1. Mathematical logic: This is the basis of mathematics, mainly studying the laws of reasoning and proof. It includes propositional logic, predicate logic and model theory.
2. Set theory: This is a branch of mathematics that studies sets and their properties, including their definition, operation and classification.
3. Algebra: This is a branch of mathematics that studies the operation rules of numbers and symbols, including group theory, ring theory, field theory, linear algebra and so on.
4. Geometry: This is a branch of mathematics that studies shapes and spaces, including Euclidean geometry, non-Euclidean geometry and analytic geometry.
5. Calculus: This is a branch of mathematics that studies changes, including limits, derivatives and integrals.
6. Probability theory and statistics: This is a branch of mathematics that studies random phenomena, including the definition, calculation and application of probability.
7. Topology: This is a branch of mathematics that studies the nature and structure of space, including connectivity, compactness and continuity.
8. Function theory: This is a branch of mathematics that studies the properties and behaviors of functions, including real analysis and complex analysis.
9. Numerical analysis: This is a branch of mathematics, which studies solving mathematical problems by numerical methods, including interpolation, approximation and numerical solution.
10. optimization theory: this is a branch of mathematics that studies finding the optimal solution under given conditions, including linear programming and nonlinear programming.
The above is only part of the mathematical principle. In fact, mathematical principles are very extensive and in-depth, involving all aspects of life.