I. Introduction to Mathematics
Mathematics is a discipline that studies the concepts of quantity, structure and space and their changes, and belongs to a formal science. Mathematics is developed by using abstract and logical reasoning to count, calculate, measure and observe the shape and motion of objects. Mathematicians expand these concepts, formulate new conjectures, and strictly deduce some theorems from the selected axioms and definitions.
Second, the origin of mathematics
Mathematics, which originated from the early production activities of human beings, is one of the six ancient arts in China. It was also regarded as the starting point of philosophy by ancient Greek scholars. Mathematics was first used for people's counting, astronomy, measurement and even trade needs.
The study of space begins with geometry, first Euclidean geometry and trigonometry similar to three-dimensional space. Later, non-Euclidean geometry came into being, which played an important role in the theory of relativity.
After the 6th century BC, Pythagoras studied mathematics as an empirical discipline, and he created the ancient Greek word μ? θ η μ α means "knowledge". Greek mathematicians have improved these mathematical methods to a considerable extent and expanded the theme of mathematics.
China made early contributions to mathematics, including introducing the value system. The popular Indo-Arabic numeral system and its operation method in the world today evolved gradually in India around 1000, and was spread to the west by Islamic mathematicians through the works of Khorezmo.
Classification of some mathematical fields:
I. Foundations and concepts
In order to clarify the basis of mathematics, mathematical logic and set theory are developed. Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. As far as mathematical logic itself is concerned, it belongs to the field of Godel's second incomplete theorem, and this is perhaps the most widely circulated achievement in logic: there are always true propositions that cannot be proved.
Second, discrete mathematics.
Discrete mathematics refers to the general name of the most useful mathematical fields for theoretical computer science, including computability theory, computational complexity theory and information theory. Complexity theory research can be regarded as the degree to which computers are more manageable; Even though some problems can be solved by computer in theory, it takes too much time or space to solve them.