Advanced algebra is an advanced algebra, which is a general term for the development of algebra to an advanced stage, and it is a specialized mathematics course.

Advanced algebra is one of the three basic courses (mathematical analysis, advanced algebra, analytic geometry) for college mathematics majors. High-rise buildings rise from the ground, the most important thing is to lay a good foundation.

This course mainly includes polynomial algebra (Chapter 2) and linear algebra (Chapters 3-11). Polynomial algebra theory includes divisibility, factorization and roots of polynomials, which is the deepening and perfection of factorization, equations and inequalities in middle school. Linear algebra theory mainly includes determinant, linear equations, matrix, quadratic form, linear space and linear transformation, Euclidean space and so on.

Higher algebra generally includes two parts: the elementary of linear algebra and polynomial. Higher algebra further expands the research object on the basis of elementary algebra, and these quantities have the characteristics of similar operation to numbers. Linear algebra is a mathematical discipline developed from solving linear equations and discussing quadratic equations. It is a very important basic subject.

Higher algebra is mostly linear algebra, with some polynomial algebra in the middle. Finally, we may talk about some nonlinear algebra knowledge such as quadratic form. Gao Dai, like several points, is the most basic professional course for mathematics majors. In terms of knowledge content, the core content of the high generation is not only the matrix theory, but also the structure theory of linear space and the linear operator theory.

The difference between line generation and high generation:

Within the curriculum framework of Chinese universities, linear algebra is usually a linear algebra course for non-mathematical science and engineering majors, while advanced algebra is a substitute course for mathematics majors. Linear algebra focuses on determinant, matrix and its transformation, linear equations, quadratic form and other relatively specific concepts, and attaches importance to calculation; Higher algebra in mathematics department may focus on linear space and linear transformation in general fields, and then emphasize the relationship between matrix and linear transformation.

Some respondents mentioned that the senior generation can talk about polynomials, which is actually very understandable. All polynomials form a linear space, and derivatives or integrals are linear transformations on it, which naturally belongs to the discussion of line generation. The determinant itself is a multivariate polynomial; Discriminant, resultant and so on are also the places where polynomial theory and matrix theory connect. Then the basic symmetric polynomial of the eigenvalue gives the coefficients of the eigenvalue polynomial, and so on.