What is the relationship between advanced algebra learning and high school mathematics?
The book Advanced Algebra consists of two parts. The first part is polynomial theory, and its connection with high school mathematics (in fact, it is not just high school mathematics, but rather elementary mathematics, including all the mathematics studied before) is simply the operation object developed on its basis. The object of operation has developed from numbers in elementary mathematics to polynomials, so you can see a series of operations such as division and reduction of polynomials in advanced algebra books. The second part is transformation, including matrix, determinant, linear space (nonlinear space) and linear transformation (nonlinear transformation). Because of the great difficulty, what is in brackets is often considered as a simple understanding. The connection between this part and elementary mathematics lies in expanding simple transformation or transformation with fewer elements in elementary mathematics into transformation with more elements. In fact, a function is a form of transformation. So advanced mathematics is actually developed on the basis of elementary mathematics. This development can be to increase the number of elements, increase the number of times, or expand the research object. There are many branches of mathematics according to the different extended contents. These branches will be introduced separately in universities, not just algebra. Similarly, mathematics is not without its merits. People who feel useless just don't find it useful. Who is in charge of this matter? Don't want to comment more. I can only say that education itself and students are responsible. If mathematics really won't have a great impact on human society, how can countries around the world list it as one of the core courses to be mastered by the next generation?