The above class is not a standard course for mathematics majors. The first step: analytic geometry, mathematical analysis and advanced algebra, and study at the same time; The second step: elementary number theory, advanced geometry, ordinary differential equation, complex variable function theory, and study at the same time; The third part: differential geometry (the classical part, that is, curve and surface theory), modern algebra (also called abstract algebra), real variable function theory, and simultaneous learning; The fourth part: point set topology, functional analysis, partial differential equations, global differential geometry, and simultaneous learning. In addition, some applied mathematics parts have been added, such as probability theory, combinatorial mathematics, operational research and so on. Elementary probability theory can be learned through mathematical analysis, while advanced probability theory needs real variable function, and other requirements are not much. Just learn mathematical analysis. If you need to know more, you can know more: complex variable function theory, group representation theory, commutative algebra, algebraic geometry, algebraic number theory, analytic number theory, Riemannian geometry, algebraic topology, differential topology, Finsler geometry, symplectic geometry, harmonic analysis, measure theory, fractal geometry, dynamic system and so on.