1. knowledge system: elementary mathematics mainly includes arithmetic, algebra, geometry and preliminary probability statistics, while advanced mathematics includes calculus, linear algebra, probability theory, mathematical statistics, complex variable functions, ordinary differential equations, partial differential equations and other branches. The knowledge system of advanced mathematics is richer and more complex.
2. Degree of abstraction: Elementary mathematics mainly studies concrete numbers and shapes, and its concepts and theorems usually have clear intuitive significance. Higher mathematics pays more attention to the study of abstract concepts, such as limit, derivative and integral, which are rarely involved in elementary mathematics.
3. Research methods: Elementary mathematics mainly adopts the method of direct proof, that is, through the known conditions and basic theorems, the conclusions to be proved are gradually deduced. In advanced mathematics, indirect proof methods, such as limit existence criterion and differential mean value theorem, are mostly used, which are rarely used in elementary mathematics.
4. Scope of application: Elementary mathematics is mainly used to solve practical problems in daily life, such as calculation and measurement. Advanced mathematics is widely used in natural science, engineering technology, social science and other fields, such as physics, computer science, economics and so on.
5. Way of thinking: Elementary mathematics pays attention to calculation and skills, which requires students to master various formulas and theorems skillfully. Higher mathematics pays more attention to cultivating students' logical thinking ability and innovative ability, and students need to learn to use mathematical tools to analyze and solve problems.
In a word, there are great differences between advanced mathematics and elementary mathematics in knowledge system, abstraction, research methods, application scope and thinking mode. Advanced mathematics is the in-depth development and expansion of elementary mathematics, and learning advanced mathematics requires a certain foundation of elementary mathematics.