1. Advanced mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics. In a broad sense, all mathematics except elementary mathematics are advanced mathematics, and some call algebra, geometry, simple set theory and logic in middle school intermediate mathematics, which is the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities.
Generally speaking, advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection.
The main contents include: series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations.
It is also a basic subject for postgraduate examinations of engineering, science and engineering and finance in colleges and universities.
2. Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions.
Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; Through analytic geometry, linear algebra can be expressed concretely.
The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.