Advanced mathematics is more advanced than elementary mathematics. Broadly speaking, all mathematics except elementary mathematics are advanced mathematics. Some refer to algebra, geometry, set theory and logic in middle school as middle school mathematics, which is regarded as the transition between elementary mathematics in primary school and junior high school and advanced mathematics in undergraduate course. Generally speaking, the main contents of higher mathematics include: limit theory, unary calculus, multivariate calculus, spatial analytic geometry and vector algebra, series theory, and primary ordinary differential equations. In the teaching materials of advanced mathematics, calculus and series theory are the main ones, supplemented by other aspects, and all kinds of teaching materials are slightly different.

Elementary mathematics: including elementary school arithmetic, middle school algebra, plane geometry, solid geometry, plane triangle, etc.

In Chinese mainland, students majoring in science and engineering (except mathematics, mathematical analysis) learn more deeply, and their textbooks are often called "advanced mathematics". Most colleges and universities use Advanced Mathematics, a textbook compiled by the Mathematics Department of Tongji University. Students majoring in literature and history often study calculus in textbooks. The majors of science and engineering and literature and history are different, and the depth is also different. Advanced mathematics studies variables, but advanced mathematics does not only study variables. As for the courses attached to Advanced Mathematics, there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study separately).

Advanced mathematics is an important basic course for undergraduates majoring in science and engineering in colleges and universities. Through the study of this course, students can acquire the basic knowledge of vector algebra, spatial analytic geometry and calculus, the necessary basic theories and common operation methods, and pay attention to cultivating students' operation ability, preliminary abstract thinking, logical reasoning and spatial imagination, so that students can get the preliminary training to solve practical problems and lay the necessary mathematical foundation for the following courses.