Applied statistical mathematics contains three words: application, statistics and mathematics. Generally speaking, applied mathematics includes two parts. Part of it is application-related mathematics, which is a branch of traditional mathematics and can be called "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.
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. Mathematics that can be applied now, or will be applied soon, is called applied mathematics.
In terms of development, such as 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.
development status
applied mathematics
China's most famous mathematical classic "Nine Chapters Arithmetic" collects 246 practical problems and pays attention to solving practical problems, which is a fine tradition of ancient mathematics in China. After the division of labor between manual labor and mental labor, a new stage of scientific development: a pure and rigorous scientific system has been created, but it is still far from real life.
Since then, mathematics has developed in two directions. On the one hand, it is pure mathematics. For example, Goldbach conjecture, Fermat's last theorem and other world-famous issues have become the focus of attention of the world. Once a breakthrough is made, it can be regarded as a major event in the history of human thought. As for non-Euclidean geometry, topology, abstract group theory, etc. Although you can't see the direct relationship with reality at first, as long as you have good mathematical knowledge, you will often find practical application in a few years. The fiber bundle theory studied by Chen Shengshen in the 1940s became a mathematical tool of gauge field discovered by Yang Zhenning and others in physics in the 1970s. The unity of this world is unbelievable.
On the other hand, applied mathematics has developed rapidly. After all, the real world is the source of mathematics development. /kloc-since the 0/7th century, social development and production demand have been the main driving forces for the development of mathematics. Newton invented calculus for the need of physics, in turn, TychoBrahe discovered Neptune by mathematical methods; The steam engine promoted the development of kinematics and thermodynamics, and pushed the mathematical analysis to a new peak. The basic laws of electromagnetism are written in differential equations. Until the 20th century, the manufacture and navigation of jet planes and spaceships, medical equipment scanned by CT, and battle plans for organizing large-scale wars were all mathematical techniques in essence.
In modern times, mathematics is not only a tool to solve problems, but also an important part of the culture of the times. Some mathematical concepts and languages have penetrated into daily life, and some mathematical principles have become necessary knowledge for people, such as area, volume, symmetry, percentage, average value, proportion, angle, etc., and have become common nouns in social life. Such as population growth rate, production statistics chart, inventory trend chart, etc. Continue to appear in newspapers, television and other mass information media; However, savings, bonds, insurance, area and volume calculation (estimation) and shopping decision-making have become unavoidable practical problems. Then the future citizens-students now must have the mathematical literacy to solve practical application problems, which calls for the application problems to be presented in the process of mathematics education and teaching.
There has been a tradition of practice in ancient mathematics in China, and it is not a new problem to attach importance to the application of mathematics in mathematics teaching. In primary schools, the application of mathematics is the focus and difficulty of teaching, and no one has ever disagreed. In junior high school, after learning plane geometry, the taste of mathematics tends to be abstract, logical reasoning is constantly strengthened, and the application of mathematics gradually fades out. However, mathematical applications have not disappeared, such as concentration problems, travel problems, and the relationship between parallelogram and iron gate is always mentioned. Just misled by some wrong ideas, people don't pay much attention to it.
Once in high school, the situation became more and more serious. Mathematics has always been the main course in middle schools. Why do you have to learn so much math? It is generally believed that mathematics is a "sieve of ability" and "gymnastics of thought", and it is nothing more than "need for further study" and "fit for thought". As for what's the use, I'm sorry, don't ask. Because of the Great Leap Forward and the Cultural Revolution, the mathematical knowledge system was destroyed. Once it was brought bad, it focused on the requirements of pure mathematics. For some time, advocating the application of mathematics has been called "pragmatism" and "short-sighted behavior". It seems that mathematics is getting farther and farther away from real life. The pure mathematical reasoning of "pinching the head and burning the tail" has become the only choice. Therefore, the design and teaching of mathematical application problems has become an urgent task.
Career prospects
Applied statistical mathematics has a wide range of employment.
Applied statistical mathematics and applied mathematics are basic majors and "parent majors" of other related majors. Whether it is scientific research data analysis, software development, three-dimensional animation production or financial insurance, international economy and trade, business administration, chemical and pharmaceutical industry, communication engineering, architectural design, etc. , can not be separated from the relevant professional knowledge of mathematics.
Strict logical thinking ability comes from a deep and solid mathematical foundation. It can be seen that the majors of mathematics and applied mathematics are the basis for engaging in other related majors. With the development and popularization of science and technology, the relationship between mathematics major and other related majors will be closer, and the application of mathematics professional knowledge will be more extensive. 87% of the people re-choose their careers based on mathematics or related majors. Because mathematics and applied mathematics are closely related to other related majors, there are many similar majors to choose from. Mathematics majors use mathematical methods to analyze and solve problems in finance and management.
Graduates can carry out basic mathematical theory research or teaching, design and development of application software, and their employment is mainly based on two-way choice and self-employment. Mainly engaged in research and teaching in science and technology, education, economy and other departments, or engaged in practical application, development, research and management in production, operation and management departments. Can be engaged in theoretical research, computer software system development, design and maintenance in scientific research departments, government departments, financial systems, universities, military units, computer software companies, communication companies and other enterprises and institutions.
For example, the graduates in Tsinghua University are mainly concentrated in companies related to the information industry, such as Huawei, Lenovo, Siemens, Founder and Tongfang, as well as some large state-owned group companies, such as Bank of China, China Life Insurance and Shanghai Baosteel.
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