The study of algebra has entered the stage of overall analysis of system structure from the study of locality. Since the emergence of group theory, there have been various branches of mathematics, such as lattice theory of ordered structure, topology, modular theory of composite structure of rings and groups, topological vector space, differential manifolds and fiber bundles with several structures at the same time. It can be said that structural thought is one of the most basic and important ideas in all branches of modern mathematics.
Calculus is a branch of mathematics, which studies the differential and integral properties of functions and their applications. It has become the foundation of other branches of mathematics, and it is also an essential tool for other natural sciences and engineering technology.
In order to make the study of fuzzy phenomena quantitative and mathematical, it is necessary to introduce new mathematical thinking methods, and fuzzy mathematics came into being. The birth and development of fuzzy mathematics is closely related to the development of computers. In order to make the computer describe and deal with the fuzziness of things and complete more complex tasks, it is necessary to establish corresponding mathematical thinking methods, which can describe and deal with fuzzy quantities and their relationships.
Functional analysis is a branch of studying the mapping from topological linear space to topological linear space satisfying various topological and algebraic conditions. It is developed from the study of variational problems, integral equations and theoretical physics. It comprehensively uses the viewpoints of function theory, geometry and modern mathematics to study functions, operators and limit theory in infinite dimensional vector space. It can be regarded as analytic geometry and mathematical analysis of infinite dimensional vector space.