Mathematics is all advanced mathematics except elementary mathematics, and some call algebra, geometry and simple set theory in middle school as intermediate mathematics, which is the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities.
Characteristics of high numbers
As a basic science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstraction and computability are the most basic and remarkable characteristics of mathematics. With a high degree of abstraction and unity, we can profoundly reveal its essential laws and make it more widely used.
Strict logicality means that in the induction and arrangement of mathematical theory, whether it is concept and expression, or judgment and reasoning, we must follow the rules of logic and the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics.
Infinitely entering mathematics is another feature of higher mathematics. Everything in the real world appears in a limited form, and infinity is a summary of their identity. Therefore, infinite entry into mathematics is the embodiment of high theorization and abstraction of mathematics. Infinity in mathematics appears in two forms: latent infinity and real infinity.
Advantages of learning advanced mathematics
1. Cultivating mathematical thinking: Advanced mathematics is not only a knowledge subject, but also a subject to cultivate mathematical thinking. By studying advanced mathematics, we can train students' logical thinking, ability to analyze and solve problems, and cultivate students' innovative consciousness and ability.
2. Lay a good foundation for mathematics: Advanced mathematics is the foundation for learning other branches of mathematics, such as probability theory, mathematical statistics, linear algebra, differential equations, etc. Only by laying a good foundation of advanced mathematics can we better learn these branches of mathematics and better apply mathematical knowledge to solve practical problems.
3. Prepare for future career development: Many professional fields need to apply advanced mathematics knowledge, such as computer science, physics, engineering, economics and so on. Mastering advanced mathematics knowledge can prepare for future career development and improve professional competitiveness.