First, mathematics.
Mathematics, English: Mathematics, from ancient Greece? θξμα(máthēma)； Often abbreviated as math or maths, it is a discipline that studies concepts such as quantity, structure, change, space and information.
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.
Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.
Second, 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.
Third, logic.
Subject: mathematical 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.