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What are the two major objects of mathematical research?
Mathematics-the science of studying quantitative relations and spatial forms in the real world.

Mathematics can be divided into two categories, one is pure mathematics and the other is applied mathematics.

Pure mathematics, also called basic mathematics, specializes in the internal laws of mathematics itself. The knowledge of algebra, geometry, calculus and probability introduced in the textbooks of primary and secondary schools belongs to pure mathematics. A remarkable feature of pure mathematics is to temporarily put aside the specific content and study the quantitative relationship and spatial form of things in pure form. For example, it doesn't matter whether it is the area of trapezoidal rice fields or the area of trapezoidal mechanical parts. All people care about is geometry.