1, basic mathematics
Basic mathematics is one of the two subjects under mathematics. Basic mathematics, also known as pure mathematics, is the core and basic part of mathematical science. Basic mathematics includes mathematical logic, number theory, algebra, geometry, topology, function theory, functional analysis and differential equations. With the rapid development of contemporary mathematics, the trend of cross-infiltration between these branches is increasingly obvious, and many new research fields and growing points have emerged.
Basic mathematics is not only the foundation of other applied mathematics disciplines, but also an indispensable language, tool and method for natural science, technical science and social science. The development of high technology and the wide application of electronic computers provide a broader application prospect for the research of basic mathematics.
2. Applied Mathematics
Applied mathematics is one of the two disciplines under mathematics. Applied mathematics is the general name of mathematical theories and methods with clear application purposes. Studying how to apply mathematical knowledge to other branches of mathematics (especially science) can be said to be the opposite of pure mathematics.
Including differential equation, vector analysis, matrix, Fourier transform, complex variable analysis, numerical method, probability theory, mathematical statistics, operational research, control theory, combinatorial mathematics, information theory and many other branches of mathematics, as well as the study of mathematical problems raised in various application fields. Computational mathematics can sometimes be regarded as a part of applied mathematics.