral, etc.
6. Discrete mathematics: the study of discrete structures and discrete objects, including graph theory, set theory, logic, etc.
7. Linear algebra: study vector space and linear mapping, including vectors, matrices, linear equations, eigenvalues and eigenvectors.
8. Numerical analysis: a discipline that studies numerical calculation methods and algorithms, including numerical solutions, numerical integration, interpolation and approximation of differential equations.
9. Topology: Study the nature and structure of space, including connectivity, compactness and continuity.
10. functional analysis: study infinite dimensional spaces and linear operators, including inner product spaces and Hilbert spaces.