Elementary mathematics mainly includes geometry and algebra. Geometry is a discipline that studies spatial forms, while algebra is a discipline that studies quantitative relations. Elementary mathematics is basically constant mathematics.
The content of advanced mathematics is very rich, which is limited to what undergraduates have learned. Mainly includes:
Analytic geometry: learning geometry by algebraic method, in which plane analytic geometry has entered middle school.
Linear algebra: study how to solve linear methods and related problems.
Advanced algebra: studying the problem of finding the roots of equations.
Calculus: study variable speed motion and curved edge quadrature. As an extension of calculus, physics department should also teach ordinary differential equations and partial differential equations.
Probability theory and mathematical statistics: study random phenomena and make inferences based on data.
All these subjects constitute the basic part of advanced mathematics, and on this basis, a magnificent building of advanced mathematics has been established.