First of all, from the content, elementary mathematics mainly includes arithmetic, algebra, geometry and elementary probability. These contents are mainly the introduction and application of basic mathematical concepts, theorems and methods. Advanced mathematics includes calculus, linear algebra, probability theory, mathematical statistics, complex variable functions, partial differential equations, etc., which is mainly an in-depth study and expansion of mathematical theory.
Secondly, from the method point of view, elementary mathematics mainly adopts intuitive and concrete methods for calculation and reasoning, while advanced mathematics mainly adopts abstract and symbolic methods for derivation and proof. For example, geometric problems in elementary mathematics can usually be solved by drawing, while calculus problems in advanced mathematics need to be solved by abstract concepts such as limit, derivative and integral.
Thirdly, from the application field, elementary mathematics is mainly used to solve practical problems in daily life, such as calculation, measurement and prediction. Advanced mathematics is mainly used in scientific research and engineering technology, such as physics, chemistry, biology, computer science, economics and other fields.
Generally speaking, the main difference between elementary mathematics and advanced mathematics lies in the depth and breadth of content, the degree of abstraction and the scope of application of methods. Elementary mathematics is the basis of learning advanced mathematics, which is the deepening and expansion of elementary mathematics.