Advanced mathematics is a basic subject formed by calculus, algebra, geometry and their overlapping contents, and is regarded as the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities. Its main contents include series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations, and it is also the basic subject of postgraduate examinations in engineering, science and finance.
In China, students majoring in science and engineering (except mathematics, who study mathematical analysis) have difficulty in learning mathematics, which is often called "advanced mathematics" in textbooks; Students majoring in literature and history learn a little shallower mathematics, and their textbooks are often called "calculus". Different majors in science and engineering, literature and history have different degrees of depth.
It is advanced mathematics that studies variables, but advanced mathematics does not only study variables. As for the courses related to "advanced mathematics", there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study independently).
The historical development of higher mathematics;
It is generally believed that the mathematics disciplines developed before16th century generally belong to the category of elementary mathematics, so the mathematics disciplines established after17th century are basically the contents of advanced mathematics. It can be seen that the category of higher mathematics can not be explained clearly by a few simple sentences or listing its branches.
Of the three branches of mathematics established before19th century, the first two were originally branches of elementary mathematics and later developed into a part of advanced mathematics, and only analysis belonged to advanced mathematics from the beginning. Calculus, the basis of analysis, is regarded as the beginning of "mathematics of variables", so studying variables is one of the characteristics of higher mathematics. The original concept of variables is a direct abstraction of variables that change in the material world, and the concept of variables in modern mathematics contains a higher level of abstraction.