Is applied mathematics a branch of mathematics?

Applied mathematics is a major, not a discipline. Learning this major will lead to many branches of 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, including the study of mathematical problems raised from various application fields. Computational mathematics can sometimes be regarded as a part of applied mathematics.

Applied mathematics contains two words: "application" and "mathematics". Generally speaking, applied mathematics consists of two parts. One part is mathematics related to application, which is a branch of traditional mathematics. We can call it "applied mathematics". The other part is the application of mathematics, that is, using mathematics as a tool to explore and solve problems in science, engineering and sociology, which is beyond the scope of traditional mathematics. 2 1 century, applied mathematics is mainly applied in two fields. One is a computer. With the rapid development of computer, a large number of software engineers who understand mathematics are needed to develop the corresponding database. The other is economics, many of which need very professional mathematics to analyze. Many related courses of applied mathematics are designed on the basis of economic examples.

Mathematics is a project in human activities. Even the purest mathematics produced by human brain is related to the laws of nature. It will be useful to master the laws of nature or other aspects sooner or later. We call mathematics that has been applied or will be applied applied applied mathematics. As far as today's development is concerned, differential equations, probability statistics, computational mathematics, computer mathematics and operational research are all within the scope of applicable mathematics. The other is "the application of mathematics". Physicists, aviation engineers, geologists, biologists, economists, etc. Mathematics needs to be used as a tool to solve various disciplines and engineering problems. Therefore, sometimes they have to transfer the mature mathematics, but sometimes they have to creatively develop new mathematical methods to deal with the unique problems they encounter. This is the application of mathematics. They are often not so strict, and often need to cooperate with the observation of experimental results and the intuition given by experience to develop mathematical methods. Therefore, applied mathematicians must have a deep understanding of the subject of applied problems in addition to a considerable level of mathematical literacy.

Traditional mathematics is divided into "pure mathematics" and "applied mathematics", and the difference between them is only in degree. Even the purest mathematics will be applied in the future. Their similarity is that they only pay attention to the mathematical content of the problem and only use mathematical standards to measure the research results. "The application of mathematics" focuses on scientific or engineering content, and mathematics is only a tool, so the measurement standards of research results are also very different.

The term "applied mathematics" did not exist before the 20th century. Great mathematicians, such as Gauss, Euler and Cauchy, all engage in both pure mathematics and applied mathematics. For example, the development of functions is basically to solve the Laplace equation caused by physics. Pure logical thinking and the explanation of natural phenomena develop in parallel. Until World War II, the application of advanced mathematics was mostly related to physics.

Before and after World War II, due to the development of aviation industry and the importance of aircraft in the war, advanced mathematics began to be widely used in mechanics and other engineering, which promoted the development of applied mechanics and applied mathematics. In the forties and fifties of last century, the main research content of applied mathematics was mechanics, and most applied mathematicians had no background in mathematics, so the nature of "application" was very strong. Since the 1960s, the situation has changed. On the one hand, the application of advanced mathematics is more and more extensive. Not only physics, engineering, chemistry, astronomy, geography, biology and medicine are using advanced mathematics, but also economics and linguistics have begun to use quite a lot of advanced mathematics, so applied mathematics has developed.

Another reason for the development of applied mathematics is that the development of mathematics is becoming more and more abstract, and gradually only mathematicians themselves and their colleagues can understand what they are doing. In this case, theoretical scientists and engineers who need mathematics have to rely on themselves, instead of relying on pure mathematicians, to start mathematics by themselves. The biggest difference between their mathematics and pure mathematics is the combination with reality: natural reality and social reality. Mathematical problems raised by natural phenomena and social development should be solved; After solving mathematical problems, the results of discussion will return to nature and society, and applied mathematics will emerge as the times require.