Mathematics majors in American universities cultivate students' exploration ability, speculative ability and logical reasoning ability, and students will also learn how to use mathematical methods to solve problems. Mathematics is not only a principle, but also a tool, which is widely used in science, medicine, engineering and industry. The following is the subdivision direction of mathematics major: Algebra and number theory are roughly divided into: arithmetic geometry (integrating number theory and algebraic geometry), representation theory, traditional algebra and number theory. Geometry: low-dimensional topology and curvature flow, mirror symmetry, symplectic geometry and affine structure, noncompact and bounded manifolds, algebraic geometry. Analysis can be roughly divided into four categories: classical analysis, functional analysis, harmonic analysis, nonlinear analysis and convex analysis. Classical analysis includes inequality theory, summability theory, approximation theory, special function theory and complex variable function theory. The active directions of functional analysis are: matrix analysis, operator theory, evolution equation, operator and function algebra. Harmonic analysis focuses on Fourier transform and wavelet transform in Euclidean space. Differential equations (including ordinary differential and partial differential) have many important and active fields and topics: 1. Geometric analysis II. Parabola and reaction-diffusion equation 3. Elliptic partial differential equation 4. Ginzburg-Landau equation 5. Nonlinear Schrodinger equation 6. Conservation Law Equation 7. Naville-Stokes Equation 8. Dynamics and Pozmann Equation 9. Ordinary differential equation 10. Power system 1. 1. Discrete Mathematics Research on Inverse Problems of Differential Equations: 1. Graph coloring related issues, including point coloring, edge coloring, circle coloring, uniform coloring, T coloring, distance binary labeling and so on. 2. Graph decomposition 3. Algebraic graph theory iv. Combinatorial counting problem 5. Finite body and its application. Probability: 1. Related research and application of Markov process and diffusion process II. Related research on probability theory in financial field III. Stochastic analysis and application of infinite dimensional space iv. Mathematical physics. Other scientific calculations can be roughly divided into matrix calculation theory and its application, and numerical theory and method of partial differential equations. Mainly through physical laws or assumptions, a suitable mathematical model is derived for scientific or engineering problems, and the problems are solved through mathematical analysis and numerical calculation or as pre-experiment predictions. The narrow sense of computational science is to design or apply effective numerical methods to solve some specific mathematical equations. Before choosing a math major in an American university, consider whether you like the following aspects: music, especially composition, art, abstract thinking, intellectual challenges, problem solving, philosophy, and like concise words. Are you good at the following aspects: attention to detail, creativity, critical thinking, mathematics, organization, quantitative analysis and spatial thinking?