On the basis of elementary algebra, advanced algebra further expands the research object and introduces many new concepts and quantities which are very different from usual ones, such as set, vector and vector space. These quantities have operational characteristics similar to numbers, but the research methods and operational methods are more complicated.
Linear algebra is a mathematical discipline developed from solving linear equations and discussing quadratic equations. It is a very important basic subject. Including determinant, matrix, n-dimensional vector, linear equations, similar matrix and quadratic form, G vector and so on.
From the course content, most advanced algebra is linear algebra, with some polynomial algebra in the middle, and finally some nonlinear algebra knowledge such as quadratic form may be talked about. Line generation is a course for non-mathematics majors, and high generation is a course for mathematics majors. The orientation of the course is different from the emphasis of the knowledge learned.
Generally speaking, line generation focuses on the cultivation of computing ability, and it is not necessary to solve the complicated mathematical principles behind it, but the calculation should be accurate and can solve practical problems. Advanced generation, like several fractions, is the most basic professional course for mathematics majors. The key point is to cultivate students' basic mathematical literacy, which requires not only computing ability, but also an understanding of knowledge system and structure, especially the accurate understanding of definition, the idea of theorem proving, what is reasoning and so on. These basic proofs are often ignored by line generation.
In terms of knowledge content, in addition to matrix theory, the core content of the high generation focuses more on the structure theory and linear operator theory of linear space, and the latter two parts are not important for line generation.