1. Calculus: Including the basic concepts, limits, derivatives, integrals and differential equations of calculus.
2. Linear algebra: including matrix, determinant, vector space, linear transformation, eigenvalue, eigenvector, orthogonal transformation, etc.
3. Probability theory and mathematical statistics: including the basic concept of probability, discrete and continuous random variables and their distribution, large number theorem, central limit theorem, etc.
4. Mathematical analysis: including real number system, sequence, series, limit, continuity, derivative, basic theorem of calculus, Fourier series, etc.
5. Complex variable function: including complex number, derivative, integral, series, analytic function, harmonic function and other basic concepts.
6. Partial differential equations: including basic concepts such as partial differential equations, first-order partial differential equations, second-order linear partial differential equations, constant coefficients and non-homogeneous partial differential equations.
7. Numerical calculation methods: including numerical integration, numerical differentiation, numerical solutions of nonlinear equations, numerical solutions of differential equations, etc.
8. Topology: including point set topology, continuous mapping, homeomorphism, compactness, Hausdorff space, manifold, etc.
9. Algebra: including group theory, ring theory, domain theory, linear algebra, Lie algebra, etc.
10. Differential geometry: including curves, surfaces, Gaussian curvature, Riemannian metric, manifolds, etc.
The above are some basic contents of undergraduate mathematics courses for general majors, and the contents of mathematics courses for different schools and majors may be different.
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