The part of mathematics that studies numbers belongs to the category of algebra; The part that studies the shape belongs to the geometric model; The connected shape number and the part involving limit operation belong to the scope of analysis. These three kinds of mathematics constitute the ontology and core of the whole mathematics. Modern research and application are different. Algebra and geometry are of course the most widely used, and most of them are used in scientific research, engineering and science. Analysis is mainly about theory and teaching. The most important requirement of analysis is strict logical proof. Personally, I feel that algebra needs practicality and understanding. Geometry, especially differential geometry, is called a gobbledygook, depending on whether you have this talent and hobby.

Attached is a joke that has been circulating for a long time in the department of mathematics in universities:

Learn real variable function ten times, functional analysis chilling;

Mechanical drawing mechanical system, quantum mechanics, quantum mechanics;

Ordinary differential calculus often does not get points, and the mathematical equation is not proved;

Stochastic process is random, and differential topology can't escape;

Microcomputer principle crisis, assembly language can not be compiled.