1. Advanced Mathematics: This is the basis of college mathematics, including calculus, sequence, limit, derivative and integral. These contents are the basis of understanding more advanced mathematical concepts.
2. Linear Algebra: This course mainly studies vector spaces (such as two-dimensional and three-dimensional spaces), linear equations, matrices, eigenvalues and eigenvectors. These contents are widely used in computer science, physics, engineering and other fields.
3. Probability theory and mathematical statistics: This course mainly studies the regularity of random phenomena, including the basic concept of probability, random variables and their distribution, law of large numbers, central limit theorem, hypothesis testing, etc. These contents are widely used in statistics, economics, finance and other fields.
4. Discrete Mathematics: This course mainly studies discrete structures, including set theory, graph theory, logic and combinatorial mathematics. These contents are widely used in computer science, cryptography, network science and other fields.
5. Real variable function and functional analysis: This course mainly studies functions on real numbers or complex numbers and their properties, including the basic concepts of real variable functions, measure theory, integral theory, functional analysis and so on. These contents are widely used in theoretical physics, partial differential equations and other fields.
6. Numerical analysis: This course mainly focuses on solving mathematical problems by numerical methods, including interpolation and approximation, numerical calculus, numerical solutions of ordinary differential equations and partial differential equations. These contents are widely used in computational mathematics, engineering calculation and other fields.
7. Optimization method: This course mainly studies the methods to find the optimal solution, including linear programming, nonlinear programming, dynamic programming, convex optimization and so on. These contents are widely used in operational research, economics, management and other fields.
8. Probability theory and stochastic process: This course mainly studies the evolution law of stochastic phenomena, including Markov chain, basic concepts of stochastic process, stationary distribution, ergodicity and so on. These contents are widely used in signal processing, communication engineering and other fields.
9. Partial differential equations: This course mainly studies partial differential equations that describe physical phenomena in nature, including elliptic partial differential equations, hyperbolic partial differential equations, parabolic partial differential equations, etc. These contents are widely used in theoretical physics, fluid mechanics and other fields.