First, the formation period of mathematics; The germination period is the initial accumulation period of mathematical knowledge and a gradual stage in the process of mathematical development. The mathematical knowledge in this period was scattered, preliminary and unsystematic, but it was the source of the history of mathematical development, which laid the foundation for the later development of mathematics.
This is the period when human beings have established the most basic mathematical concepts. Since counting, human beings have gradually established the concept of natural numbers, simple calculation methods, and recognized the most basic and simplest geometric forms. Arithmetic and geometry are not separated.
China has a long history. A large number of figures and inscriptions on stone tools, pottery, bronzes, tortoise shells and animal bones show that the concept of geometry was gradually formed in China as early as the Paleolithic. As early as five or six thousand years ago, there were mathematical symbols in ancient China. By the Shang Dynasty more than 3,000 years ago, numbers engraved on Oracle Bone Inscriptions or pottery were already very common.
At this time, the natural number is counted in decimal. There are thirteen counting units in Oracle Bone Inscriptions, ranging from one to ten to hundreds, thousands and tens of thousands. This shows that the basic concepts of mathematics were also formed in ancient China.
Second, the period of elementary mathematics (from 600 BC to1mid-7th century); The period of elementary mathematics lasted more than two thousand years from the fifth century BC to the seventeenth century AD, and ended with the establishment of advanced mathematics.
The most obvious achievement in this period is the systematic establishment of elementary mathematics, that is, arithmetic, elementary algebra, elementary geometry (plane geometry and solid geometry) and plane triangle in the current primary and secondary school curriculum.
The period of elementary mathematics can be divided into two parts according to different contents, namely, the period of geometric development (to the second century AD) and the period of algebraic priority development (from the second century AD to the seventeenth century AD). It can also be divided into "Greek period", "Oriental period" and "European Renaissance period" according to different historical conditions.
The Greek period coincided with the general prosperity of Greek culture. Greece is an ancient civilization, but compared with Babylon, Egypt, India and China, Greek civilization is a little later in the history of civilization.
Third, the period of variable mathematics (1mid-7th century to11920s); Variable mathematics came into being in17th century, and has gone through two decisive and significant steps: the first step is the generation of analytic geometry; The second step is calculus, which is to study the differential of functions in higher mathematics. It is the basic subject of mathematics.
The content mainly includes limit, differential calculus, integral calculus, equation and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols.
Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.
Fourth, the period of modern mathematics (65438+1920s); Modern mathematics. The period of modern mathematics began at the beginning of19th century. The beginning of the modern stage of mathematics development is based on all its foundations. Marked by profound changes in algebra, geometry and analysis. Modern mathematics is a subject that studies concepts such as quantity, structure, change, space and information.
/kloc-in the 0/7th century, mathematics developed by leaps and bounds, realizing the transition from constant mathematics to variable mathematics. The study of modern mathematics in China really began after the May 4th Movement in 19 19.
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Brief introduction to history:
The task of studying the history of mathematics is to find out the basic historical facts in the development of mathematics, reproduce its original features, and make scientific and reasonable explanations, explanations and evaluations on mathematical achievements, theoretical systems and development models through these historical phenomena, so as to explore the laws and cultural essence of the development of mathematical science. As the basic methods and means to study the history of mathematics, there are often historical textual research, mathematical analysis, comparative research and other methods.
Historians' duty is to tell history according to historical materials, and seeking truth from facts is the basic principle of historiography. Textual research has been formed in western history since17th century. It appeared earlier in China, especially in the Ganjia period of the Qing Dynasty, and it is still the main method of historical research. However, with the progress of the times, textual research methods are constantly improving and its application scope is expanding.
Of course, it is necessary to realize that the historical materials are true or false, and the psychological state of the researchers involved in the research process will inevitably affect the choice of research materials and the results of the research. In other words, the authenticity of the conclusions of historical textual research is relative. At the same time, we should realize that textual research is not the ultimate goal of historical research, and the study of mathematical history cannot be textual research for textual research's sake.
Baidu Encyclopedia-History of Mathematics