Linear algebra: an important part of higher algebra, the focus of linear algebra is to master the matrix, most of which is calculation. It's science and engineering, not mathematics.

Advanced algebra: There are many things to master, and abstract contents such as polynomial and bilinear function, unitary space and symplectic space are added to the content.

2. Different research directions:

Linear algebra: the research objects are vectors, vector spaces (or linear spaces), linear transformations and finite dimensional linear equations. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis;

Advanced Algebra: Students who are mainly proof and belong to the Department of Mathematics. Advanced mathematics has its inherent characteristics, that is, high abstraction, strict logic and wide application. Abstraction and calculation are the most basic and remarkable features of mathematics.

3, the actual application direction is different:

Linear algebra: 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.

Advanced Algebra: The appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into social sciences extensively and deeply.

Refer to Baidu Encyclopedia-Advanced Mathematics

Baidu encyclopedia-modern mathematics