As follows:
1. Definition
Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.
2. Logic
Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. As far as it is concerned, it is the origin of Godel's second incomplete theorem, which is perhaps the most widely circulated achievement in logic. Modern logic is divided into recursion theory, model theory and proof theory, which are closely related to theoretical computer science.
Step 3 be strict
Mathematical language is also difficult for beginners. How to make these words have more accurate meanings than everyday language also puzzles beginners. For example, the words "open" and "domain" have special meanings in mathematics.
Mathematical terms also include proper nouns such as embryo and integrability. But these special symbols and terms are used for a reason: mathematics needs accuracy more than everyday language. Mathematicians call this requirement for linguistic and logical accuracy "rigor".
4. A Brief History of Mathematics in China
Mathematics, called arithmetic in ancient times, is an important subject in ancient Chinese science. According to the characteristics of the development of ancient mathematics in China, it can be divided into five periods: the germination period; The formation of the system; Development; Prosperity and the integration of Chinese and western mathematics.
5. Space
The study of space originated from Euclidean geometry. Trigonometry combines space and numbers, including the famous Pythagorean theorem, trigonometric function and so on. Now the research on space has been extended to high-dimensional geometry, non-Euclidean geometry, topology and graph theory.
Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold.
Algebraic geometry has the description of geometric objects such as polynomial equation solution set, which combines the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.