1. Mathematics
Mathematics and applied mathematics (basic mathematics and financial mathematics), statistics (statistics and probability theory) and information and computational science (computational mathematics and information science) will be set up in the mathematics departments of most universities.
All majors are required courses: mathematical analysis, advanced algebra, analytic geometry, ordinary differential equations, abstract algebra, complex variable functions, probability theory and mathematical models. In addition, each direction will carry out in-depth study in their respective fields to varying degrees.
2. Physics
The four major mechanics of physics department (theoretical mechanics, statistical mechanics, electrodynamics and quantum mechanics) are full of mathematics, and even can be said to be completely applied mathematics courses. In addition, there are courses in mathematical physics methods, which are also courses in applied mathematics.
Therefore, physics departments (including astrophysics and astronomy majors) need to use more mathematics than ordinary science majors. How much is needed is still related to the direction. Different majors may involve real variable functions, abstract algebra, partial differential equations and even Riemannian geometry.
3. Computer
In addition to advanced mathematics, line generation and popularization, computer majors need at least specialized mathematics courses such as set theory and graph theory, mathematical logic, algorithm analysis, algebraic structure, combinatorial mathematics, numerical methods, etc., so as to lay the foundation for computer language logic and digital technology.
4. Chemistry
Chemical analysis needs basic statistics, and structural chemistry needs knowledge of quantum mechanics. The premise of learning quantum mechanics is to learn linear algebra and partial differential equations well.
5. Engineering
Almost all engineering majors are based on mathematics, physics (or chemistry, biology) and computers, and the requirements for mathematics are naturally higher, especially those related to physics, such as machinery, motors, electronics, civil engineering and water conservancy.
6. Economics
Econometrics is the soul of modern economics, and only the economic discussion involving mathematical methods is the real academic discussion. Econometrics can almost be translated into economic statistics, which itself is a course of mathematical methods.
7. Finance
In addition to economic mathematics, financial majors also need to learn risk assessment, which at least involves mathematical courses such as stochastic process, time series analysis, optimal design and financial numerical methods.
8. Sociology
Sociology majors also have specialized courses in sociological statistical methods, which naturally involve probability theory and statistics, and naturally require basic knowledge of advanced mathematics.