Mathematics education is a subject that studies the practice and methods of mathematics teaching. In addition, mathematics educators are also concerned about the tools to promote this practice and the development of its research. Mathematics education is one of the hot topics in modern society. This term has an ambiguity, which refers to both classroom practice in various places and a new subject. It has its own periodicals, conferences and so on. The most important international organization in this field is the International Mathematics Teaching Committee.

Applied mathematics is the general name of mathematical theories and methods with clear application purposes. It can be said that studying how to apply mathematical knowledge to other branches of mathematics (especially science) is the opposite of pure mathematics, including differential equation, vector analysis, matrix, Fourier transform, complex variable analysis, numerical method, probability theory, mathematical statistics, operational research, cybernetics, combinatorial mathematics, information theory and so on.