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 after17th century. Compared with elementary mathematics and secondary mathematics, mathematics is more difficult to learn, and it belongs to university courses, so it is often called "advanced mathematics".

As a basic science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstraction and calculation are the most basic and remarkable features of mathematics. Only with a high degree of abstraction and unity can we profoundly reveal its essential laws and make it more widely used.