Higher mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics and secondary mathematics. Algebra, geometry and simple set theory in middle schools are called secondary mathematics, which is regarded as the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities.

Generally speaking, advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection. The main contents include: series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations. Basic subjects for postgraduate examinations in engineering, science and engineering and finance.

History:

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.

For example, the research in mathematical analysis is limited to real variables, while other branches of mathematics study complex variables with complex values, vectors and tensors, as well as various geometric quantities and algebras, as well as random variables, fuzzy variables and variable (probability) spaces-categories and random processes.

The concept of describing the dependency between variables has developed from function to functional, transformation and even functor. Higher mathematics, like elementary mathematics, also studies spatial forms, but it is more abstract and embodies the characteristics of change, or it is studied in change. For example, the concepts of curves and surfaces have developed into general manifolds. According to Herun's program, geometry is a theory about the invariance of graphics under certain transformation groups, that is, geometry is studied by putting various spatial forms under transformation.