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What is the relationship between advanced mathematics and mathematical analysis? And the relationship between linear algebra and higher algebra? Can you have a detailed classification of mathematics s
What is the relationship between advanced mathematics and mathematical analysis? And the relationship between linear algebra and higher algebra? Can you have a detailed classification of mathematics subjects? College mathematics includes: analysis, algebra, geometry, randomness, and these basic comprehensive disciplines.

For analysis, the courses include: mathematical analysis (the most basic), complex variable function, real variable function, functional analysis and so on. As you said, advanced mathematics is a simple version of mathematical analysis.

In algebra, the courses are: advanced algebra (the most basic), modern algebra (also called abstract algebra) and so on. Higher algebra includes linear algebra and polynomial algebra. Linear algebra (for example, f(x)=Ax+b is called linear because it is a straight line) studies straight lines.

Using polynomial (including not only linear function, quadratic function, but also higher-order function) to replace a very complex function, the result is also very satisfactory.

For geometry, it is mainly analytic geometry.

Randomness, including: probability theory, mathematical statistics, stochastic processes, etc.

Other comprehensive disciplines: ordinary differential equations, partial differential equations, etc.